Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems: A Case Studies Approach 3031276345, 9783031276347

Citation preview

Mechanical Engineering Series

Biplab Das Jagadish   Editors

Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems A Case Studies Approach

Mechanical Engineering Series Series Editor Vish Prasad, University of North Texas, Mechanical & Energy Engineering,  Denton, TX, USA

The Mechanical Engineering Series presents advanced level treatment of topics on the cutting edge of mechanical engineering. Designed for use by students, researchers and practicing engineers, the series presents modern developments in mechanical engineering and its innovative applications in applied mechanics, bioengineering, dynamic systems and control, energy, energy conversion and energy systems, fluid mechanics and fluid machinery, heat and mass transfer, manufacturing science and technology, mechanical design, mechanics of materials, micro- and nano-science technology, thermal physics, tribology, and vibration and acoustics. The series features graduate-level texts, professional books, and research monographs in key engineering science concentrations.

Biplab Das  •  Jagadish Editors

Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems A Case Studies Approach

Editors Biplab Das National Institute of Technology Silchar Silchar, Assam, India

Jagadish ​SQC & OR Unit Indian Statistical Institute Bangalore Center Bangalore, Karnataka, India

ISSN 0941-5122     ISSN 2192-063X (electronic) Mechanical Engineering Series ISBN 978-3-031-27634-7    ISBN 978-3-031-27635-4 (eBook) https://doi.org/10.1007/978-3-031-27635-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface

Solar energy is an abundant in nature, and this energy can be utilized to meet the growing energy demands. Currently, the world is mostly dependent on the energy extracted from fossil fuels which are depleting continuously. Solar thermal systems are usually recognized as one of the most effective methods to exploit solar energy. Among such systems, a solar air collector (SAC) is known as a simple heat exchanger, which absorbs the solar energy and converts it into heat. The several applications of solar air collectors are space heating, drying of agricultural crops, etc. Moreover, fluctuations in thermal-physical properties of air, climatic conditions, temperature, and heat transfer rate between absorber plate and working fluid (air) are low, which results in the lower energy efficiency of SACs. Moreover, in most of the earlier studies, the exergetic analysis is performed on SAC based on the collector's absorbed energy, making it challenging to find the scope of improvement of the system. Hence the parametric study of the SAC based on the exergy supplied by the sun would be more realistic. Further, the development and application of evolutionary methods such as fuzzy techniques, MCDM methods, etc. for effective modeling and prediction of SACs under different experimental conditions have been discussed. The presented work in this book makes the book valuable for academicians, researchers, and industrial practitioners. Silchar, Assam, India Bangalore, Karnataka, India

Biplab Das Jagadish

v

Outline

• This book covers recent trends and developments in performance improvement issues of solar thermal systems. • This book includes modeling and parametric optimization issues for the practitioners of solar thermal industries. • It also highlights research advances in solar air collector (SAC) systems and their modeling and optimization issues using evolutionary methods. • This book provides an application of revolutionary methods for modeling and optimizing SACs by considering real-life case studies, which is the USP of the proposed book.

vii

Chapters Brief

Chapter 1: Introduction In this, two different sections are included. The first part is related to the brief introduction about the solar thermal collector, classification, advantages, key governing parameters, limitations, and applications, followed by the latest research and development trends in solar air collector systems. While in the second part, introduction to soft computing techniques and evolutionary techniques followed by brief developments and application status in the thermal system and future scope are discussed.

 hapter 2: Modeling and Optimization of Solar Air Collector C Using GRA This chapter contains a basic introduction, a literature review on the development of solar air collector, experimental details, an experimental evaluation of air performance of solar air collector system, followed by modeling and optimization using the GRA method, and a summary of the work.

 hapter 3: ANN-Based Modeling and Optimization C of Corrugated Solar Air Collector This covers an elementary introduction, literature review on the performance enhancement techniques of solar air collector, material and experimental methods, energetic and exergetic performance corrugated plate solar air collector, modeling and optimization using ANN method, characterization, and summary of the observed results.

ix

x

Chapters Brief

 hapter 4: Investigation of Thermal Performance of Solar C Collector Variables Using Fuzzy Logic-Based Expert System This chapter contains a basic introduction, literature review on solar insolation model, thermal modeling and optimization of SAC system using fuzzy logic-based expert system, characterization, and summary of the work.

 hapter 5: Sustainability Assessment of Solar Air Collector C Using Entropy-JAYA Method This includes a brief introduction with background, literature review on the variation of energy matrices of solar air collector, experimental procedure, environmental analysis of solar air collector, modeling and optimization using Entropy-Jaya algorithm, characterization, and conclusions.

 hapter 6: Optimization of a Photovoltaic Thermal Solar C Collector Using Entropy-VIKOR Method This contains a basic introduction, literature review on the development of solar photovoltaic thermal air collector, experimental details, experimental evaluation of air performance of solar air collector system, followed by modeling and optimization using Entropy-VIKOR method, and summary of the work.

Acknowledgment

The authors sincerely acknowledge the support of NIT Silchar and ISI Bangalore. The efforts extended by our Ph.D. scholars, Dr. Suman Debnath, Mr. Jagannath Reddy, Mr. Sujit Roy, Mr. Sovan Kr. Panja, and Mr. Pranjal Prasad Newar of NIT Silchar and Mr. Dheeraj Lal Soni of NIT Raipur, are highly acknowledged.

xi

About This Book

This book presents insights into the thermal performance of solar thermal collectors using both computational and experimental modeling. It consists of various computational and experimental case studies conducted by the authors on the solar thermal collector system. First, thermal modeling is developed considering a case study to show the effect of different governing parameters. Then a few other experimental case studies are considered to highlight the energy, exergy, and environmental performance of the solar thermal collector system. Also, the performance of a modified solar collector system is also considered to unveil the performance improvement technique. In addition, application of different evolutionary methods such as fuzzy techniques, MCDM methods like fuzzy logic-based expert system (FLDS), Artificial Neural Network (ANN), Grey relational analysis (GRA), Entropy-Jaya algorithm, Entropy-VIKOR, etc. are included.

xiii

Contents

1

Introduction����������������������������������������������������������������������������������������������    1 1.1 Introduction��������������������������������������������������������������������������������������    1 1.2 Introduction to Solar Thermal Systems��������������������������������������������    2 1.3 Classification of Solar Thermal Systems������������������������������������������    3 1.4 Applications of Solar Thermal Systems�������������������������������������������    4 1.5 Development and Research Issues in Solar Thermal Systems����������    4 1.6 Modeling and Optimization of Solar Thermal Systems�������������������    6 1.7 Introduction to Soft Computing Techniques������������������������������������    7 1.7.1 Application of Soft Computing Techniques for PV/T Systems������������������������������������������������������������������    8 1.7.2 Application of Soft Computing Techniques for Solar Flat Plate Collectors����������������������������������������������   10 1.7.3 Application of Soft Computing Techniques in Other Hybrid Energy Systems������������������������������������������   14 1.8 Summary ������������������������������������������������������������������������������������������   14 References��������������������������������������������������������������������������������������������������   15

2

 Modeling and Optimization of Solar Air Collector Using GRA����������   23 2.1 Introduction��������������������������������������������������������������������������������������   23 2.2 The Methodological Approach ��������������������������������������������������������   25 2.2.1 Modeling of Thermal Energy������������������������������������������������   25 2.2.2 Exergy Analysis��������������������������������������������������������������������   26 2.2.3 Grey Relational Analysis (GRA)������������������������������������������   27 2.2.4 Experimentation Specifics����������������������������������������������������   28 2.3 Results and Discussion ��������������������������������������������������������������������   29 2.3.1 Parametric Analysis��������������������������������������������������������������   29 2.4 Conclusion����������������������������������������������������������������������������������������   38 References��������������������������������������������������������������������������������������������������   39

3

ANN-Based Modeling and Optimization of Corrugated Solar Air Collector ��������������������������������������������������������������������������������������������   41 3.1 Introduction��������������������������������������������������������������������������������������   41 xv

xvi

Contents

3.2 Modeling of Thermal Energy������������������������������������������������������������   43 3.2.1 Thermal Analysis������������������������������������������������������������������   43 3.2.2 Exergy Analysis��������������������������������������������������������������������   44 3.2.3 Proposed ANN Model����������������������������������������������������������   45 3.2.4 Experimental Setup and Procedure��������������������������������������   47 3.3 Parametric Analysis��������������������������������������������������������������������������   48 3.3.1 Energy Efficiency������������������������������������������������������������������   48 3.3.2 Exergy Efficiency������������������������������������������������������������������   50 3.3.3 Temperature Difference��������������������������������������������������������   50 3.3.4 Pressure Drop������������������������������������������������������������������������   52 3.3.5 ANN Modeling of Corrugated SAC ������������������������������������   55 3.4 Conclusion����������������������������������������������������������������������������������������   57 References��������������������������������������������������������������������������������������������������   61 4

Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy Logic-Based Expert System ����������������������������   63 4.1 Introduction��������������������������������������������������������������������������������������   63 4.2 Modeling and Methodology��������������������������������������������������������������   66 4.2.1 Thermal Modeling����������������������������������������������������������������   66 4.2.2 Fuzzy Logic-Based Expert System��������������������������������������   67 4.2.3 Experimental Procedure��������������������������������������������������������   68 4.3 Results and Discussion ��������������������������������������������������������������������   69 4.3.1 SCSAC Parameter Optimization Using the Planned Approach ����������������������������������������������������������   69 4.3.2 Parametric Analysis��������������������������������������������������������������   71 4.4 Validation of the Proposed Method��������������������������������������������������   73 4.4.1 Confirmation Tests for Validation ����������������������������������������   73 4.5 Conclusions��������������������������������������������������������������������������������������   74 References��������������������������������������������������������������������������������������������������   74

5

Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method ����������������������������������������������������������������   77 5.1 Introduction��������������������������������������������������������������������������������������   77 5.2 Methodology and Experimentation��������������������������������������������������   81 5.2.1 Thermal Energy Modeling����������������������������������������������������   81 5.2.2 Energy Analysis��������������������������������������������������������������������   81 5.2.3 Exergy Analysis��������������������������������������������������������������������   82 5.2.4 Sustainability Index (SI) ������������������������������������������������������   83 5.2.5 Environmental Impact Factor (EIF)��������������������������������������   84 5.3 Experimental Procedure��������������������������������������������������������������������   84 5.4 Proposed Method������������������������������������������������������������������������������   85 5.5 Modelling of SAC System����������������������������������������������������������������   88 5.6 Parametric Analysis��������������������������������������������������������������������������   89 5.6.1 Variation in Solar Radiation and Ambient Temperature ������   90 5.6.2 Energy Efficiency Variation��������������������������������������������������   92 5.6.3 Exergy Efficiency Variation��������������������������������������������������   92

Contents

xvii

5.6.4 Variation of Sustainability Index������������������������������������������   92 5.6.5 Environmental Impact Factor������������������������������������������������   94 5.7 Optimization of SAC������������������������������������������������������������������������   96 5.8 Conclusion����������������������������������������������������������������������������������������   98 References��������������������������������������������������������������������������������������������������  101 6

 Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-­VIKOR Method�������������������������������������������������������������  105 6.1 Introduction��������������������������������������������������������������������������������������  105 6.2 Thermal Modelling and Experimentation����������������������������������������  108 6.2.1 Thermal Modelling ��������������������������������������������������������������  108 6.2.2 Experimental Procedure��������������������������������������������������������  110 6.3 Proposed MCDM Method����������������������������������������������������������������  111 6.4 Parametric Analysis��������������������������������������������������������������������������  113 6.4.1 Variation of Outlet Temperature ������������������������������������������  113 6.4.2 Variation of Thermal Energy Yield and Exergy Yield����������  113 6.4.3 Variation of Electrical Energy Yield and Electrical Efficiency������������������������������������������������������������������������������  114 6.4.4 Modeling of PVT System Using Proposed MCDM Method����������������������������������������������������������������������������������  117 6.4.5 Optimization Results of PVTAC Parameters������������������������  119 6.5 Confirmatory Tests����������������������������������������������������������������������������  121 6.6 Conclusions and Future Direction����������������������������������������������������  121 References��������������������������������������������������������������������������������������������������  125

Index������������������������������������������������������������������������������������������������������������������  127

About the Authors

Biplab  Das  is currently working as an Associate Professor in the Department of Mechanical Engineering, National Institute of Technology Silchar, India. Dr. Das completed his Ph.D. from NERIST, Itanagar, India, in the year of 2014. Later, he pursued his Post-Doctoral research from the University of Idaho, USA. He is the recipient of the prestigious Bhaskara Advanced Solar Energy (BASE) Fellowship from IUSSTF and DST, Govt. of India. He is also awarded a ‘DBT  Overseas Associateship’ by the Department of Biotechnology, Govt. of India. He has 15 years of experience in teaching/research and published more than 120 referred International/National Journal/ conference journal papers. Currently, Dr. Das has been involved in 10 sponsored projects as PI/Co-PI, funded by SERB, DST, Ministry of Power, and the Ministry of Climate Change, Govt. of India. He has guided nine Ph.D., and at present six Ph.D. scholars are working with him. Dr. Das serves as an editor of three books/proceedings. He has three international patent in his name. Jagadish  obtained his Ph.D. in Mechanical Engineering with specialization in Production Engineering from the National Institute of Technology Silchar and Post-graduation in Product Design and Development from the National Institute of Technology Warangal, India. He has over 3 years of industrial experience in the field of design and analysis and more than 8 years of teaching and research experience. Currently, he is working as an Assistant Professor in the SQC & OR Unit, Indian Statistical Institute, Bangalore Center, xix

xx

About the Authors

Bangalore, India, since March 2023. He received an “Institutional Award (Gold Medal)” by Institution of Engineers India and “Best Innovative Award” by Springer for his outstanding research contribution and published more than 41 research papers, 4 books, and 17 book chapters. He is a regular reviewer of various Production Engineering and optimization-related SCI indexed journals. He is the life member of professional bodies like Associate Member of Institute of Engineers (India), Committee Member of Soft Computing Club SCILAZ at NIT Silchar, and Member of American Society of Mechanical Engineers (ASME). His areas of interests are Green Manufacturing, Advanced Manufac­ turing Process, Rapid Prototyping; Computer-Aided Design/Manufacturing, Composite Machining, Compo­ site Material and Machining Characterization; Applied Soft Computing Techniques and Optimization; Renewable Energy; etc.

Chapter 1

Introduction

1.1 Introduction From a purely economic perspective, energy is essential in any country. Electricity, chemical, thermal, nuclear, and other kinds of energy are all used to meet human needs, as well as those of the industry. Fossil fuels, which are becoming scarcer, were previously used to meet these needs. The rate at which humans consume fossil fuels is higher than the rate at which these resources are renewed by subsequent geological processes [1]. Furthermore, a lot of time, effort, and money are required to transform crude oil that is easily accessible naturally into useable fuels. In addition, their ongoing usage for a wide range of purposes produces a wide range of harmful chemical compounds that are intolerable to the atmosphere and lead to pollution [2, 3]. Again, the cost of eliminating environmental contamination caused by such chemicals is high. Because of this, effectively putting them to use has emerged as a critical issue. Producing energy in a sustainable way is the single most important factor that can alter the current situation [4]. The decline of conventional energy sources is a concern to future energy needs on top of their contributions to pollution and global warming. This promotes the creation of cutting-­edge renewable energy technologies [5]. Currently, renewable energy sources such as solar, wind, and geothermal are getting more attention [6–8]. Radiation from the sun can be used to generate heat or stored energy for later use [9–11]. The collection and conversion of solar radiation energy, however, still face challenges. Utilizing solar power will reduce carbon dioxide output and hence mitigate global warming [12]. Improving the efficiency and effectiveness of these sources to meet most energy needs is the biggest challenge [11–13]. Solar photovoltaics, solar thermal systems, and a hybrid of the two are all viable methods for capturing the sun’s rays [14]. Photovoltaic (PV) cells, used in solar photovoltaic systems, transform solar energy into electricity that may be used in a wide variety of settings, from factories to homes [15, 16].

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4_1

1

2

1 Introduction

On the other hand, solar thermal collectors utilize a heat transfer media to convert solar energy into heat that may be used for either heating or cooling [9–16]. Heating water with solar radiation is an affordable solution in both developed and underdeveloped nations. In order to harness the sun’s thermal energy, some sort of fluid is required to soak up the warmth and then transport it, either directly or indirectly, to something else. Water is used more frequently than almost any other liquid. Water absorbs only 13% of the solar energy that hits it, leading to low collector thermal efficiency [17]. Incoming solar radiation is mostly controlled by nature, in terms of both strength and quality. The only way to increase the effectiveness of solar power generation system is to modify the absorber. Many scientists have dedicated their efforts to developing more efficient solar collectors. Alterations of this nature necessitate substantial financial outlays. Therefore, improving the working fluid’s thermophysical properties is the sole choice. Thus, this fluid could be used in solar photovoltaic systems to dissipate the excess heat energy produced by the PV cells. As a filter, it can prevent harmful radiation from penetrating the PV module. As Maxwell [18] noted, the thermal conductivity of a liquid could be enhanced by the addition of solids with higher thermal conductivity than liquids. Since then, many studies have been carried out to find ways to increase the thermal properties of liquids (also called base fluids) by dispersing different types of solid particles inside them. But it turned out that these fluids had a few downsides, like aggregation, clogging, erosion, and so on [19]. The particles’ large size, typically measured in millimeters or micrometers, was to blame for these restrictions. The investigation [20–24] used a variety of chemicals including water and ethylene glycol (EG). Therefore, nanofluids can be used in a wide variety of heat transfer settings [25]. Applications involving nanofluid mass transfer have emerged because of the ways in which nanoparticles alter the properties of fluids. The features of a fluid can be altered by dispersing nanoparticles in it, expanding the fluid’s potential uses [26, 27]. Spreading an absorbing chemical that can capture solar energy in water can also help to heat it [28]. Therefore, nanofluids can be used to effectively collect sunlight and transform it into usable energy [29].

1.2 Introduction to Solar Thermal Systems One type of solar technology, known as solar thermal energy (STE), turns sunlight directly into usable heat (heat). Low, medium, and high heat solar collectors are only some of the options for this type of collector. Pool and space heating are the most common applications for low-heat versions. Medium-heat types are commonly utilized for home and commercial hot water and space heating. A different name for this is solar thermal water for the home (DHW). Concentrators, like mirrors or lenses, are used by high-heat types to reach extremely high temperatures; this steam is then used to power generators, which produce electricity. All these methods share a common characteristic: they raise the temperature of the water being used in some way. The end result can be used for heating water, producing

1.3 Classification of Solar Thermal Systems (Fig. 1.1)

3

electricity, warming buildings, or powering industrial processes. Both passive and active approaches are accessible and should be used as appropriate. You can use solar thermal collectors in three different temperature ranges: Collectors for temperatures below 110° Fahrenheit often rely on metallic or nonmetallic absorbers to produce this type of low-grade heat. They are used for low-grade water and space heating, in addition to heating swimming pools. Glazed flat plate collectors with air or liquid as the heat transfer medium or concentrator collectors that concentrate the heat of incident insulation to greater than “one sun” are examples of medium-temperature collectors that deliver medium-grade heat (above 110 °F, typically 140–180 °F). The majority of households rely on them to provide hot water. In this group, you’ll also find collectors that use an evacuated tube. Utility and IPP businesses typically use high-temperature collectors, such as a parabolic dishes or trough collectors, to generate electricity for the grid at temperatures of 180°For higher. Additionally, these can be utilized for absorption cooling. The analytically computed numbers that make up a solar thermal collector’s performance rating show how much power such a collector can generate over a whole day under laboratory conditions. Since their inception, all of the solar thermal systems listed below have witnessed significant price reductions thanks to improvements in manufacturing technology and the increased efficiency of mass-producing plants.

1.3 Classification of Solar Thermal Systems (Fig. 1.1)

Fig. 1.1  Classification of solar thermal systems [30]

4

1 Introduction

1.4 Applications of Solar Thermal Systems Solar thermal energy has a wide range of potential applications, including but not limited to space heating, air conditioning, hot water production, heating of industrial processes, drying, distillation and desalination, and generation of electrical power. The following are some of the particular uses of solar thermal systems: • • • • • • •

Utilization of hot water for activities such as bathing, washing, and doing laundry. Preheating water for use in boilers. Heating water in swimming pools. Heating space in commercial buildings. Generating solar steam for use in manufacturing processes. Degreasing and phosphating in the metal finishing sector. Solar drying of food, wood, and leather.

Advantages • Energy costs are lowered. • Less pollution is produced, and there is little to no upkeep required over the course of many years. • Increased solar output during the summer. • Versatile practicality. Disadvantages • DC equipment are costly. • There is no solar power at night or on overcast days. • There is less solar energy in the winter. • The system requires a lot of space.

1.5 Development and Research Issues in Solar Thermal Systems Any attempt to implement a technology developed in a laboratory on a large scale is bound to encounter some difficulties. Nanofluids are increasingly being used as working fluids in solar thermal systems. Nanofluids may have been studied for their flow behavior and thermal performance, but there are still challenges when putting them through real-world flow conditions. Nanofluid stability is a major issue when used in solar collectors due to the large density disparity between the base fluid and the nanoparticles [30]. Nanoparticles tend to aggregate when heated to high temperatures [31]. This means less heat is lost and less heat is conducted. Nanofluids must be stable at high temperatures, which is essential for solar applications. Dispersion stability, which is a function of concentration and type of nanofluid, is a barrier to using nanofluids as working fluids in solar collectors [32]. When nanoparticles settle at the bottom of a working fluid, the surface layer becomes transparent [33]. This reduces the effectiveness of solar collectors [34] because less solar

1.5  Development and Research Issues in Solar Thermal Systems

5

radiation is absorbed. Nanomaterial size information was also left on the inner surface of solar collector flow channels due to agglomeration, which could lead to corrosion and erosion of the materials. The impact of ZrC2, TiO2, SiC, and Al2O3-water-based nanofluid flow on stainless steel, aluminum, and the copper pipe was studied by Celeta et  al. [35]. The study found that TiO2 and ZrC2 nanofluids eroded the most over time. Damage was also done to other materials, such as aluminized tubing. Consequently, it is necessary to choose the right construction materials. A number of issues, including aggregation, viscosity, and sedimentation, reduce the effectiveness of solar collectors when nanoparticle concentrations are high [36, 37]. When nanoparticles are incorporated into a working fluid, the viscosity of the fluid increases, leading to a higher pressure drop and so requiring a greater amount of pumping power. As a result, less money is spent on pumping and maintaining the system [38, 39]. There may be a way to lessen the amount of pressure lost by modifying the nanoparticle concentration and mass flow rate. Increases in both nanoparticle concentration and nanofluid flow rate increase friction [40]. Furthermore, considerable overheating may occur when the surface temperature increases in tandem with the concentration of nanoparticles. This is because of the low boiling point of nanofluids [41]. Due to their expensive precursors and energy-intensive production processes, the cost of using nanomaterials is a major concern [42]. Nanofluid-based ETSC production would be economically infeasible if not for the relatively low cost of the fluid itself and the lack of specialized equipment required to prepare stable nanofluids [43]. Heat transfer enhancement must be evaluated against the cost of producing nanoparticles and creating a stable nanofluid. Due to the presence of nanoparticles, which are inherently dangerous because of their size and make-up, nanofluids exhibit high toxicity. Using nanofluids on a large scale for solar applications would involve a large number of nanoparticles, requiring strict regulation. However, consumers using nanofluids in solar-powered appliances need to be well-versed in their safe storage, use, and disposal. The majority of the factors that have an impact on solar thermal systems have organic origins. Variations in solar radiation intensity at different locations may compromise the devices’ efficacy. For this reason, it is essential that nanofluid-based systems be flexible enough to respond to varying conditions. Since nanofluids perform better in solar thermal systems, additional study into their behavior is necessary before their use can be scaled up. These concepts pave the way for the use of nanofluids in commercial solar thermal systems: Nanoparticles that can absorb the natural radiations found in the solar spectrum are required for solar applications. Before using nanofluids in solar thermal systems, their stability, a major issue, must be studied. Nanoparticle and nanofluid productions are where your money will be most effectively spent in terms of the overall application cost. An in-depth economic analysis, including the expenses and savings due to enhanced heat transmission, is required to determine the viability of employing nanofluids in solar thermal systems. Nanofluids with nanoparticles derived from biobased materials can help cut costs and decrease exposure to potentially harmful substances. A wide range of nanomaterials can be synthesized from biological sources [44, 45]. The nanofluid’s size, shape, and concentration of nanoparticles must be optimized

6

1 Introduction

to increase dispersion stability so that it may be used in solar thermal applications. Any working fluid used in solar applications must be stable across a wide temperature range. Optical and thermophysical properties must be maintained while increasing stability, necessitating fine-tuning surfactant concentrations. To expand the scope of simulation studies and reduce the need for costly experimentation, it is necessary to identify a suitable modeling technique for a range of solar thermal systems with different geometries. Before fluid-based solar thermal systems can be commercialized, standard operating procedures and requirements for safe handling must be developed.

1.6 Modeling and Optimization of Solar Thermal Systems Experimental research into the behavior of nanofluids necessitates costly equipment and a significant investment of time. The primary purpose of utilizing a variety of nanofluids, experimental setups, and combinations is to evaluate the efficacy of solar thermal systems. However, this requires a substantial amount of effort and calls for employing many inquiry approaches. Modeling and simulation are useful instruments for studying a wide variety of parameters [46, 47]. However, it is common to practice to use experimental data to validate simulation results [48]. When simulations are able to forecast outcomes accurately, however, fewer tests are required. Lenert and Wang [49] conducted theoretical and experimental research into the efficacy of nanofluid volumetric receivers by varying the nanofluid’s thickness. The experimental data agreed with the model’s forecasts. This hybrid optimization method, developed by Mohammad Zadeh et al. [50], combines the genetic algorithm with sequential quadratic programming. It was found that the absorber tube’s temperature negatively impacted heat transmission. In an investigation, Ghasemi and Ranjbar [51] solved the three-dimensional heat transfer equations for a parabolic trough collector using the finite volume technique (FVM). Computational fluid dynamics (CFD) simulations yielded results that were quite close to experimental findings. The application of computational fluid dynamics (CFD) in the assessment of the efficiency of complex-geometry parabolic trough collectors is on the rise [52]. When simulating DASC, Balakin et  al. [53] developed a two-phase Eulerian-­ Eulerian CFD model. This was then used to determine the best parameters for controlling the nanoparticles’ size, concentration in the nanofluid, and the collector’s inclination angle and form. The Brownian and inter-phase momentum transfer terms helped clarify the connection between the two states. Singh et al. [54] also developed a modeling strategy to consider interconnected transport phenomena. However, the consequences of accumulation and nanoparticle deposition were overlooked in this model. In order to expand its applicability to flow zones dominated by Brownian motion rather than just convection, it was proposed that this model be combined with modeling methodologies such as molecular dynamics and Eulerian-­ Lagrangian. Advances in simulation studies have made it possible to investigate

1.7  Introduction to Soft Computing Techniques

7

PV/T systems numerically. Several studies have been published on the topic. Utilizing CFD, Khanjari et al. [55] looked into the efficiency of PV/T with a water-­ based nanofluid, including silver and alumina nanoparticles. Trends calculated statistically and trends seen experimentally were consistent with one another. Uncovered nanofluid sheets and tubes (PV/T) were the subjects of a numerical validation and analysis by Rejeb et al. [56]. Both the electrical and thermal efficiencies of PV/T systems were analyzed to see how they changed depending on the concentration of nanofluid, the type of nanoparticles used, and the base fluid. Sardarabadi and Passandideh-Fard [57] quantitatively assessed numerous nanofluids’ PV/T performances. With pressure-based FVM in ANSYS Fluent, Hosseinzadeh et al. [58] studied the effects of variables such as wind speed, adsorbed solar irradiance, ambient temperature, coolant flow rate and temperature, and ZnO nanoparticle concentration. A PV/T system utilizing alumina nanofluid was similarly modeled in FORTRAN [59]. Additionally, artificial neural networks have been used to study the correlation between the input and output of PV/T systems [60]. It was demonstrated that the behavior of a nanofluid based on zinc oxide in the system could be accurately anticipated using this modeling approach. Numerical studies of nanofluids in solar applications have been conducted. Rashidi et al. [61] studied evaporation and condensation in a solar still with a single incline using the volume of the fluid model. Up to a 5% increase in alumina concentration in the water volume led to a 25% increase in output. Although there were some inaccuracies because of assumptions and simplifications made in the numerical modeling, the experimental and numerical results were consistent. The efficiency of a solar still equipped with an external condenser was numerically studied by Kabeel et al. [62]. It was found to be 84.16% when using Cu2O nanoparticles and 73.85% when using Al2O3 nanoparticles. The purpose of the experiment that Das et al. [63] carried out was to explore the performance of a novel sand-coated and sand-filled (SCSF) polycarbonate sheet-based solar air collector (SAC) inside controlled indoor circumstances with varying air flow rates and solar inputs. It was discovered that the thermal efficiency of the SAC with storage was 39% and 20% greater, respectively, than that of the black paint-­ coated aluminum absorber and the sand-coated aluminum absorber.

1.7 Introduction to Soft Computing Techniques In recent years, there has been a surge of interest in the use of soft computing approaches like artificial neural networks (ANNs), genetic algorithms (GAs), fuzzy logic (FL), and cluster analysis (CA) to evaluate difficult problems in the real world. With a focus on thermal engineering, this chapter provides an overview of SC’s usefulness in energy systems. The study, design, and regulation of heat exchangers are particularly focused. The basic concepts of each method under consideration are briefly outlined and explained. There is a discussion on how this concept might be used in a variety of different energy infrastructures. The genetic algorithm (GA) and genetic programming (GP) are two examples of evolutionary algorithms (EAs),

8

1 Introduction Soft Computing Techniques

Fuzzy logic Controller

Artificial Neural Network

Evolutionary computation

Evolutionary Algorithms

Swarm Intelligence Algorithms

Genetic Algorithm Differential Evolution

Particle Swarm Optimization Ant Colony Optimization Bacterial Foraging Optimization

Fig. 1.2  Classification of soft computing techniques [64]

which are adaptive stochastic computational techniques motivated by Darwin’s evolutionary principle of natural selection, according to which the fittest members of a species survive and are favored to produce offspring. Optimization is a core part of engineering system design, and EAs are widely employed for this purpose. The GA uses binary string encoding to search for the optimal solution for a given issue, also known as the global optimum. Conversely, GP is a symbolic extension that uses a collection of potential functions to determine the best one for a particular dataset. These techniques have found usage in many fields, from banking and business to electronics and engineering to signal processing and system identification. Fuzzy logic controller, artificial neural network, and evolutionary computation are the three main categories of soft computing approaches depicted in Fig. 1.2.

1.7.1 Application of Soft Computing Techniques for PV/T Systems In recent years, several solar thermal collectors based on the wealthy design idea have been deployed for this [64–66]. As collector types and photovoltaic internal-­ external factors affect thermal efficiency (TE) [67], PV/T systems are continually evolving to meet the rising demand for thermal power. Some research [68–73] highlights recent developments and applications of flat plate PV/T, which has been used

1.7  Introduction to Soft Computing Techniques

9

in a wide range of setups and has benefited from a wide range of optimization techniques. These evaluations reveal the development of collector design in recent years and the potential for further development in the near future. To study airflow in Italy, collector tilt, and air gap, a prototype PV/T air heating system was designed and tested at Politecnico di Milano [74]. Heat-enhanced materials have become increasingly popular due to their excellent thermal performance. Elsafi and Gandhidasan [75] studied both conventional PV/T systems and compound parabolic concentrated (CPC) systems. In order to design and build the CPC and fins, we relied on a prototype double-pass PV/T system [76]. The experiment includes an in-depth analysis of both single- and dual-fan configurations. A thin flat metallic sheet (TFMS) was studied by Tonui and Tripanagnostopoulos [77], while a collector fin system was studied independently. Most research has been on finding optimal values for collector variables to improve PV/T performance. For instance, different varieties of PV/T air collectors have been fully discussed [78, 79]. These collectors can have a wide range of collector areas and length-to-width ratios. A hybrid PV/T collector with dual-channel capabilities for different working fluids was investigated by Su et al. [80]. Using hybrid PV/T models, Amori and Abd-AlRaheem [81] analyzed TE and EE for four different air types. While the water-based PV/T collector has been explored the most, the air-based system has additional benefits and is easier to operate. Air collectors for photovoltaics (PV) and thermoelectrics (T) are designed to maximize heat gain while simultaneously reducing the surface temperature of PV cells due to natural convection. Researchers have looked into how the air-type collector might improve the EE of PV modules by utilizing air flow. The gathered heat has many potential uses, including but not limited to space heating, pre-water heating, air heating, and low-temperature heating [82]. It is becoming increasingly common for residential and commercial properties to install pre-water heating systems [83]. Several strategies for enhancing PV/T efficiency are investigated here. This method uses a wide variety of mechanical and thermodynamic systems, such as the galvanized steel used as a heat absorber in the numerical modeling of the thermal collector [84]. Several methods and concepts have also been developed in the field of air-type PV/T collectors. The employment of collector insert devices to improve PV/T performance has been the subject of extensive research [84–86]. A heat sink (fins) made of aluminum(Al), brass, nickel, and a copper substance was installed in order to examine the fin materials and shapes [75]. Many dynamic models and CFD (computational fluid dynamics) assessments of the flat plate SAC have been developed as a result [87–89]. More than a few different kinds of PV/T collectors, each with their own set of advantages, have been introduced in recent years. The development of the PV/T business, notably for PV and concentrating solar power facilities, has been thoroughly researched [90]. Prediction methods based on soft computing could potentially replace the expensive PV/T test. Results for input variables that were not used in training can be accurately predicted using the prediction model. In the field of heat transfer research, the use of artificial intelligence techniques such an artificial neural network (ANN) method that provides a fair forecast to compute the thermal performance of SAC has been steadily increasing [91, 92]. With regard

10

1 Introduction

to accuracy, the ANN method has advantages over other conventional methods, especially when dealing with non-linear data [93]. To evaluate SAC performance, Varol et al. [86] modified a set of prediction models and employed three distinct soft computing strategies: artificial neural networks (ANN), an adaptive-­network-­based fuzzy inference system (ANFIS), and a support vector machine (SVM) (SVM). Esen et al. [94] conducted a case study in which they applied the SVM technique to a ground-coupled heat pump (GCHP) as a form of intelligent intervention for the purpose of indoor space heating. In another investigation, researchers attempted to foretell system effectiveness using the least-square support vector machine (LS-SVM) [95, 96], a wavelet neural network (WNN), and an artificial neural network (ANN). Using an ANN model of a thermal energy distribution model of water type PV/T [97], the OPOP was determined. Researchers in a wide variety of technological and scientific fields are currently focusing on developing and applying cutting-edge computational methods for determining optimal values, functions, and solutions to practical problems. One of these methods, NN (neural network) has recently been presented as the dominant computational strategy in a certain branch of engineering. When conventional parametric methods are inadequate, the ANN yields satisfactory outcomes. The most popular approaches to ANN training are support vector machine (SVM), back propagation (BP), and hidden Markov model (HMM). Huang et al. [98] popularized a method for training SFNs called Extreme Learning Machine (ELM) (SLFN). Also, compared to NN, training time for ELM is less because of its fast learning process and stable performance [99]. Accordingly, multiple researches using ELM applications to tackle challenges in various scientific disciplines have been carried out successfully [100–105]. In general, the ELM outperforms other algorithms like BP when it comes to how quickly they respond to new information throughout the learning process. And, ELM looks for the norm and training error of the weights. Jha et al. [106] explored the performance of photovoltaic thermal (PVT) air collector in the climatic condition of North East, India, both theoretically and practically, as the climatic condition of North East is distinct from that of the other regions of India. According to the investigation’s findings, the PVT air collector has superior thermal performance for a mass flow rate of 0.0128 kg/s. This was found to be the case. For a mass flow rate of 0.0128 kg/s, it has been observed that the thermal energy gain and exergy gain have been achieved as 152 Wh and 7.88 Wh, respectively, for a typical day in December. However, for the month of March, it has been observed that these values have increased to 185.15 Wh and 17.82 Wh, respectively, at 12.00 h.

1.7.2 Application of Soft Computing Techniques for Solar Flat Plate Collectors Fuzzy logic is discussed in this section as it relates to solar energy converters. Researchers interested in performance typically opt for the Mamdani FIS, whereas those interested in process control tend to favor the Takagi-Sugeno FIS. The studies

1.7  Introduction to Soft Computing Techniques

11

that follow focus specifically on improving solar thermal systems. Rizwan et  al. [107] attempted to estimate global sun irradiance using Mamdani FIS. This computation considers the location’s latitude, longitude, altitude, average sunshine per hour, temperature, and calendar month. Four places across four regions of India are analyzed using the fuzzy logic-based method. Solar PV system performance predictions for grid use are made using the Mamdani FIS results. The suggested FIS can reliably predict yearly global sun irradiance of roughly 94%. In order to estimate monthly solar irradiance, Ahmed et  al. [108] created a FIS-based method. Environmental factors are considered at this height. The suggested FIS can forecast the yearly global sun irradiance with an accuracy of about 97.47%. Iqdour and Zeroual [109] created a unique Takagi-Sugeno FIS-based approach to forecast daily global solar radiation. Daily global radiation can be estimated with the proposed fuzzy logic-based model, and the result is generally accurate. The proposed Takagi-Sugeno FIS estimated daily global solar radiation with an accuracy of roughly 99.39%. Fuzzy logic was initially used to estimate global solar irradiation by Zekai [110]. Three average irradiances from three separate places in southwestern Turkey are used to inform a fuzzy logic model. A similar study concluded that irradiance prediction using FIS is less complicated and more flexible than using Angstrom. In order to convert the sun’s primary energy into electricity, a solar photovoltaic module makes use of the photovoltaic effect. The effects of shade, (ii) variations in the amount of sunlight absorbed by the module’s surface area, and (iii) the generation of dust particles are all things to think about. Jose [111] claims to have demonstrated a fuzzy logic-based control system that operates in semi-­ shady environments. The Takagi-Sugeno Fuzzy Information System is proposed as an answer to this issue. The method known as P and O (perturbation and observation) is used to check if actual results match predictions. The comparison results demonstrate that the FIS is useful for keeping tabs on and managing activities. Hosseini and Farajdadian [112] explored employing Mamdani FIS to foretell how much energy the solar photovoltaic system would produce. Voltage, current, irradiance, and module temperatures are the inputs. The proposed FIS has an impressive track record for predicting the yearly global irradiance from the sun with an accuracy of almost 93%. Ramaprabha et al. [113] proposed controllers based on fuzzy logic to monitor the highest power point in uncertain conditions. The proposed controller improves upon standard practice by facilitating the identification of the point of maximum yield. Batayneh et al. [114] developed fuzzy logic to manage the tracking mechanism of a dual-axis photovoltaic installation. The inputs are four separate error signals. Fifty distinct rules based on human knowledge are used to apply the Mamdani inference method. The Mamdani FIS-based controller, unlike traditional controllers, allowed for a high degree of input and output flexibility. The model’s predictions for the simulated tests confirmed the FIS’s ability to monitor the sun over long periods efficiently. The solar flat plate fluid heating system converts solar energy to thermal energy via the thermosyphon effect. The performance of the device is affected by a number of factors, including the fluid’s mass flow rate, incident solar irradiance fluctuations, fluid inlet temperature, and overall heat loss coefficients (Sridharan

12

1 Introduction

and Anabayan [115], Sridharan and Siva Prakash [116], Sridharan, et al. [117], and Sridharan et al. [118]). Debnath et al.’s [119] fuzzy logic-based expert systems can be used to foretell how well a system would function. Tilt angle, mass flow rate, inlet temperature, and environmental conditions are the four inputs utilized to forecast the three outcomes (thermal efficiency, pressure drop, and outlet temperature). The performance of a solar flat plate air collector system may be predicted with a level of accuracy of 97.50 percent using a model based on the Mamdani FIS. Kishor et al. [120] created three unique Mamdani FIS to predict the thermal performance of the solar flat plate water collection device. Gauss, Gauss2, and the G-Gauss bell are just a few examples of the available membership functions that can be used to pick out the right people to include in the group. The comparison showed that the Mamdani FIS with a Gaussian membership function accurately predicted the thermal performance 92% of the time. Vafaei and Sah [121] introduced a fuzzy logic-­ based expert system for estimating the thermal performance of the solar flat plate water collection system, using trapezoidal membership functions for the first time. The results from the experiments are utilized to double-check the predictions. Predictive models for the required output parameters are proposed, with an accuracy of 94%. Kishor et al. [120] updated their thermosyphon solar water heating (SWH) system model, resulting in more precise estimations. Grey-box modelling based on a fuzzy system is used to provide predictions about the water temperature at the system’s exit. More than a few researchers have hypothesized that neural networks might help raise prediction quality throughout the past decade. There are three models used to test how well the fuzzy modelling approach can forecast the water temperature at the output. The first model takes in three variables: inlet water temperature, ambient temperature, and solar irradiance. The second model takes in two variables: inlet water temperature and solar irradiance. And the third model takes in just one variable: solar irradiance. Better prediction accuracy can be achieved with a three-input fuzzy model. Increases in population, technical development, and economic activity contribute to a sharp increase in energy consumed worldwide [122]. One practical use of renewable energy is the solar water heating (SWH) system. The solar thermal collector is an essential part of solar water heating systems, and for low and medium thermal applications, a flat plate collector (FPC) is commonly utilized. Major obstacles and difficulties in the expansion of SWH include the solar collector’s low thermal efficiency and high operating cost. Multi-objective particle swarm optimization (MOPSO) was researched by Hajabdollahi and Hajabdollahi [123] to enhance both cost and efficiency through testing out various FPC design parameters and analyzing the effects of Al2O3 nanoparticles. Over the past decade, numerous studies have proposed effective methods for optimizing FPC. To improve the energy efficiency by 4.9%, the Search Group Algorithm (SGA) [124] was introduced for use in an FPC-based solar water heating (SWH) system. Sequential quadratic programming (SQP) was developed by Farahat et al. [125] for exergy optimization, which aims to maximize FPC efficiency while minimizing exergy losses. In order to optimize an active SWH with FPC across a wide range of conditions and design parameters, Badr et al. [126] drew on the power of a genetic algorithm (GA). Wenceslas and

1.7  Introduction to Soft Computing Techniques

13

Ghislain [127] built a thermosyphon solar water heater and an FPC out of readily available materials using GA and revised design criteria. His method was more effective despite having a lower collecting surface area. Khademi et al. [128] contrasted SQP with GA to see whether the method was more effective at maximizing FPC exergy performance. The researchers found that the GA optimization yielded higher accuracy but slower convergence than the SQP optimization. Most studies in the literature focus on improving FPC performance at the expense of cost analysis. Concurrently, the thermoeconomics of the FPC system should be enhanced. Multiobjective FPC optimization literature is sparse. Hajabdollahi and Premnath [129] utilized MOPSO to reduce annual cost and increase efficiency. An FPC system using CuO nanofluid was simulated and optimized using MOPSO [130]. Hajabdollahi et al. [131] looked at the effects of nanofluids made of SiO2, Al2O3, and CuO on FPC systems from a thermo-economic standpoint. For the purpose of cost and efficiency estimation, a Nondominated Sorting Genetic Algorithm II was applied (NSGA-II). Traditional algorithms like MOPSO and NSGA-II have been employed almost exclusively in the relevant research, with no attempt at hybridization or other non-traditional approaches. Unfortunately, multi-objective techniques for fixing this problem have not yet been subjected to any performance testing. Debnath et al. [132] present a fuzzy logic-based expert system (FLES) in order to evaluate the thermal performance of a corrugated plate solar air collector (CPSAC) in North Eastern India under a variety of environmental circumstances. It has been seen that the FLES model can accurately predict the results with an accuracy of at least 97.5%. The ideal circumstances are found at mass flow rate 0.00785 kg/s, tilt angle 45°, solar radiation 727 W/m2, and temperature inlet 29.6 °C, and the outputs are energy efficiency 35.9%, exergy efficiency 12.8%, temperature difference 34.7 °C, and pressure drop 48.8 Pa. Reddy et al. [133] presented a novel hybrid expert system to do an energy and exergy study of a wavy plate solar air collector (WPSAC) using the system. The Sugeno-based subtractive clustering approach is utilized for the extraction of cluster centers, while the multi-criteria ratio analysis method is employed for the optimization and prediction of WPSAC parameter. According to the findings, the optimal values of energy, exergy, and carbon credit for WPSAC are obtained when the parameter values are as follows: m  =  0.00785  kg/s, = 45°, Q  =  770  W/m2, and T = 25 °C. It has been determined that the accuracy of prediction is greater than 98.1%. The values of 37.2%, 11.58%, 62 °C, and 0.0009 tonnes of carbon dioxide (CO2) were found to be the highest possible for WPSAC. The thermal performance of a solar air collector (SAC) developed by Debnath et al. [134] is studied experimentally using a fuzzy logic-based expert system in the varying climates of northeastern India (FLES). Subtractive clustering (SC) is utilized to extract optimal fuzzy IF-THEN rules, and fuzzy logic is employed to model the underlying structural analogies and causality (SAAC) variables in the FLES. The efficiency value is found to grow with mass flow rate, solar radiation, inlet temperature, and up to 45° tilt angle in experiments. However, increasing the mass flow rate also causes in increase in pressure drop. In addition, the FLES model yields respectable and comparable SAAC values. Finally, the FLES model is validated using previously published data to verify the findings.

14

1 Introduction

1.7.3 Application of Soft Computing Techniques in Other Hybrid Energy Systems Rezvani et al. [135] turned to ANN and GA techniques to improve the maximum tracking of hybrid energy sources like solar and wind. Results also indicate that this technique helps to measure the peak power output rapidly and accurately. Optimization of wind and battery hybrid energy sources was proposed by Pang et  al. [136] using a hybrid parallel (PSO-GA) approach and achieved power and energy efficiency maximization, which lowered daily expenditure by 59.62% and extended life expectancy by 1.82 years. To improve the efficiency of solar battery hybrid systems, Mellit et al. [137] applied an ANN approach, method created for appropriate sizing of system components using little input data. For optimum SPV and diesel system operation, Ohsawa et al. [138] turned to an ANN methodology. The optimization of hybrid energy sources (solar, wind, generator, batteries) was studied by Lujano-­Rojas et al. [139] using an ANN approach. Several other limitations were applied to the system, and it was discovered that EENS and NPC worked well under all of them. PSO approach was studied by Paliwal et al. [140] to optimize hybrid energy sources (SPV, wind, diesel, batteries). According to the findings, LCE was optimized to fulfill economic criteria while accounting for various restrictions. When considering annual simulations of hybrid energy sources, including SPV, wind, and fuel cells, Kaviani et al. [141] advocated using a PSO approach to estimate the impact of component output on system cost and consistency. A system composed of solar photovoltaic (SPV) cells, wind turbines, diesel generators, and batteries was optimized using the GA technique by Merei et al. [142]. A BBO algorithm that converges to simplicity was created and compared to other algorithms by Kumar et al. [143] for the hybrid energy source PV, wind, and batteries. When proposing the artificial bee colony (ABC) for optimizing hybrid energy wind, hydro, and batteries, Paliwal et al. [144] took into account both moderate and ample wind scenarios. This is a two-step process of optimization. Sizing comes first and then battery life. Battery storage designs with a capacity of 3–5 were found to be appropriate for the 1–2% LPSP sought after by Yang et al. [145].

1.8 Summary Commonly known as “solar thermal systems,” these devices convert the sun’s rays into usable heat and power. However, the bare minimum is an efficient system to make renewable energy systems more widely adopted, which is also necessary for the widespread integration of such systems. The output parameters of solar thermal systems include thermal efficiency, outlet fluid temperature, usable heat gain, etc., just as there are a variety of input factors in the form of design, operating, and environmental parameters. The process of optimization calls for a comprehensive parametric assessment of the impact of design and operating parameters on the efficiency

References

15

of solar thermal systems. Given the uncertainty of some of the climatic characteristics relevant to the ambient conditions, optimizing the performance of a solar thermal system will likewise necessitate taking into account all the operational and design parameters that are contradictory in nature. In light of this, using soft computing methods to solve these problems can be highly helpful. But in order to fully take advantage of their benefits, in-depth research on the performance of solar thermal systems using soft computing approaches is essential. Researchers found that most studies on soft computing approaches in solar thermal systems focused on improving the heat transfer of flat plate and concentrated solar thermal collectors. There is seldom any research like this. Similarly, there is a dearth of research on other types of solar thermal systems, such as line-focusing parabolic trough collectors and nonconcentrating evacuated tube collectors. The modeling and optimization of various solar energy systems thus have a great deal of room for development and the incorporation of many other individuals’ plus hybrid soft computing methodologies.

References 1. Ladjevardi, S. M., Asnaghi, A., Izadkhast, P. S., & Kashani, A. H. (2013). Applicability of graphite nanofluids in direct solar energy absorption. Solar Energy, 94, 327–334. 2. Jandacka, D., Durcanska, D., & Bujdos, M. (2017). The contribution of road traffic to particulate matter and metals in air pollution in the vicinity of an urban road. Transportation Research Part D: Transport and Environment, 50, 397–408. 3. Thind, M. P., Tessum, C. W., Azevedo, I. L., & Marshall, J. D. (2019). Fine particulate air pollution from electricity generation in the US: Health impacts by race, income, and geography. Environmental Science & Technology, 53(23), 14010–14019. 4. Saidur, R., Meng, T. C., Said, Z., Hasanuzzaman, M., & Kamyar, A. (2012). Evaluation of the effect of nanofluid-based absorbers on direct solar collector. International Journal of Heat and Mass Transfer, 55(21–22), 5899–5907. 5. Panwar, N. L., Kaushik, S. C., & Kothari, S. (2011). Role of renewable energy sources in environmental protection: A review. Renewable and Sustainable Energy Reviews, 15(3), 1513–1524. 6. Khare, V., Nema, S., & Baredar, P. (2016). Solar–wind hybrid renewable energy system: A review. Renewable and Sustainable Energy Reviews, 58, 23–33. 7. Kumar, Y., Ringenberg, J., Depuru, S.  S., Devabhaktuni, V.  K., Lee, J.  W., Nikolaidis, E., Andersen, B., & Afjeh, A. (2016). Wind energy: Trends and enabling technologies. Renewable and Sustainable Energy Reviews, 53, 209–224. 8. Fridleifsson, I. B. (2001). Geothermal energy for the benefit of the people. Renewable and Sustainable Energy Reviews, 5(3), 299–312. 9. Nwaji, G. N., Okoronkwo, C. A., Ogueke, N. V., & Anyanwu, E. E. (2019). Hybrid solar water heating/nocturnal radiation cooling system I: A review of the progress, prospects and challenges. Energy and Buildings, 198, 412–430. 10. Zhu, G., Wendelin, T., Wagner, M. J., & Kutscher, C. (2014). History, current state, and future of linear Fresnel concentrating solar collectors. Solar Energy, 103, 639–652. 11. Hegedus, S. S., & Luque, A. (2003). Status, trends, challenges and the bright future of solar electricity from photovoltaics. In Handbook of Photovoltaic Science and Engineering , pp. 1–43 12. Kreith, F., Norton, P., & Brown, D. (1990). A comparison of CO2 emissions from fossil and solar power plants in the United States. Energy, 15(12), 1181–1198.

16

1 Introduction

13. Soltowski, B., Strachan, S., Anaya-Lara, O., Frame, D., & Dolan, M. (2017, October). Using smart power management control to maximize energy utilization and reliability within a microgrid of interconnected solar home systems. In 2017 IEEE global humanitarian technology conference (GHTC) (pp. 1–5). IEEE. 14. Huide, F., Xuxin, Z., Lei, M., Tao, Z., Qixing, W., & Hongyuan, S. (2017). A comparative study on three types of solar utilization technologies for buildings: Photovoltaic, solar thermal and hybrid photovoltaic/thermal systems. Energy Conversion and Management, 140, 1–13. 15. Masuda, A., Hara, Y., Shiina, Y., Okamoto, S., & Okamoto, T. (2019). Similarity of potential-­ induced degradation in superstrate-type thin-film CdTe and Si photovoltaic modules. Japanese Journal of Applied Physics, 58(SB), SBBF07. 16. Perez-Aparicio, E., Lillo-Bravo, I., Moreno-Tejera, S., & Silva-Perez, M. (2017). Economical and environmental analysis of thermal and photovoltaic solar energy as source of heat for industrial processes, p. 180005. 17. Wang, K., He, Y., Liu, P., Kan, A., Zheng, Z., Wang, L., Xie, H., & Yu, W. (2020). Highly-­ efficient nanofluid-based direct absorption solar collector enhanced by reverse-irradiation for medium temperature applications. Renewable Energy, 159, 652–662. 18. Maxwell, J. C. (1873). A treatise on electricity and magnetism (Vol. 1). Clarendon Press. 19. Das, S. K., Choi, S. U., & Patel, H. E. (2006). Heat transfer in nanofluids – A review. Heat Transfer Engineering, 27(10), 3–19. 20. Choi, S. U., & Eastman, J. A. (1995). Enhancing thermal conductivity of fluids with nanoparticles (No. ANL/MSD/CP-84938; CONF-951135-29). Argonne National Lab (ANL). 21. Esfe, M. H., Karimipour, A., Yan, W. M., Akbari, M., Safaei, M. R., & Dahari, M. (2015). Experimental study on thermal conductivity of ethylene glycol based nanofluids containing Al2O3 nanoparticles. International Journal of Heat and Mass Transfer, 88, 728–734. 22. Eastman, J.  A., Choi, S.  U. S., Li, S., Yu, W., & Thompson, L.  J. (2001). Anomalously increased effective thermal conductivities of ethylene glycol based nanofluids containing copper nanoparticles. Applied Physics Letters, 78(6), 718. 23. Li, Q., & Xuan, Y. (2002). Convective heat transfer and flow characteristics of Cu-water nanofluid. Science in China Series E: Technolgical Science, 45(4), 408–416. 24. Galindo, J., Serrano, J. R., Guardiola, C., & Cervelló, C. (2006). Surge limit definition in a specific test bench for the characterization of automotive turbochargers. Experimental Thermal and Fluid Science, 30(5), 449–462. 25. Bhanvase, B., & Barai, D. (2021). Heat transfer applications of nanofluids. In Nanofluids for heat and mass transfer (pp. 341–85). https://doi.org/10.1016/B978-­0-­12-­821955-­3.00001-­7 26. Bhanvase, B., & Barai, D. (2021). Nanofluids for heat and mass transfer: Fundamentals, sustainable manufacturing and applications. Academic Press. 27. Bhanvase, B., & Barai, D., (2021). Other applications of nanofluids. In Nanofluids for heat and mass transfer (pp. 419–36). https://doi.org/10.1016/B978-­0-­12-­821955-­3.00012-­1. 28. Hota, S. K., & Diaz, G. (2019). Activated carbon dispersion as absorber for solar water evaporation: A parametric analysis. Solar Energy, 184, 40–51. 29. Verma, S. K., & Tiwari, A. K. (2015). Progress of nanofluid application in solar collectors: A review. Energy Conversion and Management, 100, 324–346. 30. Bhalla, V., & Tyagi, H. (2018). Parameters influencing the performance of nanoparticles-­ laden fluid-based solar thermal collectors: A review on optical properties. Renewable and Sustainable Energy Reviews, 1(84), 12–42. 31. Taylor, R.  A., Phelan, P.  E., Adrian, R.  J., Gunawan, A., & Otanicar, T.  P. (2012). Characterization of light-induced, volumetric steam generation in nanofluids. International Journal of Thermal Sciences, 56, 1–11. 32. Tong, Y., Chi, X., Kang, W., & Cho, H. (2020). Comparative investigation of efficiency sensitivity in a flat plate solar collector according to nanofluids. Applied Thermal Engineering, 174, 115346. 33. Tyagi, H., Phelan, P., & Prasher, R. (2009). Predicted efficiency of a low-temperature nanofluid-­ based direct absorption solar collector. Journal of Solar Energy Engineering, 131(4).

References

17

34. Karami, M., Bahabadi, M.  A., Delfani, S., & Ghozatloo, A. (2014). A new application of carbon nanotubes nanofluid as working fluid of low-temperature direct absorption solar collector. Solar Energy Materials and Solar Cells, 121, 114–118. 35. Celata, G. P., Annibale, F. D., & Mariani, A. (2011). Nanofluid flow effects on metal surfaces. Energia Ambiente e Innovazione, 4, 94–98. 36. Yousefi, T., Veysi, F., Shojaeizadeh, E., & Zinadini, S. (2012). An experimental investigation on the effect of Al2O3–H2O nanofluid on the efficiency of flat-plate solar collectors. Renewable Energy, 39(1), 293–298. 37. Kim, H., Ham, J., Park, C., & Cho, H. (2016). Theoretical investigation of the efficiency of a U-tube solar collector using various nanofluids. Energy, 94, 497–507. 38. Gu, M., Xu, X., Liu, X., Qiu, L., & Zhang, R. (2005). Preparation and characterization of GdTaO4: Eu3+ sol-gel luminescence thin films. Journal of Sol-Gel Science and Technology, 35(3), 193–196. 39. Hong, K., Yang, Y., Rashidi, S., Guan, Y., & Xiong, Q. (2021). Numerical simulations of a Cu–water nanofluid-based parabolic-trough solar collector. Journal of Thermal Analysis and Calorimetry, 143(6), 4183–4195. 40. Radwan, A., Ahmed, M., & Ookawara, S. (2016, June). Performance of concentrated photovoltaic cells using various microchannel heat sink designs. In Energy sustainability (Vol. 50220, p. V001T08A005). American Society of Mechanical Engineers. 41. Hussein, A. K. (2016). Applications of nanotechnology to improve the performance of solar collectors–Recent advances and overview. Renewable and Sustainable Energy Reviews, 62, 767–792. 42. Ahmadlouydarab, M., Ebadolahzadeh, M., & Ali, H. M. (2020). Effects of utilizing nanofluid as working fluid in a lab-scale designed FPSC to improve thermal absorption and efficiency. Physica A: Statistical Mechanics and its Applications, 540, 123109. 43. Sabiha, M. A., Saidur, R., Hassani, S., Said, Z., & Mekhilef, S. (2015). Energy performance of an evacuated tube solar collector using single walled carbon nanotubes nanofluids. Energy Conversion and Management, 105, 1377–1388. 44. Żółtowska, S., Bielan, Z., Zembrzuska, J., Siwińska-Ciesielczyk, K., Piasecki, A., Zielińska-­ Jurek, A., & Jesionowski, T. (2021). Modification of structured bio-carbon derived from spongin-based scaffolds with nickel compounds to produce a functional catalyst for reduction and oxidation reactions: Potential for use in environmental protection. Science of The Total Environment, 794, 148692. 45. Biswas, M. C., Jeelani, S., & Rangari, V. (2017). Influence of biobased silica/carbon hybrid nanoparticles on thermal and mechanical properties of biodegradable polymer films. Composites Communications, 4, 43–53. 46. Bhanvase, B., & Barai, D. (2021). Physical models for computational studies. In Nanofluids for heat and mass transfer (pp.  193–227). https://doi.org/10.1016/B978-­0-­12-­8219553.00002-­9 47. Bhanvase, B., & Barai, D. (2021), Computational studies on nanofluid-based systems. In Nanofluids for heat and mass transfer (pp. 229–261). 48. Bhanvase, B., & Barai, D. (2021). Actual vs theoretical behavior of nanofluids. In Nanofluids for heat and mass transfer (pp.  267–81). https://doi.org/10.1016/B978-0-12-821955-3. 00005-4 49. Lenert, A., & Wang, E. N. (2012). Optimization of nanofluid volumetric receivers for solar thermal energy conversion. Solar Energy, 86(1), 253–265. 50. Zadeh, P.  M., Sokhansefat, T., Kasaeian, A.  B., Kowsary, F., & Akbarzadeh, A. (2015). Hybrid optimization algorithm for thermal analysis in a solar parabolic trough collector based on nanofluid. Energy, 82, 857–864. 51. Ghasemi, S. E., & Ranjbar, A. A. (2017). Effect of using nanofluids on efficiency of parabolic trough collectors in solar thermal electric power plants. International Journal of Hydrogen Energy, 42(34), 21626–21634. 52. Yılmaz, İ. H., & Mwesigye, A. (2018). Modeling, simulation and performance analysis of parabolic trough solar collectors: A comprehensive review. Applied Energy, 225, 135–174.

18

1 Introduction

53. Balakin, B. V., Zhdaneev, O. V., Kosinska, A., & Kutsenko, K. V. (2019). Direct absorption solar collector with magnetic nanofluid: CFD model and parametric analysis. Renewable Energy, 136, 23–32. 54. Singh, A., Kumar, M., & Khullar, V. (2020). Comprehensive modeling, simulation and analysis of nanoparticles laden volumetric absorption based concentrating solar thermal systems in laminar flow regime. Solar Energy, 211, 31–54. 55. Khanjari, Y., Pourfayaz, F., & Kasaeian, A.  B. (2016). Numerical investigation on using of nanofluid in a water-cooled photovoltaic thermal system. Energy Conversion and Management, 122, 263–278. 56. Rejeb, O., Sardarabadi, M., Ménézo, C., Passandideh-Fard, M., Dhaou, M.  H., & Jemni, A. (2016). Numerical and model validation of uncovered nanofluid sheet and tube type photovoltaic thermal solar system. Energy Conversion and Management, 110, 367–377. 57. Sardarabadi, M., & Passandideh-Fard, M. (2016). Experimental and numerical study of metal-oxides/water nanofluids as coolant in photovoltaic thermal systems (PVT). Solar Energy Materials and Solar Cells, 157, 533–542. 58. Hosseinzadeh, M., Salari, A., Sardarabadi, M., & Passandideh-Fard, M. (2018). Optimization and parametric analysis of a nanofluid based photovoltaic thermal system: 3D numerical model with experimental validation. Energy Conversion and Management, 160, 93–108. 59. Kolahan, A., Maadi, S. R., Kazemian, A., Schenone, C., & Ma, T. (2020). Semi-3D transient simulation of a nanofluid-base photovoltaic thermal system integrated with a thermoelectric generator. Energy Conversion and Management, 220, 113073. 60. Kalani, H., Sardarabadi, M., & Passandideh-Fard, M. (2017). Using artificial neural network models and particle swarm optimization for manner prediction of a photovoltaic thermal nanofluid based collector. Applied Thermal Engineering, 113, 1170–1177. 61. Rashidi, S., Akar, S., Bovand, M., & Ellahi, R. (2018). Volume of fluid model to simulate the nanofluid flow and entropy generation in a single slope solar still. Renewable Energy, 115, 400–410. 62. Kabeel, A. E., Omara, Z. M., & Essa, F. A. (2017). Numerical investigation of modified solar still using nanofluids and external condenser. Journal of the Taiwan Institute of Chemical Engineers, 75, 77–86. 63. Das, B., Mondol, J.  D., Negi, S., Smyth, M., & Pugsley, A. (2021). Experimental performance analysis of a novel sand coated and sand filled polycarbonate sheet based solar air collector. Renewable Energy, 164, 990–1004. 64. Balamurugan, M., Sahoo, S. K., & Sukchai, S. (2017). Application of soft computing methods for grid connected PV system: A technological and status review. Renewable and Sustainable Energy Reviews, 1(75), 1493–1508. 65. Hamid, S. A., Othman, M. Y., Sopian, K., & Zaidi, S. H. (2014). An overview of photovoltaic thermal combination (PV/T combi) technology. Renewable and Sustainable Energy Reviews, 38, 212–222. 66. Hasan, M. A., & Sumathy, K. (2010). Photovoltaic thermal module concepts and their performance analysis: A review. Renewable and Sustainable Energy Reviews, 14(7), 1845–1859. 67. Lee, Y. S., & Tong, L. I. (2012). Predicting high or low transfer efficiency of photovoltaic systems using a novel hybrid methodology combining rough set theory, data envelopment analysis and genetic programming. Energies, 5(3), 545–560. 68. Kumar, A., Baredar, P., & Qureshi, U. (2015). Historical and recent development of photovoltaic thermal (PVT) technologies. Renewable and Sustainable Energy Reviews, 42, 1428–1436. 69. Chow, T.  T. (2010). A review on photovoltaic/thermal hybrid solar technology. Applied Energy, 87(2), 365–379. 70. Ibrahim, A., Othman, M. Y., Ruslan, M. H., Mat, S., & Sopian, K. (2011). Recent advances in flat plate photovoltaic/thermal (PV/T) solar collectors. Renewable and Sustainable Energy Reviews, 15(1), 352–365. 71. Hussain, F., Othman, M.  Y. H., Sopian, K., Yatim, B., Ruslan, H., & Othman, H. (2013). Design development and performance evaluation of photovoltaic/thermal (PV/T) air base solar collector. Renewable and Sustainable Energy Reviews, 25, 431–441.

References

19

72. Chandrasekar, M., Rajkumar, S., & Valavan, D. (2015). A review on the thermal regulation techniques for non integrated flat PV modules mounted on building top. Energy and Buildings, 86, 692–697. 73. Reddy, S.  R., Ebadian, M.  A., & Lin, C.  X. (2015). A review of PV–T systems: Thermal management and efficiency with single phase cooling. International Journal of Heat and Mass Transfer, 91, 861–871. 74. Aste, N., Beccali, M., & Chiesa, G. (2002). Experimental evaluation of the performance of a prototype hybrid solar photovoltaic-thermal (PV/T) air collector for the integration in sloped roof. In Proceedings of EPIC. 75. Elsafi, A. M., & Gandhidasan, P. (2015). Comparative study of double-pass flat and compound parabolic concentrated photovoltaic–thermal systems with and without fins. Energy Conversion and Management, 98, 59–68. 76. Othman, M. Y. H., Yatim, B., Sopian, K., & Bakar, M. N. A. (2005). Performance analysis of a double-pass photovoltaic/thermal (PV/T) solar collector with CPC and fins. Renewable Energy, 30(13). 77. Tonui, J. K., & Tripanagnostopoulos, Y. (2007). Improved PV/T solar collectors with heat extraction by forced or natural air circulation. Renewable Energy, 32(4), 623–637. 78. Farshchimonfared, M., Bilbao, J. I., & Sproul, A. B. (2015). Channel depth, air mass flow rate and air distribution duct diameter optimization of photovoltaic thermal (PV/T) air collectors linked to residential buildings. Renewable Energy, 76, 27–35. 79. Farshchimonfared, M., Bilbao, J. I., & Sproul, A. B. (2016). Full optimisation and sensitivity analysis of a photovoltaic–thermal (PV/T) air system linked to a typical residential building. Solar Energy, 136, 15–22. 80. Su, D., Jia, Y., Alva, G., Liu, L., & Fang, G. (2017). Comparative analyses on dynamic performances of photovoltaic–thermal solar collectors integrated with phase change materials. Energy Conversion and Management, 131, 79–89. 81. Amori, K. E., & Abd-AlRaheem, M. A. (2014). Field study of various air based photovoltaic/ thermal hybrid solar collectors. Renewable Energy, 63, 402–414. 82. Liang, R., Zhang, J., Ma, L., & Li, Y. (2015). Performance evaluation of new type hybrid photovoltaic/thermal solar collector by experimental study. Applied Thermal Engineering, 75, 487–492. 83. Edenhofer, O., Pichs-Madruga, R., Sokona, Y., Seyboth, K., Kadner, S., Zwickel, T., Eickemeier, P., Hansen, G., Schlömer, S., von Stechow, C., & Matschoss, P. (Eds.). (2011). Renewable energy sources and climate change mitigation: Special report of the intergovernmental panel on climate change. Cambridge University Press. 84. Touafek, K., Haddadi, M., & Malek, A. (2013). Design and modeling of a photovoltaic thermal collector for domestic air heating and electricity production. Energy and Buildings, 59, 21–28. 85. Tripanagnostopoulos, Y. (2007). Aspects and improvements of hybrid photovoltaic/thermal solar energy systems. Solar Energy, 81(9), 1117–1131. 86. Varol, Y., Koca, A., Oztop, H. F., & Avci, E. (2010). Forecasting of thermal energy storage performance of phase change material in a solar collector using soft computing techniques. Expert Systems with Applications, 37(4), 2724–2732. 87. Tagliafico, L.  A., Scarpa, F., & De Rosa, M. (2014). Dynamic thermal models and CFD analysis for flat-plate thermal solar collectors–A review. Renewable and Sustainable Energy Reviews, 30, 526–537. 88. Jubayer, C. M., Karava, P., & Savory, E. (2010, May). CFD simulations for evaluation of forced convective heat transfer coefficients on photovoltaic/thermal systems integrated on the windward roof surface of a low-rise building. In Proceedings of computational wind engineering conference, Chapel Hill 89. Khelifa, A., Touafek, K., Moussa, H. B., & Tabet, I. (2016). Modeling and detailed study of hybrid photovoltaic thermal (PV/T) solar collector. Solar Energy, 135, 169–176. 90. Kramer, K., & Helmers, H. (2013). The interaction of standards and innovation: Hybrid photovoltaic–thermal collectors. Solar Energy, 98, 434–439.

20

1 Introduction

91. Caner, M., Gedik, E., & Keçebaş, A. (2011). Investigation on thermal performance calculation of two type solar air collectors using artificial neural network. Expert Systems with Applications, 38(3), 1668–1674. 92. Sözen, A., Menlik, T., & Ünvar, S. (2008). Determination of efficiency of flat-plate solar collectors using neural network approach. Expert Systems with Applications, 35(4), 1533–1539. 93. Ong, C. S., Huang, J. J., & Tzeng, G. H. (2005). Building credit scoring models using genetic programming. Expert Systems with Applications, 29(1), 41–47. 94. Esen, H., Inalli, M., Sengur, A., & Esen, M. (2008). Modeling a ground-coupled heat pump system by a support vector machine. Renewable Energy, 33(8), 1814–1823. 95. Esen, H., Ozgen, F., Esen, M., & Sengur, A. (2009). Modelling of a new solar air heater through least-squares support vector machines. Expert Systems with Applications, 36(7), 10673–10682. 96. Esen, H., Ozgen, F., Esen, M., & Sengur, A. (2009). Artificial neural network and wavelet neural network approaches for modelling of a solar air heater. Expert Systems with Applications, 36(8), 11240–11248. 97. Ammar, M. B., Chaabene, M., & Chtourou, Z. (2013). Artificial neural network based control for PV/T panel to track optimum thermal and electrical power. Energy Conversion and Management, 65, 372–380. 98. Huang, G.  B., Zhu, Q.  Y., & Siew, C.  K. (2004, July). Extreme learning machine: A new learning scheme of feedforward neural networks. In 2004 ieee international joint conference on neural networks (IEEE Cat. No. 04CH37541) (Vol. 2, pp. 985–990). IEEE. 99. Huang, G. B., Zhu, Q. Y., & Siew, C. K. (2006). Real-time learning capability of neural networks. IEEE Transactions on Neural Networks, 17(4), 863–878. 100. Yu, Q., Miche, Y., Séverin, E., & Lendasse, A. (2014). Bankruptcy prediction using extreme learning machine and financial expertise. Neurocomputing, 128, 296–302. 101. Wang, X., & Han, M. (2014). Online sequential extreme learning machine with kernels for nonstationary time series prediction. Neurocomputing, 145, 90–97. 102. Ghouti, L., Sheltami, T. R., & Alutaibi, K. S. (2013). Mobility prediction in mobile ad hoc networks using extreme learning machines. Procedia Computer Science, 19, 305–312. 103. Sun, D., Liu, S., & Gong, X. (2020). Review of multimer protein–protein interaction complex topology and structure prediction. Chinese Physics B, 29(10), 108707. 104. Nian, R., He, B., Zheng, B., Van Heeswijk, M., Yu, Q., Miche, Y., & Lendasse, A. (2014). Extreme learning machine towards dynamic model hypothesis in fish ethology research. Neurocomputing, 128, 273–284. 105. Wong, P. K., Wong, K. I., Vong, C. M., & Cheung, C. S. (2015). Modeling and optimization of biodiesel engine performance using kernel-based extreme learning machine and cuckoo search. Renewable Energy, 74, 640–647. 106. Jha, P., Das, B., & Gupta, R. (2019). An experimental study of a photovoltaic thermal air collector (PVTAC): A comparison of a flat and the wavy collector. Applied Thermal Engineering, 163, 114344. 107. Rizwan, M., Jamil, M., Kirmani, S., & Kothari, D. P. (2014). Fuzzy logic based modeling and estimation of global solar energy using meteorological parameters. Energy, 70, 685–691. 108. Shuvho, M. B. A., Chowdhury, M. A., Ahmed, S., & Kashem, M. A. (2019). Prediction of solar irradiation and performance evaluation of grid connected solar 80KWp PV plant in Bangladesh. Energy Reports, 5, 714–722. 109. Iqdour, R., & Zeroual, A. (2007). Prediction of daily global solar radiation using fuzzy systems. International Journal of Sustainable Energy, 26(1), 19–29. 110. Şen, Z. (1998). Fuzzy algorithm for estimation of solar irradiation from sunshine duration. Solar Energy, 63(1), 39–49. 111. Jose, B.  K. (2020). Fuzzy based maximum power point tracking of PV array under non-­ uniform irradiance conditions. Materials Today: Proceedings, 24, 1835–1842. 112. Farajdadian, S., & Hosseini, S. H. (2019). Design of an optimal fuzzy controller to obtain maximum power in solar power generation system. Solar Energy, 182, 161–178.

References

21

113. Ramaprabha, R., Balaji, M., & Mathur, B. L. (2012). Maximum power point tracking of partially shaded solar PV system using modified Fibonacci search method with fuzzy controller. International Journal of Electrical Power & Energy Systems, 43(1), 754–765. 114. Batayneh, W., Owais, A., & Nairoukh, M. (2013). An intelligent fuzzy based tracking controller for a dual-axis solar PV system. Automation in Construction, 29, 100–106. 115. Sridharan, M., & Anabayan, K. (2014). Performance analysis on concrete photovoltaic/ thermal water collectors. International Journal of Engineering in Computer Sciences, 4(6), 12440–12443. 116. Sridharan, M., Siva Prakash, E., Joshua, R.  C., & Karthikeyan, S. (2014). Performance improving methods for series solar flat plate collectors and introduction of new verification tool. International Journal of Innovative Research in Science Engineering and Technology, 3(3), 1155–1161. 117. Sridharan, M., Siva Prakash, E., & Prasanna, N. (2014). Steady state analysis on efficiency improving methods for series flat plate solar water heaters. In Applied mechanics and materials (Vol. 592, pp. 1784–1788). Trans Tech Publications. 118. Sridharan, M., Prasanna, N., SivaPrakash, E., & VaradhaRajan, R. (2014). Experimental investigation on series solar flat plate collectors with variable mass flow rates. International Journal of Innovative Research in Science, Engineering and Technology, 3(3), 1150–1154. 119. Debnath, S., Reddy, J., & Das, B. (2019). An expert system-based modeling and optimization of corrugated plate solar air collector for North Eastern India. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(7), 1–18. 120. Kishor, N., Das, M. K., Narain, A., & Ranjan, V. P. (2010). Fuzzy model representation of thermosyphon solar water heating system. Solar Energy, 84(6), 948–955. 121. Vafaei, L.  E., & Sah, M. (2017). Predicting efficiency of flat-plate solar collector using a fuzzy inference system. Procedia Computer Science, 120, 221–228. 122. Jing, O. L., Bashir, M. J., & Kao, J. J. (2015). Solar radiation based benefit and cost evaluation for solar water heater expansion in Malaysia. Renewable and Sustainable Energy Reviews, 48, 328–335. 123. Hajabdollahi, Z., & Hajabdollahi, H. (2017). Thermo-economic modeling and multi-­objective optimization of solar water heater using flat plate collectors. Solar Energy, 155, 191–202. 124. Nallagownden, P., Huy, T. H. B., Kannan, R., & Dieu, V. N. (2019). Energetic optimization of solar water heating system with flat plate collector using search group algorithm. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 61(2), 306–322. 125. Farahat, S., Sarhaddi, F., & Ajam, H. (2009). Exergetic optimization of flat plate solar collectors. Renewable Energy, 34(4), 1169–1174. 126. Ouhammou, B., Aggour, M., & Daouchi, B. (2018). Optimization of the thermal performance of the solar water heater (SWH) using stochastic technique. International Journal of Renewable Energy Research (IJRER), 8(3), 1401–1410. 127. Wenceslas, K. Y., & Ghislain, T. (2019). Experimental validation of exergy optimization of a flat-plate solar collector in a thermosyphon solar water heater. Arabian Journal for Science and Engineering, 44(3), 2535–2549. 128. Khademi, M., Jafarkazemi, F., Ahmadifard, E., & Younesnejad, S. (2013). Optimizing exergy efficiency of flat plate solar collectors using SQP and genetic algorithm. In Applied mechanics and materials (Vol. 253, pp. 760–765). Trans Tech Publications Ltd.. 129. Hajabdollahi, F., & Premnath, K. (2017). Numerical study of the effect of nanoparticles on thermoeconomic improvement of a solar flat plate collector. Applied Thermal Engineering, 127, 390–401. 130. Hajabdollahi, H. (2018, February). Investigating the effect of nanofluid on optimal design of solar flat plate collector. In 2018 5th international conference on renewable energy: generation and applications (ICREGA) (pp. 188–191). IEEE. 131. Hajabdollahi, Z., Hajabdollahi, H., & Kim, K.  C. (2020). Multi-objective optimization of solar collector using water-based nanofluids with different types of nanoparticles. Journal of Thermal Analysis and Calorimetry, 140(3), 991–1002.

22

1 Introduction

132. Debnath, S., Reddy, J., Das, B., & Jagadish. (2019). Modeling and optimization of flat plate solar air collectors: An integrated fuzzy method. Journal of Renewable and Sustainable Energy, 11(4), 043706. 133. Reddy, J., Debnath, S., & Das, B. (2019). Energy and exergy analysis of wavy plate solar air collector using a novel hybrid expert system. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(10), 1–14. 134. Debnath, S., Reddy, J., & Das, B. (2019). Investigation of thermal performance of SAC variables using fuzzy logic based expert system. Journal of Mechanical Science and Technology, 33(8), 4013–4021. 135. Rezvani, A., Esmaeily, A., Etaati, H., & Mohammadinodoushan, M. (2019). Intelligent hybrid power generation system using new hybrid fuzzy-neural for photovoltaic system and RBFNSM for wind turbine in the grid connected mode. Frontiers in Energy, 13(1), 131–148. 136. Pang, M., Shi, Y., Wang, W., & Pang, S. (2019). Optimal sizing and control of hybrid energy storage system for wind power using hybrid parallel PSO-GA algorithm. Energy Exploration & Exploitation, 37(1), 558–578. 137. Mellit, A., Kalogirou, S. A., Hontoria, L., & Shaari, S. (2009). Artificial intelligence techniques for sizing photovoltaic systems: A review. Renewable and Sustainable Energy Reviews, 13(2), 406–419. 138. Ohsawa, Y., Emura, S. I., & Arai, K. (1992, April). Optimal operation of photovoltaic/diesel power generation system by neural network. In [1993] Proceedings of the second international forum on applications of neural networks to power systems (pp. 99–103). IEEE. 139. Lujano-Rojas, J. M., Dufo-López, R., & Bernal-Agustín, J. L. (2013). Probabilistic modelling and analysis of stand-alone hybrid power systems. Energy, 63, 19–27. 140. Paliwal, P., Patidar, N. P., & Nema, R. K. (2014). Determination of reliability constrained optimal resource mix for an autonomous hybrid power system using particle swarm optimization. Renewable Energy, 63, 194–204. 141. Kaviani, A.  K., Riahy, G.  H., & Kouhsari, S.  M. (2009). Optimal design of a reliable hydrogen-based stand-alone wind/PV generating system, considering component outages. Renewable Energy, 34(11), 2380–2390. 142. Merei, G., Berger, C., & Sauer, D. U. (2013). Optimization of an off-grid hybrid PV–Wind– Diesel system with different battery technologies using genetic algorithm. Solar Energy, 97, 460–473. 143. Kumar, R., Gupta, R. A., & Bansal, A. K. (2013). Economic analysis and power management of a stand-alone wind/photovoltaic hybrid energy system using biogeography based optimization algorithm. Swarm and Evolutionary Computation, 8, 33–43. 144. Paliwal, N. K., Singh, A. K., Singh, N. K., & Kumar, P. (2019). Optimal sizing and operation of battery storage for economic operation of hybrid power system using artificial bee colony algorithm. International Transactions on Electrical Energy Systems, 29(1), e2685. 145. Yang, H. X., Lu, L., & Burnett, J. (2003). Weather data and probability analysis of hybrid photovoltaic–wind power generation systems in Hong Kong. Renewable Energy, 28(11), 1813–1824.

Chapter 2

Modeling and Optimization of Solar Air Collector Using GRA

2.1 Introduction A solar air heater is more popular than other solar systems [1] due to its straightforward construction, low cost of maintenance, and economic viability. Flat plate solar air heaters are a prominent form of solar air heaters [2] that uses solar energy to heat air. These solar air heaters are widely used in the construction business for drying or curing concrete and clay [3, 4] and in the agricultural sector for drying fruits and vegetables [5, 6]. Typical solar air heaters feature an absorber plate and a glass cover above it, forming a confined space for air to be heated and circulated [6]. Researchers have adopted various techniques to increase the performance of solar collectors by altering the configuration of the system [7–9] in order to account for a wide variety of factors that affect the performance of solar air heaters, including mass flow rate, plate sheet material, cover type, collector dimensions, and so on. Nonetheless, there is still a significant obstacle in optimizing the thermal performance of solar air heaters. Instead of using a metal sheet, as suggested by some researchers [10], porous materials could be used for this purpose. An alternative study replaced conventional cover with perforated plexiglass to speed up the cooling process of the surface and boost the collector’s efficiency [2]. To maximize the efficiency of the solar air heater, Yang et al. [11] constructed it with offset trip fins and created a numerical model to do so. El-Khawajah et al. [12] conducted a study that was quite similar. To ensure the greatest possible financial viability of the system, [13, 14] used a combination of artificial neural networks and genetic algorithms. Optimizing the thermal performance of a flat plate solar air heater using an evolutionary algorithm and considering various operating factors [6] is another example of this type of study. Numerous energy issues are solved using multi-criteria decision-making (MCDM) approaches, including energy planning and selection, resource allocation, energy policy, and building energy management [15]. These aspects are studied in

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4_2

23

24

2  Modeling and Optimization of Solar Air Collector Using GRA

depth from simple profit maximization and cost reduction challenges to more complicated multi-criteria decision-making problems [16]. The most common criterion is investment cost, carbon dioxide emissions, efficiency, operation and maintenance cost, land utilization, fuel cost, and new job creation, as reported by Wang et al. [15]. Weighted sum method (WSM), weighted product method (WPM), analytic hierarchy process (AHP), fuzzy AHP, Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), fuzzy TOPSIS, PROMETHEE (Preference Ranking Organization Method for Enrichment Evaluation), ELECTRE (Elimination and Choice Translating Reality), and VIKOR (Value in Knowledge Organization) are examples of MCDM techniques (visekriterijumsko kompromisno rangiranje). Since every strategy has advantages, disadvantages, and potential uses, it’s hard to state one to be the best. Using multiple approaches to solve a multi-criteria decision problem, you’ll have more reliable data to base your final choice [17]. Acr et al. [18] employed GRA to determine ideal energy and exergy efficiency parameters in a novel design solar air heater (SAH). ANOVA is used to calculate correlation ratios between parameters. To predict energy and exergy efficiency, regression analysis (RA) is performed. Experimental results confirmed the RA data. Aghaie et al. [19] used the Taguchi method to optimize thermo-hydraulic behavior of airflow using a solar air heater. The rib’s unusual generic geometry allows it to generate triangular, trapezoidal, and rectangular shapes simultaneously. Rib pitch, height, tip breadth, and front projection have the most influence on thermo-­hydraulic performance. The optimal rib form is triangular, with a 0.2H rib height and P = 2H, and the rib front is perpendicular to the direction of flow (s = 0). Gunes [20] suggests a tube with loosely fitting perforated twisted tapes that can be used to determine optimal design parameter values. Taguchi method and generalized estimating equation (GRA) were used to explore the impact of various design factors, such as twist ratio, width ratio, hole diameter ratio, and Reynolds number on heat transfer (i.e., Nusselt number) and pressure drop (i.e., friction factor). Initially, every performance parameter was adjusted independently. Then, TM and GRA worked together to enhance all performance metrics. Reynolds number is the most significant element for both Nusselt number and friction factor, whereas twisting ratio and width ratio are the least significant. Chauhan [21] examined the performance of a solar thermal collector with deep-­ impacting air jets. The ideal design for impinging jet solar thermal collectors was determined using performance-defining criteria. A preference selection index-based technique has been developed to discover optimal design parameters that generate peak thermal performance with a minor friction factor within the collector duct. For this technique, the optimal stream wise pitch ratio is 0.43, span wise pitch ratio is 0.866, jet diameter ratio is 0.06, and flow Reynolds number is 16,000. Mishra et al. [22] examined the effect of flow and geometric parameters on the behavior of circular impingement air jets utilizing solar air channel (SAP). AHP-TOPSIS is used to identify geometric parameters which produce highest thermal efficiency and a negligible friction factor within SAP. Sharma et al. [23] studied performance and optimum design of multiple V barriers in a solar air channel. As a result of discrete barriers, thermal boundary layer formation on the heat-conducting surface is fading.

2.2  The Methodological Approach

25

In addition, an increase in frictional losses lowers the overall performance of the solar airflow channel. Entropy-VIKOR integrated technique, an MCDM method, to quantify quantifies these criteria as the shared accord applied to experimental data. According to Entropy-VIKOR optimization, the relative angle of attack, discrete distance ratio, and discrete width ratio of inserted V obstacle with gaps having numerical values of 0.666, 0.67, and 1.0 constitute an excellent parameter set for V obstacle design.

2.2 The Methodological Approach 2.2.1 Modeling of Thermal Energy The instantaneous efficiency of SAC is defined as the ratio of heat gain by the working fluid to the total incident solar energy affecting the collector at a given moment. Beneficial heat gain by working fluid may be calculated using the equation below.

Qg  m a c p  T2  T1 

(2.1)



where Qg is the heat gain by the working fluid, cp is the specific heat of air, ma is air mass flow rate, and T1 and T2 are working fluid temperatures at inlet and exit, respectively. The following is an estimate of energy efficiency (also known as useful instantaneous efficiency):



Qg Qab

(2.2)

where Qab = Ac(ατ)I, α (absorber plate absorptivity) is 0.875, and τ (glass’ transmittance) is 0.96, where I and Ac are solar intensity and collector area, respectively. The thermo-hydraulic efficiency, often known as effective thermal efficiency, is calculated as follows:

eff

 Pfan Qg    cn  f  Qab

  

(2.3)

where cnf is the conversion factor for converting one type of energy to another, such as thermal to mechanical energy, and the value of that factor is 0.2. Pfan is fan power. At an average temperature, the physical characteristics of a fluid (air) are studied.

Tavg   T2  T1  / 2



(2.4)

26

2  Modeling and Optimization of Solar Air Collector Using GRA

2.2.2 Exergy Analysis Second law efficiency may be represented as [11]:

 II  1 

 xdest  xin

(2.5)

where ηII is the exergy efficiency and εxdest and εxin are exergy destruction and exergy input, respectively. The rate of change of overall exergy destructed can be expressed as:



 1  T 4 4  T   exdest    1   am    am   Qab  ma .c p .  T2  T1   3  Tab  3  Tab     T2 P  ma .c p .Tam ln  ma . R.Tam . ln 2 T1 P1

(2.6)

where εxdest is exergy destruction, Tam and Tab are ambient and absorber temperatures, Qab is energy incident on collector surface, ma is the mass flow rate of air, cp is the specific heat of fluid, R is gas constant, T2 is outlet temperature of collector, T1 is the inlet temperature of collector, and P1 and P2 are pressure entry and exit of the collector. Further the second law efficiency may be expressed as follows:

 II 

 xp  xin

 1

 xdest  xin

(2.7)

where εxp is real exergy, taking collector pressure drop into account, and is calculated as follows:

 x p   xout   xwork



Te Pfan Tin



m  P   f  fan

 xwork 



(2.8) (2.9)



.

Pfan

(2.10)

where ηfan is the efficiency of the fan (blower) and is set to 0.9.

2.2  The Methodological Approach

27

2.2.3 Grey Relational Analysis (GRA) This study uses GRA to determine optimum parameters in energy and exergy efficiencies of SAH. In GRA, each response (energy and exergy) determined from the experiment was normalized in the range of 0–1. Generally, normalizations can be performed using Eqs. (2.11, 2.12, and 2.13). In this study, normalization of experimental results using higher the better characteristic given by Eq. (2.11) was performed. In the case of “higher the better,” original array can be normalized as follows: yi  k  

xi0  k   min xi0  k 

max xi0  k   min xi0  k 

(2.11)

In the case of “lower the better,” original array can be normalized as follows: yi  k  

max xi0  k   xi0  k 

max xi0  k   min xi0  k 

(2.12)

And finally for “nominal the better”: yi  k   1 

xi0  k   x 0 max xi0  k   x 0

(2.13)

0 where yi(k) is the normalization value of grey relational generation, max xi  k  is 0 0 0 the maximum value of the xi  k  value, min xi  k  is the minimum value of xi  k  , and x0 represents optimum value. In GRA, grey relational grade is determined by identifying y0(k) and yi(k) (i = 1, 2... 19; k = 1, 2, 3, 4) relational grades of nine arrays. Grey relational coefficient ξi(k) can be calculated as follows:



 min   max  0 i  k    max





 0 i  k   y0  k   yi  k 





 max  max ji max k y0  k   yi  k 





 min  min ji min k y0  k   yi  k 



i  k  

(2.14) (2.15) (2.16) (2.17)

where Δ0i(k) is deviation value between y0(k)andyi(k), φ is distinguishing coefficient with φ∈ [0, 1], and generally φ = 0.5 is used. Δmin is the minimum value of Δ0i and Δmax is the maximum value of Δ0i. Overall grey relational grade ϒi is calculated using Eq. (2.18).

28

2  Modeling and Optimization of Solar Air Collector Using GRA

1 k 1  i  k  n n

i 



(2.18)

where n is the number of process responses. A high grey relational generation grade indicates a strong correlation between y0(k) and yi(k). If two compared series have same values, grey relational grade is found to be 1. ϒi used to find out the proximity of compared series value to reference series value.

2.2.4 Experimentation Specifics During December 2018 and January 2019, tests were administered at NIT Silchar, India. A flat absorber plate and 0.005-m-thick double glazing are maintained inside the box to reduce top-side losses. The collector box is 2 m long by 1 m wide and 0.200 m deep. The rear and sides of collector are insulated to prevent heat loss. Both inflow and outflow holes have circular perforations with a diameter of 0.04 m to maintain airflow. Figure 2.1 depicts a diagrammatic illustration of the experimental setup. A blower with variable speed is utilized to heat the absorber plate. Measurements are taken as pressure drop across absorber, temperature at various points along the collector’s input and output, and solar radiation at different times of the day. The experimentation with variable mass flow rates (0.0039–0.0156 kg/s) and tilt angles (15–45°) is investigated for open atmosphere conditions of Silchar, Northeast India.

n tio

dia

ra lar

So

SUN

tlet

Ou

late

rp

ing

laz

G ble

u Do

be sor

t ab

Fla

ionon lat ti suula l iinns a ml

er a Tehrm

Th

Collector box

ir

et A

Inl

Thermocouples

Fig. 2.1  Schematic diagram of flat plate solar air collector

Air

2.3 Results and Discussion

29

2.3 Results and Discussion In this section, results of experimental findings on SAC performance of trapezoidal profile absorber plate and flat plate absorber plate are presented under climatic condition of Silchar, northeastern region of India. Present experimentation was carried out for four mass flow rate of air (0.0039  kg/s, 0.0078  kg/s, 0.0117  kg/s, and 0.0156 kg/s) and tilt angle (15°, 30°, 45°) for flat plate SAC. Proceeding sections illustrate the behavior of various parameters through a graphical version of temperature rise, energy efficiency, and exergy efficiency for daytime, varying mass flow rates and increasing tilt angles.

2.3.1 Parametric Analysis 2.3.1.1 Variation of Temperature Rise Figure 2.2a–c illustrates the variation of daytime temperature rise for inclination angles of 15°, 30°, and 45° for four distinct mass flow rates. It is revealed that, if the difference between inlet and ambient temperatures is less, air temperature rise generally varies almost linearly with solar radiation. In the present study, results indicate that temperature rise increases during the day, peaks at midday, and then decreases. It also demonstrates that raising tilt angle increases temperature rise, with 45° tilt angle having a better value than 15° and 30° tilt angles; this impacts the collector’s performance. Moreover, results indicate that magnitude of temperature rise decreases as the mass flow rate of air increases. The reason is that air with a higher mass flow rate stays on hot surfaces for a shorter period than air with a lower mass flow rate. However, as output heat is a function of mass flow rate and temperature rise, quantitative effect of this decline on collector’s performance may not be proportional. The highest temperature measured for considered flat plate SAC was 71.1 °C during daytime hours of 12:00 to 13:00 h for a mass flow rate of 0.0039 kg/s and a tilt angle of 45°. 2.3.1.2 Variation of Energy Efficiency Variation in energy efficiency with time is shown in Fig.  2.3a–c. Generally, the magnitude of efficiency attains a peak at noon and then decreases during the afternoon. The trend is akin to solar radiation, which is the main driving factor of efficiency. However, at a similar range of solar radiation in morning and afternoon, magnitudes of efficiency are different; this indicates a higher amount of thermal losses in the morning due to lesser ambient temperature. Experimental trials have been carried out with different mass flow rates of air (0.0039–0.0156 kg/s) at varying tilt angles (15°, 30°, and 45°). Results indicate that energy efficiency rises with

30

2  Modeling and Optimization of Solar Air Collector Using GRA 90 0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 15° 80

Temperature rise (°C)

70 60 50 40 30 20 10 0 9

10

11

12

13

14

15

Time (hours)

(a) 70

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 30°

Temperature rise (°C)

60

50

40

30

20

10

0 9

10

11

12

Time (hours)

(b) Fig. 2.2  Variation of temperature rise with time

13

14

15

2.3 Results and Discussion

31

70 0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 45° 60

Temperature rise (°C)

50

40

30

20

10

0 9

10

11

12

13

14

15

Time (hours)

(c) Fig. 2.2 (continued)

an increase in mass flow rate of air. The reason may be due to better extraction of heat by flowing air. Further, an increase in inclination angle from 15° to 45° results a raise in efficiency up to 44.8%. The reason may be due to the better chimney effect that enhances heat transfer. Maximum energy efficiency found at tilt angle 45° for mass flow rate 0.0156 kg/s is 27.02% for flat plate SAC. 2.3.1.3 Variation of Exergy Efficiency Exergy efficiency variation of SAC is shown in Fig. 2.4a–c. The magnitude of the exergy increases with the rise in daytime till noon after it declining during the afternoon. An initial exponential increase in the value of exergy efficiency is linked with a quantitative increase in the rate of heat transfers from the absorber plate. Further, augmenting in average temperature of working fluid also helps to enhance heat transfer quality. During the second half of the day, the rate of heat transfer is decreased both quantity-wise and quality-wise, resulting in low exergy efficiency. Maximum exergy efficiency reaches up to 11.8% at 45° tilt angle for the mass flow rate of 0.0039 kg/s at noon time for flat plate SAC.

2  Modeling and Optimization of Solar Air Collector Using GRA

32

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Energy efficeincy(%)

25

Tilt angle 15°

20

15

10

5

0 9

10

11

12

13

14

15

Time (hours)

(a) 0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

35

Energy efficiency (%)

30

Tilt angle 30°

25

20

15

10

5

0 9

10

11

12

Time (hours)

(b) Fig. 2.3  Variation of energy efficiency with time

13

14

15

2.3 Results and Discussion

33

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

45 Tilt angle 45° 40

Energy efficiency (%)

35 30 25 20 15 10 5 0 9

10

11

12

13

14

15

Time (hours)

(c) Fig. 2.3 (continued)

2.3.1.4 Variation of Pressure Drop Variation in pressure drop with the mass flow rate for the present experimental investigation of flat plate SAC is shown in Fig. 2.5. Behavior of pressure drop is escalating with rising mass flow rate and increasing tilt angle. Pressure drop also rises due to air requisite to overcome the higher gravitational effect. The trends of pressure drop at different tilt angles are similar but vary in magnitude. The current study observed maximum pressure drop occurred at a tilt angle of 45° for mass flow rate of 0.0156 kg/s which is 94 Pa for flat plate. The pressure drop varies from tilt angle 15–45° and is 1.96 Pa for 0.0039 kg/s and 94 Pa for 0.0156 kg/s, respectively. 2.3.1.5 Optimization of Solar Air Collector The energy and exergy efficiencies of SAHs were computed and analyzed based on the results of experiments. Analyses were carried out based on information gathered during midday when the level of solar radiation was at its peak. Equations were utilized in this process. GRA approach was utilized to optimize the parameters that had an effect on energy and exergy efficiency. This study focused on four diverse

34

2  Modeling and Optimization of Solar Air Collector Using GRA

12

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 15°

Exergy efficiency (%)

10

8

6

4

2

0 9

10

11

12

13

14

15

Time (hours)

(a)

14

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 30°

Exergy efficiency (%)

12

10

8

6

4

2

0 9

10

11

12

Time (hours)

(b) Fig. 2.4  Variation of exergy efficiency with time

13

14

15

35

2.3 Results and Discussion 18 0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 45° 16

Exergy efficiency (%)

14 12 10 8 6 4 2 0 9

10

11

12

13

Time (hours)

(c) Fig. 2.4 (continued)

Fig. 2.5  Variation of pressure drop with the mass flow rate

14

15

36

2  Modeling and Optimization of Solar Air Collector Using GRA

Table 2.1  Parameters and levels used in the experiments Parameters Mass flow rate (kg/s) Solar radiation (W/m2) Tilt angle (θ) Inlet temperature (Tin)

Levels 1 0.0039 350 15 13

2 0.0117 727 30 22

3 0.0156 916 45 30

Table 2.2  Decision matrix of SAC Trails 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Temperature rise 39.2 22 26.4 45.8 31.8 63.4 11.3 24.5 22.1 11.4 10.6 18.6 8 23.1 18.8 17.6 8.1 17.8 9.1

Energy efficiency 18.013 20.946 18.246 9.796 22.358 16.690 17.847 10.106 24.611 16.065 11.809 18.114 17.914 12.446 15.284 17.189 13.586 8.827 18.801

Exergy efficiency 8.673 5.939 5.325 7.326 8.781 11.041 0.915 5.521 6.432 0.611 0.936 4.103 0.528 5.533 4.901 6.615 2.670 4.879 1.876

Pressure drop 21.715 83.385 42.05 1.056 63.765 8.81 66.765 4.905 94.1 54.955 10.81 66.765 94.1 10.81 28.525 28.525 42.05 1.0562 83.385

parameters such as mass flow rate, solar radiation, tilt angle, and the inlet temperature. Table 2.1 presents experimental parameters and levels. An experimental array in the form of an orthogonal array was created to accommodate two response variables that corresponded to three grade components that were related to three parameters. The choice matrix that corresponds to experiment numbers and related energy and exergy efficiencies may be seen in Table 2.2; these efficiencies are response variables. As a result of this, a technique to array normalization known as “higher is better” was chosen. Table  2.3 displays the absolute deviation values that correspond to all of the derived measurement findings when applied to the normalized values. The grey relationship coefficients for all of the experiments were determined using Eq. (2.14), and the calculations were performed with these coefficients. As seen in Table  2.4 and Fig.  2.6, the result attained for experiment 9 was 0.733, which was the highest possible.

2.3 Results and Discussion

37

Table 2.3  Normalization matrix of SAC T rise 0.436 0.747 0.667 0.317 0.570 0 0.940 0.702 0.745 0.938 0.953 0.808 1 0.727 0.805 0.826 0.998 0.823 0.980

Efficiency 0.418 0.232 0.403 0.938 0.142 0.501 0.428 0.918 0 0.541 0.811 0.411 0.424 0.770 0.590 0.470 0.698 1 0.368

Exergy 0.225 0.485 0.543 0.353 0.214 0 0.963 0.525 0.438 0.992 0.961 0.659 1 0.523 0.584 0.421 0.796 0.586 0.871

Pressure 0.777 0.115 0.559 1 0.326 0.916 0.293 0.958 0 0.420 0.895 0.293 0 0.895 0.704 0.704 0.559 1 0.115

Table 2.4  Grey relational coefficient and grey relational grade Trails 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

T rise 0.533 0.400 0.428 0.611 0.467 1 0.347 0.415 0.401 0.347 0.344 0.382 0.333 0.407 0.383 0.376 0.333 0.377 0.337

Efficiency 0.544 0.682 0.553 0.347 0.777 0.499 0.538 0.352 1 0.480 0.381 0.548 0.540 0.393 0.458 0.515 0.417 0.333 0.575

Exergy 0.689 0.507 0.479 0.585 0.699 1 0.341 0.487 0.532 0.335 0.342 0.431 0.333 0.488 0.461 0.542 0.385 0.460 0.364

Pressure 0.391 0.812 0.471 0.333 0.605 0.352 0.629 0.342 1 0.543 0.358 0.629 1 0.358 0.415 0.415 0.471 0.333 0.812

GRG 0.539 0.601 0.483 0.469 0.637 0.713 0.464 0.399 0.733 0.426 0.356 0.497 0.551 0.411 0.429 0.462 0.402 0.376 0.522

Rank 6 4 9 10 3 2 11 17 1 14 19 8 5 15 13 12 16 18 7

38

2  Modeling and Optimization of Solar Air Collector Using GRA

0.75 0.70

Grey relational grade

0.65 0.60 0.55 0.50 0.45 0.40 0.35 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15 16 17 18 19 20

Trails Fig. 2.6  Grey relational grade flat plate solar air collector

The average was obtained by averaging sum of values of same grade for each parameter. This operation was repeated in the second and third grade for each parameter, which produces a response table for grey relational grades. When normalization was performed based on the “higher the better” approach, it provided an optimum array for maximum energy and exergy efficiencies of SAC.

2.4 Conclusion To maximize energy and exergy efficiency, GRA was used to find optimal values for SAC, mass flow rate, tilt angle, solar radiation, and inlet temperature. Following is a synopsis of the study’s findings and interpretations. The analysis revealed that the best input parameters for a SAC are a mass flow rate of 0.0156 kg/s, a tilt angle of 45°, solar radiation of 764.48 W/m2, an inlet temperature of 21.72 °C, corresponding output parameters of energy efficiency of 24.61%, exergy efficiency of 6.43%, a temperature rise of 22.1 °C, and a pressure drop of 94.1 Pa. Experimental and predicted results have converged well within the ranges of applied parameters, as indicated by verification results. With these valuable findings, GRA can be successfully used to select SAC design parameters that maximize energy and exergy efficiency.

References

39

References 1. Bhagoria, J.  L., Saini, J.  S., & Solanki, S.  C. (2002). Heat transfer coefficient and friction factor correlations for rectangular solar air heater duct having transverse wedge shaped rib roughness on the absorber plate. Renewable Energy, 25(3), 341–369. 2. Nowzari, R., Mirzaei, N., & Aldabbagh, L. B. Y. (2015). Finding the best configuration for a solar air heater by design and analysis of experiment. Energy Conversion and Management, 100, 131–137. 3. Diao, Y., Kato, S., & Hiyama, K. (2011, December). Development of an optimal design aid system based on building information modeling. Building Simulation, 4(4), 315–320. 4. Fontanella, G., Basciotti, D., Dubisch, F., Judex, F., Preisler, A., Hettfleisch, C., Vukovic, V., & Selke, T. (2012, September). Calibration and validation of a solar thermal system model in Modelica. Building Simulation, 5(3), 293–300. 5. Jairaj, K. S., Singh, S. P., & Srikant, K. (2009). A review of solar dryers developed for grape drying. Solar Energy, 83(9), 1698–1712. 6. Chabane, F., Moummi, N., Benramache, S., Bensahal, D., Belahssen, O., & Lemmadi, Z. (2010). Thermal performance optimization of a flat plate solar air heater using genetic algorithm. Applied Energy, 87(5), 1793–1799. 7. Ho, C. D., Hsiao, C. F., Chang, H., Tien, Y. E., & Hong, Z. S. (2017). Efficiency of recycling double-pass V-corrugated solar air collectors. Energies, 10(7), 875. 8. Zheng, W., Zhang, H., You, S., & Fu, Y. (2017). Experimental investigation of the transpired solar air collectors and metal corrugated packing solar air collectors. Energies, 10(3), 302. 9. Yeh, H. M., & Ho, C. D. (2012). Collector efficiency in downward-type double-pass solar air heaters with attached fins and operated by external recycle. Energies, 5(8), 2692–2707. 10. Lin, W., Gao, W., & Liu, T. (2006). A parametric study on the thermal performance of cross-­ corrugated solar air collectors. Applied Thermal Engineering, 26(10), 1043–1053. 11. Yang, M., Yang, X., Li, X., Wang, Z., & Wang, P. (2014). Design and optimization of a solar air heater with offset strip fin absorber plate. Applied Energy, 113, 1349–1362. 12. El-Khawajah, M. F., Aldabbagh, L. B. Y., & Egelioglu, F. (2011). The effect of using transverse fins on a double pass flow solar air heater using wire mesh as an absorber. Solar Energy, 85(7), 1479–1487. 13. Gholap, A. K., & Khan, J. A. (2007). Design and multi-objective optimization of heat exchangers for refrigerators. Applied Energy, 84(12), 1226–1239. 14. Hedayatizadeh, M., Sarhaddi, F., Safavinejad, A., Ranjbar, F., & Chaji, H. (2016). Exergy loss-based efficiency optimization of a double-pass/glazed v-corrugated plate solar air heater. Energy, 94, 799–810. 15. Wang, J.  J., Jing, Y.  Y., Zhang, C.  F., & Zhao, J.  H. (2009). Review on multi-criteria decision analysis aid in sustainable energy decision-making. Renewable and Sustainable Energy Reviews, 13(9), 2263–2278. 16. Stein, E. W. (2013). A comprehensive multi-criteria model to rank electric energy production technologies. Renewable and Sustainable Energy Reviews, 22, 640–654. 17. Mulliner, E., Malys, N., & Maliene, V. (2016). Comparative analysis of MCDM methods for the assessment of sustainable housing affordability. Omega, 59, 146–156. 18. Acır, A., Canlı, M.  E., Ata, İ., & Çakıroğlu, R. (2017). Parametric optimization of energy and exergy analyses of a novel solar air heater with grey relational analysis. Applied Thermal Engineering, 122, 330–338. 19. Aghaie, A.  Z., Rahimi, A.  B., & Akbarzadeh, A. (2015). A general optimized geometry of angled ribs for enhancing the thermo-hydraulic behavior of a solar air heater channel–A Taguchi approach. Renewable Energy, 83, 47–54. 20. Gunes, S., Senyigit, E., Karakaya, E., & Ozceyhan, V. (2019). Optimization of heat transfer and pressure drop in a tube with loose-fit perforated twisted tapes by Taguchi method and grey relational analysis. Journal of Thermal Analysis and Calorimetry, 136(4), 1795–1806.

40

2  Modeling and Optimization of Solar Air Collector Using GRA

21. Chauhan, R., Singh, T., Thakur, N. S., & Patnaik, A. (2016). Optimization of parameters in solar thermal collector provided with impinging air jets based upon preference selection index method. Renewable Energy, 99, 118–126. 22. Mishra, P. K., Nadda, R., Kumar, R., Rana, A., Sethi, M., & Ekileski, A. (2018). Optimization of multiple arcs protrusion obstacle parameters using AHP-TOPSIS approach in an impingement jet solar air passage. Heat and Mass Transfer, 54(12), 3797–3808. 23. Sharma, A., Chauhan, R., Singh, T., Kumar, A., Kumar, R., & Sethi, M. (2017). Optimizing discrete V obstacle parameters using a novel entropy-VIKOR approach in a solar air flow channel. Renewable Energy, 106, 310–320.

Chapter 3

ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

3.1 Introduction Energy is considered as a vital factor in economic development. Its usage has become a critical concern in the last decades because of a rapid increase in energy demand. Further, environmental issues of conventional energy resources such as climate change and global warming are continuously imposing us for alternative sources of energy. Among renewable energy systems, solar thermal energy has received considerable attention in recent decades as an alternative energy resource for hot water, space heating, and cooling applications. Solar thermal is considered as the most economical alternative. Solar water and space heating represent the majority of solar thermal applications in domestic, commercial, and industrial sectors. They are considered as the most cost-effective alternatives among all the solar thermal technologies currently available [1, 2]. Modeling the performance characteristics of solar thermal systems has been a research interest for many decades. With increasing emphasis on reducing energy consumption, extensive research has been carried out to model these systems. When a solar system is designed, the engineers seek a solution that gives maximum efficiency with minimum cost and solution time. Thermal performance analyses of solar thermal energy systems (STES) are too complex; analytical computer codes usually require a large amount of computer power and require considerable time to give accurate predictions. It is therefore very important for designers and engineers to be able to select the optimum system quickly and accurately [3–5]. Artificial neural networks (ANNs) have been used in many engineering applications. This method can be used in the modeling of complex physical phenomena, such as in thermal engineering. The use of ANN in heating, ventilating, and air conditioning systems, solar thermal energy systems, solar radiation, modeling and controls, power generation systems, and load forecasting is becoming increasingly popular in the last two decades. The ANN approach, apart from reducing the overall © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4_3

41

42

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

time required, is that it is possible to find solutions that make solar energy applications more viable and thus more attractive to potential users. ANNs are able to learn the key information patterns within the multi-dimensional information domain. The neural network method falls under the computational intelligence generic non-linear analogue techniques. Reviews of applications of ANNs in thermal engineering, particularly on renewable energy systems, are presented in [4–7]. In the last decade, extensive works using ANNs in energy systems have been published [8–31]. Some examples are as follows: In the work of Kalogirou et al. [21], the objective was to train an ANN to predict the useful energy extracted from solar domestic hot water systems and the temperature rise of the stored water with minimum of input data. Physical characteristics of the system, such as collector area, storage type, capacity, mean storage tank heat loss coefficient, weather conditions, mean ambient air temperature, and mean cold water temperature, were used as input data. Farkas and Géczy-Víg [22] developed ANN models for three different types of solar thermal collectors to predict the outlet temperature of the solar collectors based on the inlet temperature, the ambient air temperature, and the global solar radiation. Lecoeuche and Lalot [23] presented an application of ANNs to predict the in situ everyday performance of solar air collectors. The output of the ANN is the outlet temperature of the collector, and inputs to the network are the solar radiation and the thermal heat loss coefficients. In the study of Kalogirou [24], different ANNs were used to predict the collector parameters describing the instantaneous efficiency, the incidence angle modifier coefficients at longitudinal and transverse directions, the collector time constant, the collector stagnation temperature, and the collector heat capacity. This method is proposed as a useful tool for engineers to obtain the performance parameters of new collector designs without the need to perform tests. In the work of Sözen et al. [25], the ANN method was applied to determine the efficiency of flat plate solar thermal collectors. As input data, the collector temperature, date, time, solar radiation, declination angle, azimuth angle, and tilt angle were used. Kurt et al. [26] used ANNs for predicting thermal performance parameters of a solar cooker. A feed-forward neural network based on back propagation algorithm was developed to predict the thermal performance of a solar cooker with and without a reflector. The thermal performance parameters were the absorber plate, enclosure air, and pot water temperatures. The experimental data set consisted of 126 values. Souliotis et al. [27] combined an ANN method and TRNSYS to predict the performance of an integrated collector storage prototype. The input data for the ANN model were the month, the ambient air temperature, total radiation, wind speed, and incidence. The output data was the mean storage tank temperature. In the study of Géczy-Víg and Farkas [28], an ANN model was introduced for modeling the layer temperatures in a storage tank of a solar thermal system. The model was based on the measured data of a domestic hot water system. The input data were the temperature distribution in the storage tank, the ambient air temperature, mass flow rate of collector loop, load, and the temperature of the layers in previous time steps. The introduced ANN model consisted of two parts describing the load periods and the periods between the loads. Fischer et al. [29] showed that the ANN approach could be an appropriate alternative to the

3.2  Modeling of Thermal Energy

43

state-of-the-art modeling of solar collectors as described in the European Standard EN 12975-2. To compare the different approaches of modeling investigations for a conventional flat plate collector and an evacuated “Sydney” tubular collector, they carried out testing based on performance measurements according to the Standard EN 12975-2. The obtained results showed better agreement between measured and calculated collector output for the ANN approach compared with the state-of-the-art modeling. The investigations also showed that for the ANN approach, special test sequences have to be designed. The determination of the ANN that fits the thermal performance of the collector in the best way depends significantly on the expertise of the user. In the study of Benli [30], two different surface-shaped solar air collectors were constructed and examined experimentally: corrugated and trapeze-shaped. The experiments were carried out in October under the weather conditions of Elazığ, Turkey. A feed-forward Levenberg-Marquardt (LM) neural network based on back propagation algorithm was developed to predict thermal performances of the solar air collectors. In the work of Kalogirou et al. [31], ANNs were used for the performance prediction of large solar systems. The ANN method is used to predict the expected daily energy output for typical operating conditions, as well as the temperature level the storage tank can reach by the end of the daily operation cycle. Experimental measurements from 226 days have been used to investigate the ability of ANN to predict the energy behavior of a typical large solar system. Since the performance of a solar thermal energy system depends on various factors, there still remain a number of challenging efforts in the performance predictive methodology to be addressed. Despite diverse research efforts made so far, the comprehensive integrated energy system performance considering the effects of seasons, weather, operating, and design parameters on the performance of thermal storage systems has been undertaken only partially. For this reason, the study was focused on the applicability of ANN method for an integrated solar thermal energy system. This paper describes the applicability of ANNs to predict the performance of a solar thermal energy system for residential, domestic hot water (DHW), and space heating (SH) applications. For this objective, then, using some of the experimental data for training, an ANN model for the system based on the back propagation algorithm was developed. This investigation demonstrates that the ANN method can alternatively and reliably be applied to predict the performance of a solar air collector.

3.2 Modeling of Thermal Energy 3.2.1 Thermal Analysis The instantaneous efficiency of solar air collectors is defined as the ratio of heat gain by the working fluid to total incoming solar energy affecting the collector at any given moment. The beneficial heat gain induced by the working fluid may be calculated using the equation below.

44

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

Qg  m a c p  T2  T1 



(3.1)



where Qg is the working fluid’s useful heat gain, Cp is the specific heat of air, m a is the mass flow rate of air, and T1 and T2 are the working fluid’s temperatures at the inlet and exit, respectively.



Qg Qab

(3.2)

where Qab = Ac (ατ)I is the energy incident on the collector surface, absorber plate absorptivity (α) is 0.875, and the glass’ transmittance (τ) is 0.96, where I and Ac are the solar intensity and the collector area, respectively. The thermohydraulic efficiency, often known as the effective thermal efficiency, is calculated as follows:

eff

 Pfan Qu    cn  f  Qab

  

(3.3)

where cnf is the conversion factor for converting one type of energy to another, such as thermal to mechanical energy, and the value of that factor is 0.2. Pfan is the fan power. At an average temperature, the physical characteristics of a fluid (air) are studied. Tavg   T2  T1  / 2



(3.4)



3.2.2 Exergy Analysis The efficiency of the second law may be represented as [11]:

 II  1 

 xdest  xin

(3.5)

where ηII is exergy efficiency and εxdest and εxin are exergy destruction and exergy input, respectively. The rate of change of overall exergy destructed can be expressed as: exdest



 1  T 4 4  T      1   am    am   Qab  ma .c p .  T2  T1   3  Tab  3  Tab     T P  ma .c p .Tam ln 2  ma . R.Tam . ln 2 T1 P1

(3.6)

3.2  Modeling of Thermal Energy

45

where Tam and Tab are the ambient and absorber temperatures, R is the gas constant, T2 is outlet temperature of the collector, T1 is inlet temperature of the collector, and P1 and P2 are pressure at entry and exit of collector. The efficiency of the second law may be expressed as follows:

 II 

 xp  xin

 1

 xdest  xin

(3.7)

where εxp is the real exergy, taking collector pressure drop into account, and is calculated as follows:

 x p   xout   xwork



Te Pfan Tin



m  P   f  fan

 xwork 



(3.8) (3.9)



.

Pfan

(3.10)

where ηfan is the efficiency of the fan (blower) and is set to 0.9.

3.2.3 Proposed ANN Model The proposed research work used MLPNN model and is a feed forward-backward propagation ANN to predict the energy, exergy, temperature difference, and pressure drop by considering four input parameters such as mass flow rate, inlet temperature, solar radiation, and tilt angle. The structure of the model is developed in three different layers such as the input layer, hidden layer, and output layer. The model is developed based on the multilayer perceptron neural network model with 10 neuron giving an optimal value for all the combinations considered. During the training and testing process, the input parameters enter the feed-forward neural networks which are shown in Fig. 3.1. Each product of input parameters (Mi) and a weight function (Wij) are summed into the junction and summed with bias (bj) of the neurons, as mentioned in Eq. 3.19. In the present investigation, the input parameters such as mass flow rate, inlet temperature, solar radiation, and tilt angle are considered. Similarly, the output parameters energy, exergy, temperature difference, and pressure drop are considered. Finally, performance prediction models were developed for all three output parameters considered (Eqs. 3.20, 3.21, and 3.22). Based on the trial-and-error method, all the combinations considered VAF and RMSE. The proposed research work used an MLPNN model, a feed forwardbackward propagation ANN, to predict the energy, exergy, temperature difference, and pressure drop by considering four input parameters: time, solar radiation, ambient temperature, and top and rare temperature. The structure of the model is

46

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

Fig. 3.1  Graphical representation of the MLPANN model [32]

developed in three different layers such as the input layer, hidden layer, and output layer. The development is based on the multilayer perceptron neural network model with six neurons giving an optimal value for all the combinations considered. The optimal setting parameters of SAC are mass flow rate 0.0118 kg/s, tilt angle 45°, solar radiation 621 W/m2, and inlet temperature 33.8 °C, and corresponding output values are temperature rise 28.99 °C, energy efficiency 13.45%, exergy efficiency 1.022%, and pressure drop 73.75 Pa.



 i 1  X     Wij M i    b j n   VAF  1 







var  y 

 100

(3.20)

1 i 1 2   y  y N N

(3.21)

1 i 1 Ai  Pi   100 N N Ai

(3.22)

RMSE  MAPE 

var  y  y 

(3.19)

3.2  Modeling of Thermal Energy

47

3.2.4 Experimental Setup and Procedure In the thermal energy experiments, a solar air collector was used for a single pass, and the experiments were performed in the summer season using the corrugated SAC in Silchar, Northeastern India. A wooden collector box is used with a dimension of 1.52 × 0.52 m and depth of 0.055 m. A circular hole on the rear side of the collector with a dimension of 0.02 m diameter is the airflow entrance, and the same dimension of the circular hole at the front side is used as the airflow exit. An aluminum plate has been used as the absorber plate with a dimension of 1.5 m × 0.5 m × 0.001 m. The whole surface of the absorber plate is painted with black paint to absorb more radiation energy and transfer a sufficient amount of heat to the flowing fluid. A blower of 0.56 HP capacity has been installed for pressuring air through the collector channel. The schematic diagram of the experimental setup is shown in Fig. 3.2. The experiments have been performed at three different mass flow rates, and data are stored through a data logger UT35A in constant intervals throughout the day times. The temperature sensors are used to measure the temperature at different points of the collector and the working fluid. PT100-type thermocouple sensors [accuracy ±0.1 °C] are placed at the constant interval at three points on the absorber plate along the axial length of the absorber (L1  =  0.375  m, L2 = 0.75 m, L3 = 1.125 m). Further, sensors are placed on the absorber at the same axial locations to measure the working fluid temperature and inlet and outlet temperature. In these experiments, pyranometer DWR 8101, Sr. No. 147007, range 0–4000 W/m2 has been used to measure the incoming total solar radiation on the solar air collector surface. The anemometer of model number 131121 measures air velocity. Pressure drop has been evaluated using the U-tube manometer of 50-0-50 MM WC, which is located at the inlet and outlet of the collector. Table 3.1 shows the sample experimental data of SAC.

SUN

n

tio

dia

ra lar

So

Glazing Corrugated absorber plate Air outlet

Air inlet Thermal insulation

Fig. 3.2  Schematic diagram of experimental setup of SAC

48

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

Table 3.1  Sample experimental results of corrugated SAC Mass flow rate 0.0078 0.0078 0.0078 0.0118 0.0118 0.0058 0.0039 0.0039 0.0094 0.0039 0.0094 0.0078 0.0118 0.0094 0.0039 0.0118 0.0078 0.0039 0.0118 0.0058 0.0118

Tilt angle 60 30 45 60 30 30 45 60 45 30 30 60 45 60 60 30 45 45 45 45 60

Solar radiation 763 750 450 652 681 410 846 437 730 781 464 271 993 319 842 691 289 499 621 1086 390

Temperature inlet 31.2 32.5 29.5 31.2 33.1 30 32.9 29.7 33.7 31.5 32.3 24.1 32 31.4 32.7 28 30.1 32.9 33.8 27.6 27.1

Temperature difference 25.065 23.013 21.418 30.520 26.581 14.068 20.586 17.916 33.094 15.871 20.399 18.890 34.008 23.058 16.898 21.016 33.367 15.060 28.991 27.506 16.411

Exergy efficiency 6.322 7.608 2.533 4.358 5.069 1.337 11.835 4.961 9.746 10.259 1.165 2.325 8.193 0.986 9.008 0.870 11.949 2.439 1.022 12.63 1.64

Energy efficiency 22.793 20 13 18.259 17 10.630 32.888 14.9 31.869 20.298 10.6 10.291 22.1 8.6 26.310 7.9 29.101 20.8 13.459 30.398 9.088

Pressure drop 44.145 24.525 34.335 78.48 63.765 14.715 9.81 19.62 53.955 4.905 39.24 44.145 73.575 58.86 19.62 63.765 34.335 9.81 73.575 24.525 78.48

3.3 Parametric Analysis 3.3.1 Energy Efficiency The variation in energy efficiency with time is shown in Fig. 3.3a–c. In general, the magnitude of efficiency attains a peak at noon and then decreases during the afternoon. The trend is like the trend of solar radiation, which is the main driving factor of efficiency. However, at a similar range of solar radiation in the morning and afternoon, magnitudes of efficiency are different; this indicates the higher amount of thermal losses in the morning due to lower ambient temperature. The experimental trials have been carried out with different mass flow rates of air (0.0039–0.0118 kg/s) at varying tilt angles (30°, 45°, and 60°). Results indicate that energy efficiency rises with the increase in air mass flow rate. This may be due to better extraction of heat by the traveling air. Further, an increase in inclination angle from 30° to 45° increases efficiency by up to 44.8%. This is due to the better chimney effect that enhances heat transfer. The maximum energy efficiency found at a tilt angle of 45° for a mass flow rate of 0.0118 kg/s is 27.02% in corrugated SAC.

3.3  Parametric Analysis

49

35

Tilt angle 30° 30

Energy efficiency (%)

25

20

15 0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

10

5

0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

14:30

15:30

16:30

Time (hours)

(a) 40

Tilt angle 45° 35

Energy eficiency (%)

30 25 20 0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

15 10 5 0 8:30

9:30

10:30

11:30

12:30

13:30

Time (hours)

(b) Fig. 3.3  Variation of energy efficiency: (a) 30°, (b) 45°, (c) 60°

50

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector 40 35

Tilt angle 60°

Energy efficiency (%)

30 25 20 15

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

10 5 0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(c) Fig. 3.3 (continued)

3.3.2 Exergy Efficiency The variation in the exergy efficiency of the solar air collector is shown in Fig. 3.4a–c. It is seen that the magnitude of exergy keeps on increasing with the rise in daytime till noon; thereafter, it starts decreasing during the afternoon. An initial exponential increase in the value of exergy efficiency is linked with the quantitative increase in the rate of heat transfers from the absorber plate. Further, an increase in the working fluid’s average temperature also helps enhance the heat transfer quality. During the second half of the day, the heat transfer rate is decreased both quantity wise and quality wise, resulting in lower exergy efficiency. The maximum exergy efficiency reaches up to 11.8% at a 45° tilt angle for 0.0039 kg/s at noon in corrugated SAC.

3.3.3 Temperature Difference The variation of temperature rise (ΔT) with daytime is depicted in Fig. 3.5a–c at various inclination angles of 30°, 45°, and 60° for four different mass flow rates. It is acknowledged that if the variation in the air inlet and ambient temperature is

3.3  Parametric Analysis

51

12

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

Tilt angle 30°

Exergy eficiency (%)

10

8

6

4

2

0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(a) 14 12

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

Tilt angle 45°

Exergy eficiency (%)

10 8 6 4 2 0 8:30

9:30

10:30

11:30

12:30

13:30

Time (hours)

(b) Fig. 3.4  Variation of exergy efficiency: (a) 30°, (b) 45°, (c) 60°

14:30

15:30

16:30

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

52 12

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

Tilt angle 60°

Exergy eficiency (%)

10

8

6

4

2

0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(c) Fig. 3.4 (continued)

lower, air temperature rise generally varies almost linearly with solar radiation. The present experimental results revealed that temperature increases with daytime reaching its peak at noon and then decreases. It also reveals that increasing the tilt angle increases the temperature rise as the tilt angle of 45° has a higher value than the tilt angle of 30° and 45°. Moreover, results reveal that with the increase in air mass flow rate, the magnitude of ΔT decreases. This may be explained by the comparatively lower resident time of air with the hot surfaces, in case of a higher mass flow rate compared to that of the lower mass flow rate of air. But the quantitative effect of this reduction on the performance of the collector may not be proportional since output heat is a product of mass flow rate and ΔT. The maximum temperature observed for the considered corrugated SAC is 71.1 °C, which occurred during the daytime from 12.00 to 13.00 h for 0.0039 kg/s mass flow rate at a tilt angle of 45°.

3.3.4 Pressure Drop The variations of pressure drop for the present experimental investigation of corrugated SAC are shown in Fig.  3.6. The behavior of pressure drop increases with increasing mass flow rate, and it is noticed that with increasing tilt angle, the pressure drop also increases due to air needing to overcome the higher gravitational

3.3  Parametric Analysis

53

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

Tilt angle 30°

30

Temperature difference (°C)

25

20

15

10

5

0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(a) 45 40

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

Tilt angle 45°

Temperature difference (°C)

35 30 25 20 15 10 5 0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

Time (hours)

(b) Fig. 3.5  Variation of temperature differences: (a) 30°, (b) 45°, (c) 60°

15:30

16:30

54

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector 40

Tilt angle 60°

0.0039kg/s 0.0058kg/s 0.0078kg/s 0.0094kg/s 0.0118kg/s

35

Temperature difference (°C)

30 25 20 15 10 5 0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(c) Fig. 3.5 (continued)

80

30° 45° 60°

70

Pressure drop (Pa)

60 50 40 30 20 10 0 0.004

0.006

0.008

Mass flow rate (kg/s) Fig. 3.6  Variation of pressure drop with mass flow rate

0.010

0.012

3.3  Parametric Analysis

55

effect. The trends of the pressure drop in the different tilt angles are similar but vary in magnitude. The present study observed the maximum pressure drop occurred for tilt angle 30° to 60° is 4.96 Pa for 0.0039 kg/s and 78 Pa for 0.0118 kg/s, respectively.

3.3.5 ANN Modeling of Corrugated SAC The SAC system modeled by ANN has four inputs and four outputs. The input variables of SAH systems are mass flow rate, solar radiation, tilt angle, and inlet temperature entering the collector unit, whereas temperature difference, second law efficiencies, and pressure drop constitute the model’s output variables. All network calculations were performed using MATLAB standard software. The data set for the system’s efficiency included 21 data patterns for each. From these, 15 data patterns were used for training the ANN. The remaining six patterns were used as the test data set. The architecture and training parameters for ANN are shown in Fig. 3.7. The input parameters, such as solar radiation, inlet temperature, mass flow rate, and tilt angle, were considered in the present investigation. Similarly, the output is energy, exergy, temperature rise, and pressure drop considered. Finally, performance prediction models were developed for all four output parameters considered (Eqs.  3.20, 3.21, and 3.22), based on the trial-and-error method. The mean square error (MSE) shows the best validation performance, as shown in Fig.  3.8. Regression analysis also carried out in the study shows an R-value of 0.99 (Fig. 3.9, Table 3.2). Table 3.3 shows the weights and bias of the optimum model’s (4-10-4) four outputs (energy, exergy, temperature rise, and pressure drop). Based on the above observations, the predicted and experimental values

Hidden layer Input layer

Output layer

Energy efficiency Mass flow rate T difference Solar radiation Exergy efficiency Tilt angle Pressure drop Inlet temperature

Fig. 3.7  Architecture of ANN model for corrugated SAC

Fig. 3.8  Best validation performance using MSE

Fig. 3.9  Regression analysis

3.4 Conclusion

57

Table 3.2  Weights and bias of the optimum model’s (4-10-4) four outputs (energy, exergy, temperature rise, and pressure drop) Weights between the input and hidden layer (W10*4) 4.77 2.047 −6.686 2.257 7.060 −4.494 −0.425 −0.796 1.222 2.956 −2.953 1.488 −10.244 −10.611 8.766 −1.170 5.549 2.336 −2.982 2.325 9.863 5.965 −3.571 0.054 3.544 0.912 1.082 −2.832 2.497 1.792 −6.202 0.060 −3.939 1.341 −2.614 3.420 2.0417 1.109 −2.688 0.022 Bias in the hidden layer (B4*10) [−3.171, −2.673, −0.214, 0.216, 0.731, 5.131, −8.785, 0.7493, −5.864, −1.297] [3.845, −1.356, −0.558, −0.203, 2.359, 2.191, 3.926, −7.849, −2.672, −3.408] [−0.439, −2.099, 3.596, −0.285, −3.203, 2.720, −5.906, −0.810, −4.470, 0.374] [0.166, 9.789, −8.491, −6.432, 7.153, −0.218, 4.821, 3.021, 6.819, −0.308] Weights to the output layer (W1*10) [5.946, −2.238, 3.122, 0.956, 4.874, −3.667, 0.218, −0.541,-0.835, 2.562] Bias in the output layer (B4*1) [2.358, −3.666, −1.023, −1.058]

are plotted and are shown in Figs. 3.10, 3.11, 3.12, and 3.13, respectively. Finally, Table 3.3 shows predicted data and experimental data comparison for error analysis for all the combinations considering for four inputs with one hidden layer for ten neurons. The optimal setting parameters of SAC are mass flow rate 0.0118 kg/s, tilt angle 45°, solar radiation 621 W/m2, and inlet temperature 33.8 °C, and corresponding output values are temperature rise 28.99 °C, energy efficiency 13.45%, exergy efficiency 1.022%, and pressure drop 73.75 Pa.

3.4 Conclusion This chapter aims to use neural networks to calculate the performance of corrugated SAC. An ANN method was intended to adopt a system for efficient modeling, which did not require a pre-knowledge about the system. The proposed methodology’s performance was evaluated using several statistical validation parameters. Four output parameters were used in the model. System design parameters, working conditions, different temperatures, etc. significantly affect the efficiency of corrugated SAC. The optimal setting parameters of SAC are mass flow rate 0.0118 kg/s, tilt angle 45°, solar radiation 621  W/m2, and inlet temperature 33.8  °C, and

Temperature rise Experimental Predicted 25.065 25.149 23.013 23.366 21.518 22.055 30.520 30.547 26.581 26.851 14.068 14.264 20.586 20.742 17.516 16.972 33.094 33.140 15.871 14.989 20.399 20.485 18.890 18.820 34.008 33.901 23.058 22.165 16.898 16.964 21.016 20.811 33.361 33.320 15.060 15.218 28.990 29.208 27.506 27.799 16.411 16.455

Error 0.083 0.353 0.537 0.027 0.269 0.196 0.156 −0.543 0.045 −0.881 0.0856 −0.070 −0.107 −0.892 0.065 −0.205 −0.041 0.158 0.217 0.293 0.044

Exergy efficiency Experimental Predicted 6.322 6.366 7.608 7.616 10.853 11.281 4.358 4.311 5.069 4.958 1.337 1.400 11.835 11.864 7.961 8.179 9.746 9.733 10.259 9.876 1.165 1.195 2.325 2.325 8.193 8.055 1.986 1.630 9.008 9.150 7.987 8.507 11.949 11.897 2.439 2.540 1.522 2.001 12.633 12.550 1.648 1.668 Error 0.0439 0.007 0.427 −0.047 −0.110 0.062 0.029 0.217 −0.013 −0.383 0.029 −0.005 −0.138 −0.355 0.142 0.520 −0.051 0.100 0.479 −0.083 0.019

Pressure drop Experimental 44.145 24.525 34.335 78.481 63.765 14.715 9.813 19.622 53.955 4.905 39.241 44.145 73.575 58.864 19.625 63.765 34.335 9.816 73.575 24.525 78.487 Predicted 44.110 23.889 35.268 78.442 63.381 14.569 9.748 18.892 53.293 6.074 38.698 43.609 73.462 59.858 19.335 62.151 34.163 9.586 74.461 24.030 78.445

Error −0.034 −0.635 0.933 −0.037 −0.383 −0.145 −0.061 −0.727 −0.661 1.169 −0.541 −0.535 −0.112 0.998 −0.284 −1.613 −0.171 −0.223 0.886 −0.494 −0.034

Table 3.3  Predicted data for all the combinations considered for four inputs with one hidden layer for ten neurons Energy efficiency Experimental Predicted 22.793 22.879 20.356 19.837 13.253 14.261 18.259 18.269 17.342 16.900 10.630 10.653 32.888 32.675 14.902 15.004 31.869 31.806 20.298 21.576 10.601 10.483 10.291 10.253 22.100 22.518 8.603 9.302 26.310 26.106 7.923 8.393 29.101 28.993 20.812 20.403 13.459 14.206 30.398 30.321 9.088 9.074

Error 0.086 −0.162 1.261 0.009 −0.099 0.023 −0.212 0.104 −0.062 1.277 −0.116 −0.038 0.418 0.702 −0.204 0.493 −0.108 −0.396 0.746 −0.077 −0.013

58 3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

59

3.4 Conclusion

y=-0.2299+1.0095*x

Predicted temperature rise

35

R2=0.997

30

25

20

15 15

20

25

30

35

Experimental temperature rise Fig. 3.10  Temperature rise predicted and experimental values

14 y=0.0534+0.996*x R2 =0.996

Predicted exergy efficiency

12 10 8 6 4 2 0 0

2

4

6

8

10

Experimental exergy efficiency Fig. 3.11  Exergy efficiency predicted and experimental values

12

14

60

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

35 y=0.554+0.979*x R2 =0.996

Predicted energy efficiency

30

25

20

15

10

5 5

10

15

20

25

30

35

Experimental energy efficiency Fig. 3.12  Temperature rise predicted and experimental values

80

y=0.1017+0.999*x R2 =0.99

Predicted pressure drop

70 60 50 40 30 20 10 0 0

10

20

30

40

50

Experimental pressure drop Fig. 3.13  Temperature rise predicted and experimental values

60

70

80

References

61

corresponding output values are temperature rise 28.99  °C, energy efficiency 13.45%, exergy efficiency 1.022%, and pressure drop 73.75 Pa. Compared to classical methods, the advantages of the ANN are speed, simplicity, and the capacity to learn from examples. So, experimental studies can be reduced to a minimum at the place where the uses of ANNs are appropriate, and solar engineering efforts can be reduced in these areas. This study demonstrates that an ANN can be used efficiently instead of a simulation of mathematical models for calculating efficiency. Finally, this approach has clear advantages over the other existing methods and could easily be adopted in energy systems.

References 1. Kalogirou, S. A. (1999). Applications of artificial neural networks in energy systems. Energy Conversion and Management, 40(10), 1073–1087. 2. Mekhilef, S., Saidur, R., & Safari, A. (2011). A review on solar energy use in industries. Renewable and Sustainable Energy Reviews, 15(4), 1777–1790. 3. Kalogirou, S. A. (2000). Applications of artificial neural-networks for energy systems. Applied Energy, 67(1–2), 17–35. 4. Kalogirou, S. A. (2001). Artificial neural networks in renewable energy systems applications: A review. Renewable and Sustainable Energy Reviews, 5(4), 373–401. 5. Kalogirou, S. A. (2004). Optimization of solar systems using artificial neural-networks and genetic algorithms. Applied Energy, 77(4), 383–405. 6. Kalogirou, S., & Sencan, A. (2010). Artificial intelligence techniques in solar energy applications. In Solar collectors and panels, theory and applications (Vol. 15 , pp. 315–340). 7. Mohanraj, M., Jayaraj, S., & Muraleedharan, C. (2012). Applications of artificial neural networks for refrigeration, air-conditioning and heat pump systems – A review. Renewable and Sustainable Energy Reviews, 16(2), 1340–1358. 8. Kalogirou, S., Lalot, S., Florides, G., & Desmet, B. (2008). Development of a neural networkbased fault diagnostic system for solar thermal applications. Solar Energy, 82(2), 164–172. 9. Mohandes, M., Rehman, S., & Halawani, T. O. (1998). Estimation of global solar radiation using artificial neural networks. Renewable Energy, 14(1–4), 179–184. 10. Diaz, G., Sen, M., Yang, K. T., & McClain, R. L. (1999). Simulation of heat exchanger performance by artificial neural networks. Hvac&R Research, 5(3), 195–208. 11. Pacheco-Vega, A., Sen, M., Yang, K. T., & McClain, R. L. (2001). Neural network analysis of fin-tube refrigerating heat exchanger with limited experimental data. International Journal of Heat and Mass Transfer, 44(4), 763–770. 12. Chow, T.  T., Zhang, G.  Q., Lin, Z., & Song, C.  L. (2002). Global optimization of absorption chiller system by genetic algorithm and neural network. Energy and Buildings, 34(1), 103–109. 13. Sözen, A., Arcaklioǧlu, E., & Özalp, M. (2003). A new approach to thermodynamic analysis of ejector–absorption cycle: Artificial neural networks. Applied Thermal Engineering, 23(8), 937–952. 14. Sözen, A., & Akçayol, M. A. (2004). Modelling (using artificial neural-networks) the performance parameters of a solar-driven ejector-absorption cycle. Applied Energy, 79(3), 309–325. 15. Islamoglu, Y., & Kurt, A. (2004). Heat transfer analysis using ANNs with experimental data for air flowing in corrugated channels. International Journal of Heat and Mass Transfer, 47(6–7), 1361–1365.

62

3  ANN-Based Modeling and Optimization of Corrugated Solar Air Collector

16. Esen, H., Inalli, M., Sengur, A., & Esen, M. (2008). Performance prediction of a groundcoupled heat pump system using artificial neural networks. Expert Systems with Applications, 35(4), 1940–1948. 17. Akbari, S., Hemingson, H. B., Beriault, D., Simonson, C. J., & Besant, R. W. (2012). Application of neural networks to predict the steady state performance of a run-around membrane energy exchanger. International Journal of Heat and Mass Transfer, 55(5–6), 1628–1641. 18. Palau, A., Velo, E., & Puigjaner, L. (1999). Use of neural networks and expert systems to control a gas/solid sorption chilling machine: Utilisation des réseaux neuronaux et des systèmes experts pour réguler une machine frigorifique à sorption gaz/solide. International Journal of Refrigeration, 22(1), 59–66. 19. Sharma, R., Singhal, D., Ghosh, R., & Dwivedi, A. (1999). Potential applications of artificial neural networks to thermodynamics: Vapor–liquid equilibrium predictions. Computers & Chemical Engineering, 23(3), 385–390. 20. Bechtler, H., Browne, M. W., Bansal, P. K., & Kecman, V. (2001). New approach to dynamic modelling of vapour-compression liquid chillers: Artificial neural networks. Applied Thermal Engineering, 21(9), 941–953. 21. Kalogirou, S.  A., Panteliou, S., & Dentsoras, A. (1999). Modeling of solar domestic water heating systems using artificial neural networks. Solar Energy, 65(6), 335–342. 22. Farkas, I., & Geczy-Vıg, P. (2003). Neural network modelling of flat-plate solar collectors. Computers and Electronics in Agriculture, 40(1–3), 87–102. 23. Lecoeuche, S., & Lalot, S. (2005). Prediction of the daily performance of solar collectors. International Communications in Heat and Mass Transfer, 32(5), 603–611. 24. Kalogirou, S. A. (2006). Prediction of flat-plate collector performance parameters using artificial neural networks. Solar Energy, 80(3), 248–259. 25. Sözen, A., Menlik, T., & Ünvar, S. (2008). Determination of efficiency of flat-plate solar collectors using neural network approach. Expert Systems with Applications, 35(4), 1533–1539. 26. Kurt, H., Atik, K., Özkaymak, M., & Recebli, Z. (2008). Thermal performance parameters estimation of hot box type solar cooker by using artificial neural network. International Journal of Thermal Sciences, 47(2), 192–200. 27. Souliotis, M., Kalogirou, S., & Tripanagnostopoulos, Y. (2009). Modelling of an ICS solar water heater using artificial neural networks and TRNSYS. Renewable Energy, 34(5), 1333–1339. 28. Géczy-Víg, P., & Farkas, I. (2010). Neural network modelling of thermal stratification in a solar DHW storage. Solar Energy, 84(5), 801–806. 29. Fischer, S., Frey, P., & Drück, H. (2012). A comparison between state-of-the-art and neural network modelling of solar collectors. Sol. Energy, 86(11), 3268–3277. 30. Benli, H. (2013). Determination of thermal performance calculation of two different types solar air collectors with the use of artificial neural networks. International Journal of Heat and Mass Transfer, 60, 1–7. 31. Kalogirou, S. A., Mathioulakis, E., & Belessiotis, V. (2014). Artificial neural networks for the performance prediction of large solar systems. Renewable Energy, 63, 90–97. 32. Mazloom, M.  S., Rezaei, F., Hemmati-Sarapardeh, A., Husein, M.  M., Zendehboudi, S., & Bemani, A. (2020). Artificial intelligence based methods for asphaltenes adsorption by nanocomposites: Application of group method of data handling, least squares support vector machine, and artificial neural networks. Nanomaterials 6, 10(5), 890.

Chapter 4

Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy Logic-Based Expert System

4.1 Introduction Growth in the usage of solar thermal systems to gather solar energy has resulted from an increase in energy demand, the depletion of fossil fuels, and environmental concerns. Solar air collectors (SACs) are one type of solar thermal system that transfers heat through heat exchangers. SACs can be used for various purposes, including heating rooms and drying agricultural produce. SACs have several problems, including fluctuating solar radiation and decreased heat absorption capacity of air. As a result, ongoing efforts are directed to increase the pace at which heat is transferred to improve performance. Ozturk and Demirel [1] noted the SAC’s exergy analysis can be used to determine its dimensions and scope of development. As a result, every thermal energy system’s energy and exergy study will offer the necessary data. Numerous studies on SAC’s exergy and energy analysis have been conducted, including those by Gupta and Kaushik [2]. The heat transmission between the absorber plate and the working fluid has been studied experimentally by Esen [3] using various variants of SAC. Alta et al. [4] published a study on optimizing SAC design and parametric analysis. The results reveal that exergy efficiency varies with the mass flow rate in a leakage-proof system. Saidur et al. [5] have done a novel investigation into flat plate SAC. Temperature, time, mass flow rate, and other variables are studied from an exergy perspective. A theoretical prototypical based on SAC’s energetic and exergetic investigation has been suggested by Jafarkazemi and Ahmadifard [6]. Velmurugan and Kalaivanan [7] performed an energy and exergy analysis on the SAC based on the collector’s geometry. Suzuki [8] has created a mathematical model for the energy-exergy analysis of SAC. The absorption loss has been estimated at 60% compared to the others. Using experimental data from various climates, Sun et al. [9] have verified the numerical results of SAC. A particular mass flow rate of air is found to have a detrimental effect on the performance of © The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4_4

63

64

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

SAC. The heat transport characteristics of a vertical channel have been studied theoretically by Das and Giri [10]. The findings show that convective heat transport generates local entropy. A non-dimensional model developed by Baritto and Bracamonte [11] may be used to forecast the output temperature distribution in a flat plate SAC under non-isothermal circumstances. Output air temperature is correlated with the controlling parameters. Hegazy [12] presented the thermo-hydraulic study of a flat plate air collector with variable width. For the same amount of fan power, the researchers found that variable width collectors reduced the amount of usable heat and also reduced the rise in air temperature. The geometric parameter has been found to influence thermo-hydraulic performance. A theoretical and experimental evaluation of the thermal efficiency and exergy of solar air collectors was undertaken by Ferouali et  al. [13]. The thermal efficiency of a double-pass SAC may be up to 17% higher than that of a single-pass SAC. A solar simulator was used by Espinosa and Valladares [14] to assess and validate SAC’s performance. Additional reports claim that the simulator can all simulate varied geometries, working fluids, and circumstances. According to Debnath et  al. [15], the SAC’s configuration was tested by changing the mass flow rate. Many studies on SAC’s energy and exergy analysis have focused on a few key metrics for gauging the system’s efficiency. However, much hasn’t been focused on adjusting the SAC parameter to obtain the optimal parameters. For India’s northeastern area, the literature on energy and exergy studies of SACs is limited. The performance of any SAC, in addition, is highly dependent on the many features and operating variables that are present. The interaction of these attributes/ variables produces the best possible results, which can directly or indirectly impact SAC’s performance. As is customary in the industry, SAC qualities are chosen according to the specialist’s judgment or standard handbook. However, this technique of selection may not produce reliable results. Furthermore, SAC performance is thought to be complicated and non-linear, posing challenges in developing a solid empirical model to regulate SAC features, as previously indicated. Again, determining the most advantageous attributes/parameters for every solar system was laden with risk, imprecision, and vagueness information. As a result, the use of fuzzybased modeling to forecast and improve the SAC parameters is necessary. Several academics have previously focused on the modelling and optimization/ prediction of various solar systems using evolutionary algorithms [16–20]. Kalogirou [16] estimated collector coefficients, time constants, stagnation temperatures, and incidence angle modifier coefficients in their investigation. Esen et  al. [17] predicted output temperature and thermal efficiency, and they considered inlet air temperature, absorber plate temperature, and solar radiation intensity. Caner et al. [18] considered several variables, including absorber model type, outlet and inlet air temperatures, trial length, ambient temperature, absorber temperature, solar radiation input, and output (efficiency). Benli [19] took into account temperature, air entrance and exit temperatures, ambient temperature, mass flow rate, and solar radiation. Ghritlahre and Prasad [20] built an ANN model with input layers of mass flow rate, intake air and ambient air temperature, solar radiation, output layers of beneficial heat gain, air temperature difference, and thermal efficiency. Kamthania

4.2  Modeling and Methodology

65

and Tiwari [21] have presented the feedforward ANN algorithm for a PVT air collector in five cities in India. Researchers in [16–21] used the available experimental dataset to train their models and then tested them using the experimental dataset to check whether they were correct. Finally, a specific batch of data output parameters were estimated using trained models. Varun and Siddhartha [22] used a genetic algorithm (GA) to optimize the thermal performance of a flat plate SAC by considering air velocity, collector inclination angle, absorber plate emissivity, and the number of panes. According to the findings, GA supplies flat plate SAC with the optimal characteristics. Stochastic iterative perturbation (SIPT) was used in another study by Varun et al. [23] to predict the ideal settings for smooth flat plate solar air heaters. Different Reynolds numbers were used to study plate emissivity, temperature rise, etc. On the other hand, the suggested model was shown to give results comparable to those of the genetic algorithm and random search global (RSG) optimization strategies. In their investigation, Siddhartha et al. [24] used particle swarm optimization (PSO) to optimize the SAC. Furthermore, compared to experimental data, PSO accurately estimates SAC parameters like flexibility, speed, and global convergence. Vafaei and Sah [25] used a Mamdani fuzzy inference method to forecast the SAC’s efficiency. According to this study, Mamdani-based fuzzy inference systems produce the best outcomes for a SAC. To do an energy-­economic analysis of solar water heaters, Mohanty et al. [26] used the ANFIS model using input parameters such as water temperature, time spent in direct sunlight, and humidity levels. Compared to MLP and radial-based functions, the ANFIS model delivers comparable and adequate results (RBF). Erenturk and Erenturk [27] employed three techniques to predict the output temperature of a UTC air heating system: the grey modeling (GM) methodology, an artificial neural network (ANN), and an adaptive neuro-­fuzzy inference system (ANFIS). The ANFIS algorithm produces better and similar results for UTC air heating systems than the GM and ANN algorithms. According to a study of previous works, several evolutionary algorithms [16–27] have been employed for modelling and optimization/prediction of different solar systems. On the other hand, the suggested methods were complicated and needed complete knowledge of the solar system. The algorithms were chosen using a hitand-miss strategy based on a mathematical assumption about input and output properties. Because of this, it takes a lot of time and a lot of trials to develop an accurate model as the number of process factors increases. Solar system modelers have also used ANN, GA, and PSO sparingly. However, to obtain reliable predictions, these models necessitate excessive data from the outset [20–22]. SAC is a more complex problem to model and optimize using existing approaches because of the imprecise, unclear, and uncertain information and data that go along with the non-linearity and interconnectedness of SAC. When trying to estimate such data, a fuzzy theory or approach is essential. A fuzzy logic model for optimizing thermal systems has been developed by numerous works using Mamdani. However, this model was time-consuming owing to defuzzification; complicated computation techniques, difficult IF-THEN rule formulation, and less flexibility. An integrated model based on the Takagi-Kang model

66

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

and the subtractive clustering approach was developed to address these concerns [28, 29]. In the suggested paradigm, one of the most critical phases is to choose the correct IF-THEN statements. Researchers have used the Mamdani approach to look at these issues in the past. However, the Mamdani technique indeed uses an expert’s judgment or some standard handbook to determine the IF-THEN rules, which does not yield better outcomes [30]. The fuzzy system, therefore, necessitates the identification of the most optimal IF-THEN rules, which can be accomplished using the subtractive clustering technique [31]. The SC-TSK-FL method was used to address the inadequacies of the aforementioned model in solar system modeling and optimization/prediction. . This method combines the SC clustering method used. The TSK-FL method is used to optimize/ predict FPSAC parameters, while the SC technique is utilized to determine the IF-THEN rules.

4.2 Modeling and Methodology 4.2.1 Thermal Modeling A thermal system’s basic design and performance can be determined by doing an energy analysis. The first law of thermodynamics is castoff to calculate energy efficiency. The usable thermal gain of the solar air collector can be calculated [15]:

Qg  mc p  T2  T1 



(4.1)

Using Eq. (4.2), we can determine how much solar radiation is incident on the collector plane.

Qi = I s Ac

(4.2)

As a result, a solar thermal system’s energy efficiency is defined as a ratio of the usable thermal gain over the collector surface to the total incident solar radiation. Equation (4.3) can be used to evaluate energy efficiency [15].

ee 

Qg Qi

(4.3)

where ηee is for energy efficiency, Qg stands for heat transferred to the air, Qi stands for solar radiation occurrence on the absorber area, m stands for the mass flow rate of air, and cp stands for specific heat capacity. The outflow temperature is T2, the inlet temperature is T1, solar radiation is Is, and the collector area is Ac.

4.2  Modeling and Methodology

67

4.2.2 Fuzzy Logic-Based Expert System In this section, the fuzzy logic-based expert system (FLES), as shown in Fig. 4.2, is used for modeling and performance analysis of solar air collectors (SAC). The FLES consists of the subtractive clustering (SC) method coupled with TagakiSugeno-Knag Fuzzy Logic (TSK-FL) model. First, the database development is generated via experimentation in SAC under different climatic conditions in northeastern India. Second, the normalization of data is done. Third, fuzzification of the data is carried out using a membership function (MF) using normalized relative grade (Zi) values for each of the performance variables of the SAC during optimization, while the system or input parameters and their corresponding levels of the SAC for prediction models. The strategy of the proposed method is illustrated in Fig.  4.1. The fuzzification process defines the degree of membership for each of the performance variables of SAC in a fuzzy set between 0 and 1. The present work uses the Gaussian membership function to map fuzzy sets.

Fig. 4.1  Proposed method of SC-TSK-FL approach

68

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

Then, the TSK-based fuzzy interference engine will perform the interference engine to generate TSK-­based fuzzy rules based on the data obtained from the SC technique [26]. Mainly SC method determines both cluster numbers and their corresponding cluster center using the following expressions: K



Ci  e

2      Xi  X j  /  pa / 2     

j 1

2

(4.4)

where pa is a positive constant that defines the cluster radius and values in the range of [0, 1] and Ci denotes the cluster center for each system parameter sequence [26]. After determining optimum cluster numbers (N) and their corresponding cluster center (C) for each of the output/input parameters, the construction of TSK-FL model is done in that best fits the data using minimum rules. The generalized Type-I order TSK-FL model (Takagi and Sugeno [29], Sugeno and Kang [28]) for multiinput and single output (with multiple output variables and unknown coefficients) for the kth rule can be expressed using Eq. (4.5). Rulei : IFY1 isBi1 ANDIFY2 isBi 2 ANDIFY3 isBi 3 AND.. ANDIF Xn is Sin THENE mi   i1 Z1   i 2 Z 2   i 3 Z 3   in Z n  i



(4.5)

where Y1, Y2, Y3,.............Yn denotes the fuzzy variables; Bi1, Bi2.............Bin represents the fuzzy cluster sets defined in the antecedent space; αi1, αi2, αi3, .........αin and βi are unknown coefficients for the ith rule; Z1, Z2, Z3,.........Zn is fuzzy output values; and Emi values are the weighted output fuzzy values for the ith rule [34].

4.2.3 Experimental Procedure Sand-coated SAC precise dimensions have been studied and built. The collector dimensions (SAC) were 2.04 m long, 1.04 m wide, and 0.20 m tall. The absorber plate (2 m × 1 m) was painted black to maximize solar radiation absorption. Glass wool thermal insulation of 0.025 m thick was used to insulate the collector box’s sides and bottom to reduce heat loss. To enable solar rays into the collector, 0.004-m-thick double-glazing transparent panes were utilized. As a result of using double glazing, collector performance has been improved. Sand coated with 0.150 mm grain size, experimental tests are conducted in open atmospheric conditions. The input parameters are changing mass flow rate, fixed collector tilt angle (30°), and varying solar radiation along with the ambient temperature. The present study considered three input parameters (mass flow rates, solar radiation, inlet temperature, and fixed tilt angle) and three output parameters (temperature rise, energy efficiency, and pressure drop) (Fig. 4.2).

4.3  Results and Discussion

69

d r ra

la So

SUN

ion

iat

et

tl Ou

ing

le ub

Do

z Gla

t Fla

ir

so

ab

l ma

er

Th

300

A et Inl

r rbe

Air

te

pla

n

tio

ula ins

Collector box

Metal frame

Fig. 4.2  Schematic diagram of SCSAC

4.3 Results and Discussion 4.3.1 SCSAC Parameter Optimization Using the Planned Approach The SCSAC process parameters are optimized in this section to show that the perfect procedure is achievable. Three independent (input) variables (mass flow rate, solar radiation, and intake temperature) with a fixed tilt angle and three dependent output parameters (energy efficiency, temperature increase, and pressure drop) are investigated in this paper. In the southern part of India, 36 trial runs were conducted under varied climatic conditions, and the appropriate output parameters for SCSAC were calculated based on these settings. Figure 4.3a–c shows how data points (input parameters) are fuzzified first using the appropriate membership function. For simplicity, only Gaussian membership functions are considered in this study. Equation 4.4 is used to determine the input and output parameter clustering. The results can be obtained in Table 4.1 by searching for the optimum number of cluster centers and their associated membership values. The first column indicates that there are 16 cluster centers, while the second column shows how many data points in the cluster reflect the membership values of each parameter [32]. The stronger the link between the parameter and the cluster center, the higher the membership value. Using Eq. (4.4), rules based on SC clustering are then established for each cluster center, and a total of 12 rules were created based on the data in Table 4.1. This is followed by the process of defuzzing the data points and extracting crisp values for the cluster centers [33].

70

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

Fig. 4.3  Membership function plots: (a) mass flow rate, (b) solar radiation, (c) temperature inlet Table 4.1  Subtractive clustering means clustering centers Cluster center 1 2 3 4 5

Mass flow rate 0.020 0.025 0.015 0.020 0.010

Solar radiation 801 686 880 589 920

Temperature inlet 34.90 34.90 34.95 31.91 37.00

Temperature rise 32.90 22.87 46.15 19.36 53.92

Energy efficiency 41.27 39.72 37.15 29.34 31.31

Pressure drop 34.84 54.96 21.56 34.84 4.95

6 7 8 9 10 11 12 S

0.015 0.025 0.025 0.010 0.015 0.010 0.010 0.0034

488 502 921 686 490 371 478 139.46

35.83 30.82 36.87 31.14 28.81 32.83 27.00 2.33

19.90 10.73 33.34 28.00 16.73 13.21 18.55 12.49

29.41 26.74 44.42 20.55 22.34 18.52 16.89 6.36

21.56 54.96 54.96 4.95 21.56 4.95 4.95 11.49

SCSAC output parameters were also predicted using the research’s prediction models. Section 2.3 describes the procedure to be followed for prediction. FPSAC performance parameters are simulated using the MATLAB toolbox software for a wide range of system inputs. An optimal setting was determined using a simulation, with the values of mass flow rate (0.0175  kg/s), tilt angle (30°), solar radiation (674  W/m2), and temperature inlet (31.5  °C) being the values that were found. Defuzzified output parameters include temperature rise (29 °C), energy efficiency (16%), and pressure drop (5.62 Pa) based on the optimal setting. Figure 4.4 shows

4.3  Results and Discussion

71

Fig. 4.4  Graphical rule viewer for temperature rise, energy efficiency, and pressure drop

the graphical rule viewer for temperature rise, energy efficiency, exergy efficiency, and pressure drop.

4.3.2 Parametric Analysis 4.3.2.1 Temperature Rise Variation The temperature difference (inlet and outlet) at the SCSAC variation with respect to mass flow rate, solar radiation, and temperature inlet is shown in Fig.  4.5a, b. According to the results, increasing the airflow rate lowers the temperature differential value in a monotonic way. This may be due to the fluid spending less time in the collector. At the same time, given the same amount of heat transfer, an increase in mass flow compensates for a drop-in temperature. It increases initially, but it starts to decline after reaching a particular value. In other words, the more excellent temperature value indicates that more heat is transferred. From both temperature and mass flow rate points of view, it may be argued that a medium and lower mass flow rate will result in a higher temperature difference. The range of temperature difference in SCSAC is 9.9–63.9 °C. Consider how solar radiation and the ambient temperature affect temperature rise. Because temperature is directly proportional to solar radiation, the higher the solar radiation, the higher the temperature, and thus the more solar insulation the collector can absorb. The quantity of heat loss from the collector (convection and radiation) decreases as the ambient temperature increases. This might also explain why temperatures are lower in the mornings and afternoons when solar energy and ambient temperature are lower than in the midday sun. To get the most significant temperature increase value, the maximum solar insulation and the highest ambient temperature, i.e., noontime, are necessary. The maximum and minimum solar radiations are 978 and 371 W/m2, respectively.

72

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

Fig. 4.5  Variation of temperature difference surface graphs: (a) mass flow rate and solar radiation, (b) mass flow rate and temperature inlet

Fig. 4.6  Variation of energy efficiency surface graphs: (a) mass flow rate and solar radiation, (b) mass flow rate and temperature inlet

4.3.2.2 Energy Efficiency Variation The variance in SCSAC thermal efficiency is seen in Fig. 4.6a, b. As the rate of air mass flow increases, it expands in a predictable pattern. A greater mass flow rate is preferable since it is the most significant property of a solar collector, even if it needs a higher pumping power. The growth rate beyond 0.015  kg/s is relatively modest, according to a deeper inspection of the pattern. The highest energy efficiency for solar radiation is between 500 and 750 W/m2, often attained during midday. As the value of temperature rises, the value of efficiency rises with it. For one point, more solar radiation causes a more significant temperature, meaning that more energy is available for conversion, yet increased temperature also decreases leakage losses. Furthermore, the greatest temperature and solar radiation values are required to get the highest efficiency value. Consequently, the highest temperature and medium solar radiation will provide the best results in terms of efficiency. The greatest possible temperature is also attainable at noon, as is the highest possible solar radiation. The energy efficiency varies from 16.8 to 44.42% for the SCSAC.

4.4  Validation of the Proposed Method

73

Fig. 4.7  Variation of pressure drop surface graph with mass flow rate and solar radiation

4.3.2.3 Pressure Drop Figure 4.7 depicts the change in pressure drop as a function of mass flow rate. The results reveal that increasing air mass flow rate raises pressure drop value, indicating that more pumping power is required. The rate of increment of pressure drop grows in a parabolic function; the mass flow rate reaches up to 0.015 kg/s, as seen in the graph. The flow rate must be kept at 0.020 kg/s or below to keep pumping power to a minimum. In addition, the pressure drop value seems to climb in proportion to the increase in mass flow rate. The mass flow rate of slow airflow might be due to a larger gravitational pull. A medium value and a lower mass flow rate value are selected for less pumping power as a final point. The pressure drop varies between 4.90 Pa and 54.1 Pa for all considered mass flow rate ranges from 0.010 to 0.025 kg/s.

4.4 Validation of the Proposed Method 4.4.1 Confirmation Tests for Validation It is necessary to do confirmatory tests to ensure that the chosen processing parameters are working optimally. The optimal configuration determined by the suggested model is used to analyze the confirmatory tests. Confirmatory test results are listed in Table 4.2. Comparable findings were found between FPSAC proposed model and the FPSAC follow-up test results.

74

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

Table 4.2  Confirmatory test outcomes Optimal conditions for SCSAC Mass flow Tilt angle Solar rate (30°) radiation (0.0175 kg/s) (674 W/m2) Confirmatory test results SC-TSK-FL

Inlet temperature (31.5 °C)

Output parameters for SCSAC Energy Temperature efficiency Pressure rise °C % drop Pa 31.2 17.9 7.41 29 16 5.62

4.5 Conclusions The use of an expert system in the practical demonstration of a sand-coated solar air collector (SCSAC) is given. The SC technique is employed for cluster center extraction, while TSK-FL is used for SCSAC parameter optimization and prediction. In this experiment, 36 trials of experimentation in open atmospheric conditions are carried out by varying the mass flow rate of air, fixed collector tilt angle, solar radiation, and inlet temperature and determining the corresponding output parameters such as energy efficiency, temperature rise, and pressure drop. The optimization of SCSAC parameters and parametric analysis is then carried out utilizing a unique hybrid expert system. The input variables, mass flow rate of 0.0175 kg/s, tilt angle of 30°, solar radiation of 674 W/m2, and inlet temperature of 31.5 °C, were found to be the ideal settings after simulation. The output optimal parameters, including temperature rise (29  °C), energy efficiency (16%), and pressure drop (5.62  Pa), are achieved based on the optimal setting. And the values are well comparable to the experimental results for SCSAC.  Further, the results are also compared with the other hybrid method results; the % error is less than 5% which is acceptable.

References 1. Öztürk, H. H., & Demirel, Y. (2004). Exergy-based performance analysis of packed-bed solar air heaters. International Journal of Energy Research, 28(5), 423–432. 2. Gupta, M. K., & Kaushik, S. C. (2008). Exergetic performance evaluation and parametric studies of solar air heater. Energy, 33(11), 1691–1702. 3. Esen, H. (2008). Experimental energy and exergy analysis of a double-flow solar air heater having different obstacles on absorber plates. Building and Environment, 43(6), 1046–1054. 4. Alta, D., Bilgili, E., Ertekin, C., & Yaldiz, O. (2010). Experimental investigation of three different solar air heaters: Energy and exergy analyses. Applied Energy, 87(10), 2953–2973. 5. Saidur, R., BoroumandJazi, G., Mekhlif, S., & Jameel, M. (2012). Exergy analysis of solar energy applications. Renewable and Sustainable Energy Reviews, 16(1), 350–356. 6. Jafarkazemi, F., & Ahmadifard, E. (2013). Energetic and exergetic evaluation of flat plate solar collectors. Renewable Energy, 56, 55–63. 7. Velmurugan, P., & Kalaivanan, R. (2015). Energy and exergy analysis of solar air heaters with varied geometries. Arabian Journal for Science and Engineering, 40(4), 1173–1186. 8. Suzuki, A. (1988). A fundamental equation for exergy balance on solar collectors. Journal of Solar Energy Engineering, 110(2), 102–106.

References

75

9. Sun, C., Liu, Y., Duan, C., Zheng, Y., Chang, H., & Shu, S. (2016). A mathematical model to investigate on the thermal performance of a flat plate solar air collector and its experimental verification. Energy Conversion and Management, 115, 43–51. 10. Das, B., & Giri, A. (2014). Second law analysis of an array of vertical plate-finned heat sink undergoing mixed convection. International Communications in Heat and Mass Transfer, 56, 42–49. 11. Baritto, M., & Bracamonte, J. (2012). A dimensionless model for the outlet temperature of a nonisothermal flat plate solar collector for air heating. Solar Energy, 86(1), 647–653. 12. Hegazy, A. A. (2000). Thermohydraulic performance of air heating solar collectors with variable width, flat absorber plates. Energy Conversion and Management, 41(13), 1361–1378. 13. El Ferouali, H., Zoukit, A., Salhi, I., El Kilali, T., Doubabi, S., & Abdenouri, N. (2018). Thermal efficiency and exergy enhancement of solar air heaters, comparative study and experimental investigation. Journal of Renewable and Sustainable Energy, 10(4), 043709. 14. Pérez-Espinosa, R., & García-Valladares, O. (2018). Solar Collector Simulator (SolCoSi): A new validated model for predicting the thermal performance of flat plate solar collectors. Journal of Renewable and Sustainable Energy, 10(1), 013705. 15. Debnath, S., Das, B., Randive, P. R., & Pandey, K. M. (2018). Performance analysis of solar air collector in the climatic condition of north eastern India. Energy, 165, 281–298. 16. Kalogirou, S. A. (2006). Prediction of flat-plate collector performance parameters using artificial neural networks. Solar Energy, 80(3), 248–259. 17. Esen, H., Ozgen, F., Esen, M., & Sengur, A. (2009). Artificial neural network and wavelet neural network approaches for modelling of a solar air heater. Expert Systems with Applications, 36(8), 11240–11248. 18. Caner, M., Gedik, E., & Keçebaş, A. (2011). Investigation on thermal performance calculation of two type solar air collectors using artificial neural network. Expert Systems with Applications, 38(3), 1668–1674. 19. Benli, H. (2013). Determination of thermal performance calculation of two different types solar air collectors with the use of artificial neural networks. International Journal of Heat and Mass Transfer, 60, 1–7. 20. Ghritlahre, H. K., & Prasad, R. K. (2017). Prediction of thermal performance of unidirectional flow porous bed solar air heater with optimal training function using artificial neural network. Energy Procedia, 109, 369–376. 21. Kamthania, D., & Tiwari, G. N. (2012). Performance analysis of a hybrid photovoltaic thermal double pass air collector using ANN. Applied Solar Energy, 48(3), 186–192. 22. Chabane, F., Moummi, N., Benramache, S., Bensahal, D., Belahssen, O., & Lemmadi, Z. (2010). Thermal performance optimization of a flat plate solar air heater using genetic algorithm. Applied Energy, 87(5), 1793–1799. 23. Varun, Sharma, N., Bhat, I. K., & Grover, D. (2011). Optimization of a smooth flat plate solar air heater using stochastic iterative perturbation technique. Solar Energy, 85(9), 2331–2337. 24. Siddhartha, Sharma, N., & Varun. (2012). A particle swarm optimization algorithm for optimization of thermal performance of a smooth flat plate solar air heater. Energy, 38(1), 406–413. 25. Vafaei, L. E., & Sah, M. (2017). Predicting efficiency of flat-plate solar collector using a fuzzy inference system. Procedia Computer Science, 120, 221–228. 26. Mohanty, S., Rout, A., Patra, P. K., & Sahoo, S. S. (2017). ANFIS based solar radiation data forecasting for energy and economic study of solar water heaters in eastern India. International Journal of Control Theory Applications, 10, 179–190. 27. Erenturk, S., & Erenturk, K. (2018). Comparisons of novel modeling techniques to analyze thermal performance of unglazed transpired solar collectors. Measurement, 116, 412–421. 28. Sugeno, M., & Kang, G.  T. (1986). Fuzzy modelling and control of multilayer incinerator. Fuzzy Sets and Systems, 18(3), 329–345. 29. Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 1, 116–132.

76

4  Investigation of Thermal Performance of Solar Collector Variables Using Fuzzy…

30. Hamam, A., & Georganas, N.  D. (2008, October). A comparison of Mamdani and Sugeno fuzzy inference systems for evaluating the quality of experience of Hapto-Audio-Visual applications. In 2008 IEEE international workshop on haptic audio visual environments and games (pp. 87–92). IEEE. 31. Chiu, S.  L. (1994). Fuzzy model identification based on cluster estimation. Journal of Intelligent & Fuzzy Systems, 2(3), 267–278. 32. Bahrehmand, D., Ameri, M., & Gholampour, M. (2015). Energy and exergy analysis of different solar air collector systems with forced convection. Renewable Energy, 83, 1119–1130. 33. Bellos, E., & Tzivanidis, C. (2017). A detailed exergetic analysis of parabolic trough collectors. Energy Conversion and Management, 149, 275–292. 34. Debnath, S., Reddy, J., & Jagadish, D. B. (2019). An expert system-based modeling and optimization of corrugated plate solar air collector for north eastern India. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(7), 1–8.

Chapter 5

Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

5.1 Introduction As electromagnetic waves travel from the sun to Earth’s surface, solar energy is one of the renewable sources of energy. Using a solar air collector (SAC), solar energy can be transformed into thermal energy for agricultural drying, home heating, and commercial and industrial applications. SAC is a straightforward appliance for heating air using the sun’s rays. This setup includes a collector box, absorber plate, top glazing, base plate, and thermal insulation. Absorber plates have black paint on their surfaces to efficiently convert solar light into heat energy. This heat is collected from an absorber plate by passing air via a carefully measured duct enclosed in glass. Since air has a low density as a working medium and a poor thermal capacity, SAC requires more space for air handling than liquids. Increasing the convective heat transfer rate is one solution to SAC’s problems. Key parameters that determine SAC performance include the absorber plate profile, the length and depth of the collection box, the number of glass covers and their types, the speed of the wind, the amount of sunlight available, the type of insulation used, and the use of a selective coating. The following sections highlight the various design configurations that various writers have proposed to create a more efficient SAC. Gupta and Kaushik [1], Esen [2], and Alta et al. [3] are just a few of the researchers who have examined the efficacy of solar air collectors. Researchers aim to optimize the design by doing parametric analysis, leading to better performance thanks to a modified collector. However, recommendations for optimal design are made solely based on experimental data or expert opinion. Jafarkazemi and Ahmadifard [4], Suzuki [5], and Velmurugan and Kalaivanan [6] have looked into the efficiency and environmental impact of solar air collectors. Adding a fin to the absorber plate of a solar collector can help reduce the overall efficiency losses. Sansaniwal et al. investigated solar energy applications in depth [7]. Since exergy efficiency is

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4_5

77

78

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

concerned with the irreversibility of energy, it has been argued that energy efficiency may be superior. Drying using SAC was the focus of research by Fudholi and Sopian [8]. Indoor studies showed that energy efficiency could be anywhere from 30% to 79%, while exergy efficiency can be anywhere from 8% to 61%. However, outdoor trials have an energy efficiency of 28–62% and an exergy efficiency of 30–57%. Akpinar [9], Omojaro, and Aldabbagh [10] have changed the absorber plate of a SAC in an effort to produce secondary flow and improve the collector’s thermal performance. A conical obstruction and an observer have been used by Yang et al. [11], Mahmood [12], and Ghiami and Ghiami [13]. Offset strip fins and longitudinal baffles have been used by Abuska [14]. Reddy et al. [15] compared two types of solar air collectors (SACs) with distinct absorber plates, flat and trapezoidal, with their energy and exergy characteristics. Experiments were performed at 15°, 30°, and 45° of tilt with mass flow rates (MFR) ranging from 0.0039 kg/s to 0.0156 kg/s in free air. As MFR increased, the outlet temperature dropped, and the heat removal rate increased. Increasing the MFR by a factor of three improves thermal efficiency by 60%, while exergy efficiency is decreased by 39%. Its efficiency also went up by 38–66% when the inclination angle went from 15° to 45°. Experiments are performed to look at how well solar air collectors work in the climate of Northeastern India by Debanth et al. [16]. The analysis considered several governing parameters, including collector tilt angles of 30°, 45°, and 60° degrees, single and double glazing, mass flow rate ranging from 0.0039 to 0.0118 kg/s, and two distinct absorber plates (plain and corrugated). Due to the reduction of top losses, the results show that the double-glazing absorber plate always delivers higher performance from both an energy and exergy point of view. The conversion efficiency of the collector has been improved by increasing the air mass flow rate. There is as much as a 10–17% rise in the system’s overall efficiency whenever the mass flow rate is increased. Because of the increased heat transfer area and the better turbulence effect, using corrugated plates results in a 14% increase in efficiency. Reddy et al. [17] performed experimental analysis, and compared to conventional SACs, those with sand coating on their absorber plate were more efficient. Compared to Type I (uncoated) SAC, sand-coated SACs could increase energy efficiency by as much as 13% for SAC having a sand coating (with 0.075 mm dia of sand). Das et al. [18] carried out an experimental investigation to explore the performance of novel sand-­coated and sand-filled (SCSF) polycarbonate sheet-based solar air collector (SAC) inside controlled indoor circumstances with varying air flow rates and solar inputs. It was discovered that the thermal efficiency of the SAC with storage was 39% and 20% greater, respectively, than that of the black paint-coated aluminum absorber and the sand-coated aluminum absorber. Most of these studies focus on reducing pressure drop and increasing thermal efficiency through experimentally determined optimum design parameters. Gupta et  al. [19] researched a hybrid photovoltaic-­ thermal sun dryer for drying green chillies. The purpose of this research was to study the performance parameters of the dryer under the climatic conditions of the Northeastern Indian region. According to the findings, the rate at which moisture is evaporated during the solar drying process is 130% more than the rate at which it occurs during the natural open sun drying process.

5.1 Introduction

79

Priyam and Chand [20, 21] conducted a theoretical study with the collector and a wavy fin of varying amplitudes and durations. It has been shown that the air mass flow rate and fin spacing influence thermal and thermo-hydraulic performance. Hatami and Jing [22] performed a numerical simulation with different heat flow conditions on the top and wavy bottom plates while keeping the temperature constant. Recently, Hussein et al. [23] provided a comprehensive analysis of nanotechnology’s potential in absorption solar collectors. Hussein [24] suggested that solar collector performance can be enhanced by employing nanotechnology. Heat transfer and entropy production in a curvy channel filled with copper-water nano-­fluid have been studied by Dormohammadi et al. [25]. Increasing the nanoparticle volume fraction from 0.1 to 10 reduces entropy production and enhances heat transmission. Later, Hatami et  al. [26] investigated the effect of nanoparticles on heat conduction in a sinusoidally wavy channel with various wave amplitudes. The results show that SiO2 nanoparticles can increase thermal conductivity. For instance, Mondol et al. [27] recently looked into fluid mixing in a raccoon- and serpentine-­ type wavy channel. The mixing index can determine the suitable mixer for each value of Re. These studies [20–27] could help researchers learn more about the efficiency of SAC equipped with a wavy channel/absorber plate. Due to the complexity of the problem, multi-criteria decision-making (MCDM) techniques can be employed to determine the best settings for operating parameters like temperature to the collector, compression pressure ratio, etc. The necessity of determining the weights of criteria in MCDM problem-solving cannot be overstated. The entropy approach is a scientifically sound way to quantify relative importance. It was first presented by Shannon and colleagues [28]. In order to provide relative importance to the many indications used in the fuzzy synthetic evaluation of water quality assessment, the entropy technique was employed [29]. The authors discovered that the entropy method significantly reduces labor requirements when compared to the conventional fuzzy synthetic method. They discovered that when there are N monitoring sites, the workload associated with assigning weights can be cut down to 1/N of its original value. Debnath et al. [30] presents a fuzzy logic-based expert system (FLES) in order to evaluate the thermal performance of a corrugated plate solar air collector (CPSAC) in Northeastern India under a variety of environmental circumstances. It has been seen that the FLES model can accurately predict the results with an accuracy of at least 97.5%. The ideal circumstances are found at mass flow rate 0.00785 kg/s, tilt angle 45°, solar radiation 727 W/m2, and temperature inlet 29.6 °C, and the outputs are energy efficiency 35.9%, exergy efficiency 12.8%, temperature rise 34.7 °C, and pressure drop 48.8 Pa. Reedy et al. [31] presented a novel hybrid expert system in order to do an energy and exergy study of a wavy plate solar air collector (WPSAC) using the system. The Sugeno-­ based subtractive clustering approach is utilized for the extraction of cluster centers, while the multi-criteria ratio analysis method is employed for the optimization and prediction of WPSAC parameter. According to the findings, the optimal values of energy, exergy, and carbon credit for WPSAC are obtained when the parameter values are as follows: mass flow rate 0.00785 kg/s, tilt angle 45°, solar radiation 770 W/ m2, and temperature inlet 25 °C. Corresponding output values are energy efficiency

80

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

37.22%, exergy efficiency 11.58%, temperature rise 62 °C, and 0.0009 tonnes of carbon dioxide (CO2) which were found to be the highest possible for WPSAC. It has been determined that the accuracy of prediction is greater than 98.1%. Huang [32] developed an index system for assessing coal mine safety. The entropy weight approach was used by the author to calculate the relative importance of each index. After narrowing down their options, the authors used TOPSIS to settle on a final recommendation. When compared to the fuzzy synthetic evaluation approach, the BP artificial neural network, and other evaluations, the authors determined that the TOPSIS method, which uses entropy weights, was the simplest, clearest, and most acceptable. For information selection, Huang [32] presented an approach that uses both the TOPSIS algorithm and entropy weights. The authors used the information entropy approach and the TOPSIS method to objectively weigh evaluation criteria and rank information system options, respectively. The photovoltaic fed distributed static compensator’s proportional plus integral controller coefficients, and filter parameters were optimized by Mishra and Ray [33] using the JAYA method (PV-DSTATCOM). The JAYA and TLBO algorithms find the best solution by the 300th and 850th iteration, respectively, while GEM does not converge to the best cost function value until the 1000th iteration. When it comes to maximizing efficiency in electricity distribution networks, Warid et al. [34] turned to the JAYA algorithm. Results show a decrease in processing time and improvement in convergence characteristics. Rao et al. [35] suggested the JAYA technique, a meta-heuristic optimization algorithm. Newly suggested algorithm JAYA has been shown to provide promising results in solving both confined and unconstrained optimization problems. It’s a straightforward algorithm that may be written as a single eq. A population entity’s goal in this optimization technique is to move closer to the optimal solution and further away from the suboptimal ones. By implementing the JAYA method, Rao and Saroj [36] found the best possible size for a microchannel heat sink. The results obtained by the JAYA algorithm were found to be superior to those obtained by the TLBO method and the hybrid MOE algorithm. The JAYA algorithm also outperformed the TLBO method in terms of convergence characteristics. It is clear from the literature that there are a variety of approaches to determining weights for an MCDM procedure. However, the entropy technique, being objective, does not rely on the decision maker’s subjective judgments in the same way that other methods, such as AHP, do. The entropy approach of mathematical modeling is used to derive the weights. The JAYA approach outperforms other methods like TOPSIS, TLBO, GEM, etc., in terms of optimal outcome and computational time spent because of its simplicity and faster convergence rate. That’s why, in this chapter, we use a JAYA approach that incorporates entropy to finetune a SAC.

5.2  Methodology and Experimentation

81

5.2 Methodology and Experimentation 5.2.1 Thermal Energy Modeling The SAC used has a single pass between the absorber plate and the bottom plate. The corrugated absorber plate increases the thermal performance of the SAC, which improves the outlet temperature. To model the considered SAC, the following assumptions are made to simplify the analysis: • • • • •

Steady-state performance of solar collector. There is no absorption of solar energy by the glass cover. There is no air leakage from the collector and negligible edge loss. The air temperature varies in the flow direction only. Temperature drop through the bottom plate, absorber plate, and glass cover is negligible. • Assuming air is an ideal gas and has constant specific heat. • A thermal loss due to conduction and radiation loss due to insulation caused by wind is assumed negligible.

5.2.2 Energy Analysis The energy efficiency of the SAC can be estimated based on the first law of thermodynamics. The first law efficiency of the SAC is defined as the ratio of the useful energy gain to the solar radiation incoming to the heater. To determine energy efficiency, the following equations are considered:

Qg  ma .c p .  T2  T1 

I 

Qg Ac I



(5.1) (5.2)



where Qg is the useful energy gain, ma is the mass flow rate of air, cp is the specific heat of air, T2 is the outlet temperature of the collector, T1 is the inlet temperature of the collector, ηI is energy efficiency, Ac is the collector aperture area, and I is the solar radiation. The mean temperature (Tavg) of the outlet and inlet of the SAC is considered for the physical properties of air and is determined by the following equation:



Tavg 

T2  T1  2



(5.3)

82

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

5.2.3 Exergy Analysis Exergy analysis is an important technique to establish strategies for the design and process of numerous industrial practices where the optimal usage of energy is measured as a key issue. The exergy efficiency states the ratio of exergy gain by the fluid to the exergy input to the system. Exergy analysis is based on the second law of thermodynamics. Exergy calculations per unit of time can be expressed as follows:

  xin    xout    xdest

(5.4)

Or Eq. (5.4) can be written as:

 xdest   xmass ,out   xwork   xheat   xmass ,in



(5.5)

where εxin and εxout are the rate of exergy in and exit from the collector and εxdestis the rate of irreversibility or exergy destruction of collector. The rate of change of overall exergy is as follows:



 T   xdest   mout xout  W    1  am  Qab   m in xin  Tab 

(5.6a)

The above equation can be written as:



 T  xdest    1  am  Tab

  Qab   m in xin   mout xout  W 

(5.6b)

where xin and xout are the flow exergy into the collector and exergy exit from the collector, W is rate of work (power), Tam is ambient temperature, Tab is absorber plate temperature, Qabis energy incident on the collector surface, and min and mout are fluid entry and exit of the collector, respectively. The specific exergy at the inlet and exit can be given as:

xin   hin  he   Tam  sin  se 



xout   hout  he   Tam  sout  se 

(5.7)



(5.8)



Eqs. (5.7) and (5.8) can be expressed as:

xin  xout   hin  hout   Tam  sin  sout 



(5.9)

5.2  Methodology and Experimentation

83

So Eq. (5.6b) can be written as, using Eqs. (5.7) and (5.8):



 T   xdest   1  am  Qab  ma ( hout  hin   Tam  sout  sin    Tab 

(5.10)

where hin is inlet enthalpy, hout is outlet enthalpy, sin is the entropy of the collector inlet, and sout is the entropy of the collector outlet. Qab is the amount of energy absorbed by the absorber plate. The enthalpy and entropy change of the solar air collector is written as:

h  hout  hin  c p  T2  T1  s  sout  sin  c p . ln



(5.11)



T2 P  R. ln 2 T1 P1

(5.12)

where Δh and Δs are the changes of enthalpy and entropy, R is the specific gas constant, and P1 and P2 are the pressure at the inlet and outlet of the collector. In general, the exergy balance equation can be expressed as:  T  T P exdest    1  a  I .   . Ac  ma .c p .  T2  T1   ma .c p .Tam ln 2  ma . R.Tam . ln 2 (51.3) T1 P1  Tab  The second law of efficiency can be expressed as follows:

 II  1 

 xdest  xin

(5.14)

5.2.4 Sustainability Index (SI) The sustainability index, which is a function of exergy efficiency, is used to estimate the effective use of SAC. The sustainability index (SI) can be determined by using exergy efficiency as: SI 

1 1   II

(5.15)

where SI is the sustainability index and ηII is exergy efficiency.

84

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

5.2.5 Environmental Impact Factor (EIF) The exergy losses are increasing, and it is a threat to the environment. The environmental impact factor estimates whether exergy losses damage the environment. The environmental impact factor is defined as the inverse of the exergetic sustainability index. 1 SI

EIF =



(5.16)

where EIF is the environmental impact factor and SI is the sustainability index.

5.3 Experimental Procedure The present experimental investigation has been conducted under the climatic condition of Silchar, Northeastern region of India. The SAC consists of a collector box, base plate, absorber plate, glazing cover, and thermal insulation. The size of the collector box 2.04 m × 1.04 m (length × breadth) and 0.2 m (depth) is schematically shown in Fig. 5.1. The dimensions of the trapezoidal plate are 2 m × 1 m with a thickness of 0.05 mm. To improve the absorbance of solar radiation, the whole surface of the absorber plate is coated with black paint. To reduce the top losses, glazing is used in SAC with size of 2.04 m × 1.04 m of 4 mm thickness. A centrifugal

la

SUN

ion

iat

d r ra

So

et

tl Ou

l

ub

Do

g

zin

la eG

z

pe

Tra

o

bs

la

a oid

r rbe

n tioon uullaati s s n n i l ail

ram erhme Th T

300

et

Inl

Air

te

pla

Collector box

Thermocouples

Fig. 5.1  Schematic diagram of trapezoidal plate solar air collector

Air

5.4  Proposed Method

85

Table 5.1  Consolidated table showing the effect of the major operating parameters (four inputs) on the energy efficiency, exergy efficiency, sustainability index, and environmental impact factor Input parameters Mass flow Tilt rate angle 0.0117 15 0.0039 30 0.0117 45 0.0039 15 0.0156 30 0.0039 45 0.0117 15 0.0156 30 0.0039 15 0.0078 30 0.0156 45 0.0078 45 0.0078 45 0.0117 45 0.0156 45 0.0039 30 0.0078 15

Solar radiation 823.541 725.998 916.937 855.599 855.072 790.401 426.769 477.734 457.321 915.466 688.208 297.515 401.304 305.340 390.784 298.567 450.162

Temperature inlet 29.5 31.5 30.5 31.2 26.2 30.6 28.8 31.5 32 34.8 32.9 31.4 20.8 31.6 21.8 25.6 22.8

Output parameters Energy Exergy efficiency efficiency 19.560 5.428 14.738 10.632 24.429 8.180 9.849 6.136 23.102 5.837 17.926 12.511 18.460 1.884 21.823 1.516 8.056 3.564 20.593 10.958 24.603 5.119 16.467 5.550 19.631 9.974 20.795 0.090 28.083 4.541 13.652 8.296 11.928 4.282

SI 1.057 1.118 1.089 1.065 1.061 1.143 1.019 1.015 1.036 1.123 1.053 1.058 1.110 1.009 1.047 1.090 1.044

ENV 0.945 0.893 0.918 0.938 0.941 0.874 0.981 0.984 0.964 0.890 0.948 0.944 0.900 0.999 0.954 0.917 0.957

blower forces the air into the collector box and considers a single pass downward of the absorber plate. This investigation considered tilt angles (15°, 30°, 45°), and the air mass flow rate varies from 0.0039 kg/s to 0.0156 kg/s with a constant increment of 0.0039 kg/s. The measuring instruments used in this study are RTD PT-100 temperature sensors used to measure the temperature of the SAC parts (inlet, outlet, ambient, absorber plate). A pyranometer is used to capture the solar intensity, an anemometer is used to measure the air velocity, and a U-tube manometer is used to measure the pressure difference across the SAC. The input and output parameters of the experimentation are tabulated in Table 5.1.

5.4 Proposed Method In this work, entropy method is coupled with JAYA method to select the appropriate input setting to get the optimum output results. The entropy method is used for the determination of weight for each output parameter, and JAYA method is used for optimization and ranking [36]. Step 1: Formulation of a Decision Matrix In this step, decision matrix is useful for looking at a large set of performance value systematically. It consists of number of criteria and number of alternatives.

86

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

DMij   xij 

m n



 x11 x  21      x  m1

x12 x22   xm 2

  x1n    x2 n             xmn 

(5.17)

where DMij is the decision matrix, xij represents the performance value of ith alternative on jth criteria, m represents the number of experiments, and n represents the number of criteria. Step 2: Normalization of Decision Matrix Normalization process converts the decision matrix Eq. (5.17) into a dimensionless matrix. Decision matrix consists of jth criteria. One is beneficiary criteria which is determined using Eq. (5.18), and the other is non-beneficiary criteria calculated using Eq. (5.19). For the beneficial criteria, decision matrix is normalized as follows: rij 

xij max j xij

,  i  1, mandj  1,.n 

(5.18)

For the non-beneficial criteria, decision matrix is normalized as follows: rij 

min j xij

,min xij  0,  i  1,.mandj  1, n 

xij

j

(5.19)

where rij is normalized performance value for ith experiment and jth criteria. maxj xij represents the maximum value of jth criteria, and minj xij represents the minimum value of jth criteria. Step 3: Calculation of Criteria’s Weight Using Entropy Method After the normalization of the matrix, weight of each criterion is determined using Eq. (5.22). Weight of a criterion indicates the priority assigned to the criterion by the decision-maker. For calculation of weight, critical entropy is required which is calculated using Eqs. (5.20 and 5.21). According to the definition of entropy, entropy of the jth criteria is determined by: i 1



Hj  

 fij ln fij m

fij 

ln m rij i 1

 rij m

,  i  1,.mandj  1, n 

(5.20) (5.21)

,  i  1,.mandj  1, n 

5.4  Proposed Method

87

Entropy weight of the jth criteria is determined by the following equation: wj 

1 Hj j 1

j 1

n   Hj

,  w j  1,  j  1, n 

(5.22)

n



n

where Hj is entropy of jth criteria and wj indicates the weight of the jth criteria, respectively. Step 4: Formulation of Weighted Normalized Decision Matrix In this step, the normalized value of each criterion is multiplied by its corresponding weight value to get the weighted normalized matrix. During the calculation of criteria, weight obtained by entropy method Eq. (5.22) is multiplied by the decision matrix Eq. (5.17). The resulting weighted decision matrix is given below:



 w1  x11   w1  x21 WN ij         w1  xm1

w2  x12 w2  x22   w2  xm 2

  w j  x1n     w j  x2 n              w j  xmn 

(5.23)

where WNij is weighted normalize decision matrix, wj is weight of jth criteria, and xmn is performance value of mth experiment and nth criteria. Step 5: Determination of Overall Score Matrix Using JAYA In this step, the overall score matrix Eq. (5.25) is evaluated by using JAYA method using Eq. (5.24). The elements of the Zm1 are taken as population and iteration till convergence is reached. For this method, the best solution and the worst solution are first identified from the population. The best solution of the criteria is considered as a beneficiary criterion, while worse is considered as non-beneficial criteria. The overall score matrix is calculated using the following equation:

Z newi  Z oldi  r1  Z best  || Z i ||  r2  Z worst  || Z i ||

Z m1

 z11  z   21          z   m1 



(5.24)

(5.25)

where Znew i is updated matrix after iteration, Zbest is the best solution of the objective function criteria, and Zworst is the worst solution of the objective function criteria at the ith iteration. r1 and r2 are two random numbers between 0 and 1.

88

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

Table 5.2  Normalized decision matrix for SAC system Trials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Energy 0.696 0.524 0.869 0.350 0.822 0.638 0.6573 0.777 0.286 0.733 0.876 0.586 0.699 0.740 1 0.486 0.424

Exergy 0.433 0.849 0.653 0.490 0.466 1 0.150 0.121 0.284 0.875 0.409 0.443 0.797 0.007 0.363 0.663 0.342

SI 0.925 0.978 0.952 0.932 0.929 1 0.891 0.888 0.907 0.982 0.922 0.926 0.971 0.875 0.916 0.954 0.914

ENV 0.946 0.894 0.919 0.939 0.942 0.875 0.982 0.985 0.965 0.891 0.949 0.945 0.901 1 0.955 0.917 0.958

At last, the ranking of alternatives is carried out based on overall score of individual alternatives. Here, the ranking is carried out descending order of the overall score values. The highest overall score for individual alternative is ranked as first, and lower overall score for individual is ranked as last.

5.5 Modelling of SAC System In this section, the modelling of SAC system is illustrated using entropy and JAYA method. First, a decision matrix is created, taking the output parameters as criteria and the number of trials as alternatives. Here, there is a total of 17 trials taken as alternatives, and 4 output parameters like energy, exergy, sustainability index, and environmental impact factor of SAC are taken as criteria to form the decision matrix as shown in Eq. (5.17), and the decision matrix is tabulated in Table 5.1. Second, normalization of the decision matrix is done using Eqs. (5.18, 5.19, and 5.20), which convert the different units of hybrid system parameters into dimensionless values in the range of 0 to 1. The normalized values are tabulated in Table 5.2. Third, after normalization of the decision matrix, entropy method is used to calculate weights for each criterion. In this method, entropy values are calculated from Eqs. (5.21 and 5.22), and using these entropy values, weights of the criteria are calculated using Eq. (5.23) and are tabulated in Table 5.3. The obtained weights for the output parameters, i.e., energy efficiency, exergy efficiency, sustainability index, and environmental index, are 0.250, 0.252, 0.248, and 0.248, respectively. From the

5.6  Parametric Analysis

89

Table 5.3  Corresponding weights of each criterion for the SAC system Sl. no. 1 2 3 4

Criteria Energy efficiency Exergy efficiency Sustainability index Environmental index

Weight (wj) 0.250 0.252 0.248 0.248

Table 5.4  Weighted normalized matrix for SAC system Trials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Energy 0.174 0.131 0.218 0.087 0.206 0.160 0.164 0.194 0.071 0.183 0.219 0.147 0.175 0.185 0.250 0.121 0.106

Exergy 0.109 0.214 0.165 0.123 0.117 0.252 0.038 0.030 0.071 0.221 0.103 0.111 0.201 0.001 0.091 0.167 0.086

SI 0.230 0.243 0.236 0.232 0.231 0.248 0.221 0.220 0.223 0.244 0.229 0.230 0.241 0.217 0.227 0.237 0.227

ENV 0.234 0.221 0.228 0.233 0.233 0.217 0.243 0.244 0.239 0.221 0.235 0.234 0.225 0.248 0.237 0.227 0.237

obtained weights, it can be concluded that the performance on the SAC is the most influencing criteria. Fourth, a weighted normalized matrix is tabulated in Table 5.4 by multiplying the obtained weights from entropy weight method with the corresponding normalized value of the output parameters using Eq. (5.24). Fifth, the response of each criterion for every trial in the weighted normalized matrix is added for the beneficial criteria and subtracted for the non-beneficial criteria. This creates a new single-column matrix, on which JAYA method is applied for optimization, and an overall score matrix is obtained, which is tabulated in Table 5.5.

5.6 Parametric Analysis In this work, four different MFRs (0.0039  kg/s, 0.0078  kg/s, 0.0117  kg/s, and 0.0156 kg/s) and three tilt angles (15°, 30°, and 45°) effect on trapezoidal plate used for experimentation. The following sections illustrate the performances of various

90

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

Table 5.5  Overall score of each trial for the SAC system Trials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Score 0.831 0.905 0.949 0.7440 0.878 0.986 0.734 0.761 0.662 0.976 0.877 0.800 0.942 0.716 0.900 0.837 0.721

parameters via graphical representations of the solar radiation, ambient temperature, energy efficiency, exergy efficiency, sustainability index, and environmental impact factor for different MFRs and tilt angles.

5.6.1 Variation in Solar Radiation and Ambient Temperature The hourly variations for solar radiation characteristics and ambient temperature are shown in Fig. 5.2a, b. All the experimental trial runs are carried out in open atmospheric conditions, where the solar radiation and ambient temperature fluctuations occur, captured with the help of a data logger. It is seen that it starts to increase in the morning, achieves maximum in the noon, and then starts declining in the afternoon. The slope of the temperature curve lesser in the afternoon than the first half of the day is due to effect of diffuse radiation. The solar intensity plays an important role in SAC performance. On experiment days, trial runs are performed for approximately 9 h (from 8:00 AM to 4:00 PM). It was noticed that ambient temperature and solar radiation intensity varied from 16 °C to 32 °C and 266 W/m2 to 941.8 W/m2 under Silchar climatic conditions, respectively.

5.6  Parametric Analysis

91

1100 Day1 Day2 Day3 Day4 Day5 Day6 Day7 Day8 Day9 Day10 Day11 Day12

1000 900

Solar radiation (W/m2)

800 700 600 500 400 300 200 100 0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

15:30

16:30

Time (hours)

(a) 33 30

Ambient temperature (°C)

27 24 21

Day1 Day2 Day3 Day4 Day5 Day6 Day7 Day8 Day9 Day10 Day11 Day12

18 15 12 9 6 3 0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

Time (hours)

(b) Fig. 5.2 (a, b) Variation of solar radiation and ambient temperature

92

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

5.6.2 Energy Efficiency Variation Variation in the energy efficiency during the daytime is shown in Fig. 5.3a–c. The energy efficiency starts to increase gradually before noon and reaches its maximum at noon and starts to reduce gradually in the afternoon. Furthermore, the energy efficiency increases with the mass flow rate, which is because of better heat extraction by air flowing in the collector. The maximum energy efficiency at MFR of 0.0156 kg/s is 29.32% for trapezoidal SAC. The energy efficiency deviation rises with changing the collector tilt angle from 15° to 45° such that the energy efficiency reaches 44.8%. In addition, the shape of the trapezoidal plate increases fluid turbulence, which significantly improves the convective heat transfer rate. This is because the trapezoidal absorber plate provides a larger surface area than the flat plate, allowing it to absorb the maximum solar intensity.

5.6.3 Exergy Efficiency Variation Variation in the SAC exergy efficiency is depicted in Fig. 5.4a–c. This trend is very much like those for the solar intensity and temperature rise. An initial exponential increment in exergy efficiency is linked to a quantitative increase in heat transfer rate from the absorber plate. Further, increasing average temperature of air contributes to improving the heat transfer quality. During afternoon, heat transfer rate decreases in both quantity and quality, resulting in a lower exergy efficiency. In the middle of the day, at tilt angle of 45°and MFR of 0.0039 kg/s, the highest exergy efficiency of 12.8% is noticed for trapezoidal SAC.

5.6.4 Variation of Sustainability Index The sustainability index is an assessment based on the second law of thermodynamics. Figure 5.5a–c shows the variation of sustainability index with day time for different tilt angles with varying mass flow rates. The trend of sustainability index directly depends on the exergy efficiency, solar radiation, and the temperature rise. Thus, the trend of the sustainability index is like that of the trend of solar radiation. It increases gradually during the forenoon, reaches peak at around noon time, and then starts decreasing gradually. The maximum sustainability index of the present study is found to be 1.146 for trapezoidal plate SAC.

93

5.6  Parametric Analysis

24

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 15

Energy efficiency (%)

20

16

12

8

4

0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(a) 30

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 30

Energy efficiency (%)

25

20

15

10

5

0 8:30

9:30

10:30

11:30

12:30

13:30

Time (hours)

(b) Fig. 5.3 (a–c) Variation of energy efficiency with time

14:30

15:30

16:30

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

94 35

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 45 30

Energy efficiency (%)

25

20

15

10

5

0 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time(hours)

(c) Fig. 5.3 (continued)

5.6.5 Environmental Impact Factor Environmental impact factor indicates the damage of environment due to unusable waste exergy output or exergy destruction. Exergy analysis is directly linked to sustainability and environmental impact of energetic processes. For a thermodynamically ideal/reversible process, there are no exergy losses, the exergy efficiency will have a value 1 or 100%, and the process would be completely sustainable, whereas in real thermodynamic irreversible processes, exergy destruction and losses will occur, and then the exergy efficiency will approach a zero value. Results indicate that the environmental impact factor is highly affected by the amount of solar radiation, as shown in Fig. 5.6a–c. At noon, since the amount of solar radiation reaches a maximum value, the environmental impact factor has become a minimum value. In the present study, the minimum value of environmental impact factor is found to be 0.93 for trapezoidal plate SAC. This result is obtained at noon time with a mass flow rate of 0.0039 kg/s and at 450 tilt angle.

5.6  Parametric Analysis

8

95

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 15

7

Exergy efficiency (%)

6 5 4 3 2 1 0

8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(a) 12

Tilt angle 30

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Exergy efficiency (%)

10

8

6

4

2

0 8:30

9:30

10:30

11:30

12:30

13:30

Time (hours)

(b) Fig. 5.4  Variation of exergy efficiency (a) 15° (b) 30° (c) 45°

14:30

15:30

16:30

96

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

14

0.0039 kg/s 0.0078 kg/s 0.0117 kg/s 0.0156 kg/s

Tilt angle 45

12

Exergy efficiency (%)

10 8 6 4 2 0

8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(c) Fig. 5.4 (continued)

5.7 Optimization of SAC After implementing the hybrid MCDM technique, entropy-JAYA method found an overall score matrix for each trial which is tabulated in Table 5.6. The overall score of trials is obtained as 0.831, 0.905, 0.949, 0.744, 0.878, 0.986, 0.761, 0.622, 0.976, 0.877, 0.800, 0.942, 0.71, 0.900, 0.837, 0.721, and 0.721, respectively. The ranking of alternatives is carried out based on overall score of individual alternatives, which is tabulated in Table 5.6. Here, the ranking is carried out in ascending order of the overall score values. The highest overall score for an individual alternative is ranked first, and lower overall score for individual is ranked last. So, trial 6 is ranked first, i.e., input parameter of trial 6 gives better results than any other alternatives in this experiment. The results show that trial no. 6 yields the highest overall score among the other trials represented in Fig. 5.7. The optimal setting of trapezoidal plate SAC obtained is at 0.0039 kg/s mass flow rate, 45° tilt angle, 790.40 W/m2, and inlet temperature 30.6 °C, and corresponding optimal output parameters are energy efficiency 17.92%, exergy efficiency 12.51%, sustainability index 1.14, and environmental impact factor 0.87.

5.7  Optimization of SAC

1.08

97

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 15°

1.07

Sustainability index

1.06 1.05 1.04 1.03 1.02 1.01 1.00 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(a)

1.14

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 30°

Sustainability index

1.12 1.10 1.08 1.06 1.04 1.02 1.00 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

Time (hours)

(b) Fig. 5.5  Variation of sustainability index with time (a) 15° (b) 30° (c) 45°

16:30

98

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

1.16

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 45

1.14

Sustainability index

1.12 1.10 1.08 1.06 1.04 1.02 1.00 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

(c) Fig. 5.5 (continued)

5.8 Conclusion In this chapter, modeling and optimization of the SAC are discussed. An integrated MCDM method, entropy with JAYA method, is applied for the modeling and parameter optimization of the hybrid thermal system. Here entropy method is used to obtain weights, while JAYA is for optimization of parameters. From the results, we can conclude that trial number 6 yields the highest score values compared to the other 16 experiments and provides the optimal input parameters for the SAC thermal system. The optimal settings for trapezoidal plate SAC obtained are at 0.0039  kg/s mass flow rate, 45° tilt angle, 790.40  W/m2, and inlet temperature 30.6 °C, and corresponding optimal output parameters are energy efficiency 17.92%, exergy efficiency 12.51%, sustainability index 1.14, and environmental impact factor 0.87. This entropy-JAYA method can be used for other energy systems optimization to obtain optimal parameter settings for the systems.

5.8 Conclusion

99

1.00

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 15

Environmental impact factor

0.99 0.98 0.97 0.96 0.95 0.94 0.93 0.92 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

14:30

15:30

16:30

Time(hours)

(a)

Environmental impact factor

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

Tilt angle 30

1.00

0.98

0.96

0.94

0.92

0.90

0.88 8:30

9:30

10:30

11:30

12:30

13:30

Time (hours)

(b) Fig. 5.6  Variation of environmental impact factor with time (a) 15° (b) 30° (c) 45°

100

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

0.0039kg/s 0.0078kg/s 0.0117kg/s 0.0156kg/s

1.00 Tilt angle 45

Environmental imppact factor

0.98

0.96

0.94

0.92

0.90

0.88

0.86 8:30

9:30

10:30

11:30

12:30

13:30

14:30

15:30

Time (hours)

(c) Fig. 5.6 (continued)

Table 5.6  Overall scoring and ranking of trials for the trapezoidal SAC Trials 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Score 0.831 0.905 0.949 0.744 0.878 0.986 0.734 0.761 0.662 0.976 0.877 0.800 0.942 0.716 0.900 0.837 0.721

Rank 10 5 3 13 7 1 14 12 17 2 8 11 4 16 6 9 15

16:30

101

References

1.00 0.95

Overall score

0.90 0.85 0.80 0.75 0.70 0.65 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18

Trails

Fig. 5.7  Overall scoring and ranking of trials for the trapezoidal SAC

References 1. Gupta, M. K., & Kaushik, S. C. (2008). Exergetic performance evaluation and parametric studies of solar air heater. Energy, 33(11), 1691–1702. 2. Esen, H. (2008). Experimental energy and exergy analysis of a double-flow solar air heater having different obstacles on absorber plates. Building and Environment, 43(6), 1046–1054. 3. Alta, D., Bilgili, E., Ertekin, C., & Yaldiz, O. (2010). Experimental investigation of three different solar air heaters: Energy and exergy analyses. Applied Energy, 87(10), 2953–2973. 4. Jafarkazemi, F., & Ahmadifard, E. (2013). Energetic and exergetic evaluation of flat plate solar collectors. Renewable Energy, 56, 55–63. 5. Suzuki, A. (1988). Fundamental equation for exergy balance on solar collectors. Journal Solar Energy Engineering, 110(2), 102–106. 6. Velmurugan, P., & Kalaivanan, R. (2015). Thermal performance studies on multi-pass fl ­ at-­plate solar air heater with longitudinal fins: An analytical approach. Arabian Journal for Science and Engineering, 40(4), 1141–1150. 7. Sansaniwal, S. K., Sharma, V., & Mathur, J. (2018). Energy and exergy analyses of various typical solar energy applications: A comprehensive review. Renewable and Sustainable Energy Reviews, 82, 1576–1601. 8. Fudholi, A., & Sopian, K. (2019). A review of solar air flat plate collector for drying application. Renewable and Sustainable Energy Reviews, 102, 333–345. 9. Akpinar, E. K., & Koçyiğit, F. (2010). Energy and exergy analysis of a new flat-plate solar air heater having different obstacles on absorber plates. Applied Energy, 87(11), 3438–3450. 10. Omojaro, A. P., & Aldabbagh, L. B. Y. (2010). Experimental performance of single and double pass solar air heater with fins and steel wire mesh as absorber. Applied Energy, 87(12), 3759–3765.

102

5  Sustainability Assessment of Solar Air Collector Using Entropy-JAYA Method

11. Yang, M., Yang, X., Li, X., Wang, Z., & Wang, P. (2014). Design and optimization of a solar air heater with offset strip fin absorber plate. Applied Energy, 113, 1349–1362. 12. Mahmood, A. J. (2017). Experimental study of a solar air heater with a new arrangement of transverse longitudinal baffles. Journal of Solar Energy Engineering, 139(3), 31004. 13. Ghiami, A., & Ghiami, S. (2018). Comparative study based on energy and exergy analyses of a baffled solar air heater with latent storage collector. Applied Thermal Engineering, 133, 797–808. 14. Abuşka, M. (2018). Energy and exergy analysis of solar air heater having new design absorber plate with conical surface. Applied Thermal Engineering, 131, 115–124. 15. Reddy, J., Jagadish, N.  S., Das, B., Ali Ehyaei, M., & Assad, M.  E. (2022). Energy and exergy analysis of a trapezoidal absorber plate-based solar air collector. Energy Science & Engineering, 10(4), 1067–1082. 16. Debnath, S., Das, B., Randive, P. R., & Pandey, K. M. (2018). Performance analysis of solar air collector in the climatic condition of north eastern India. Energy, 15(165), 281–298. 17. Reddy, J., Roy, S., & Jagadish, D. B. (2021). Performance evaluation of sand coated absorber based solar air collector. Journal of Building Engineering, 1(44), 102973. 18. Das, B., Mondol, J. D., Negi, S., Smyth, M., & Pugsley, A. (2021). Experimental performance analysis of a novel sand coated and sand filled polycarbonate sheet based solar air collector. Renewable Energy, 1(164), 990–1004. 19. Gupta, A., Das, B., & Mondol, J. D. (2022). Experimental and theoretical performance analysis of a hybrid photovoltaic-thermal (PVT) solar air dryer for green chillies. International Journal of Ambient Energy, 43(1), 2423–2431. 20. Priyam, A., & Chand, P. (2016). Thermal and thermohydraulic performance of wavy finned absorber solar air heater. Solar Energy, 130, 250–259. 21. Priyam, A., & Chand, P. (2018). Effect of wavelength and amplitude on the performance of wavy finned absorber solar air heater. Renewable energy, 119, 690–702. 22. Hatami, M., & Jing, D. (2017). Optimization of wavy direct absorber solar collector (WDASC) using Al2O3-water nanofluid and RSM analysis. Applied Thermal Engineering, 121, 1040–1050. 23. Hussein, A. K., Walunj, A., & Kolsi, L. (2016). Applications of nanotechnology to enhance the performance of the direct absorption solar collectors. Journal of Thermal Engineering, 2(1), 529–540. 24. Hussein, A. K. (2016). Applications of nanotechnology to improve the performance of solar collectors–Recent advances and overview. Renewable and Sustainable Energy Reviews, 62, 767–792. 25. Dormohammadi, R., Farzaneh-Gord, M., Ebrahimi-Moghadam, A., & Ahmadi, M. H. (2018). Heat transfer and entropy generation of the nanofluid flow inside sinusoidal wavy channels. Journal of Molecular Liquids, 269, 229–240. 26. Hatami, M., Kheirkhah, A., Ghanbari-Rad, H., & Jing, D. (2019). Numerical heat transfer enhancement using different nanofluids flow through venturi and wavy tubes. Case Studies in Thermal Engineering, 13, 100368. 27. Mondal, B., Mehta, S. K., Patowari, P. K., & Pati, S. (2019). Numerical study of mixing in wavy micromixers: Comparison between raccoon and serpentine mixer. Chemical Engineering and Processing-Process Intensification, 136, 44–61. 28. Zou, Z., Sun, J., & Ren, G. (2005). Study and application on the entropy method for determination of weight of evaluating indicators in fuzzy synthetic evaluation for water quality assessment. Acta Scientiae Circumstantiae, 25(4), 552–556. 29. Li, X., Wang, K., Liu, L., Xin, J., Yang, H., & Gao, C. (2011). Application of the entropy weight and TOPSIS method in safety evaluation of coal mines. Procedia Engineering, 26, 2085–2091. 30. Debnath, S., Reddy, J., & Jagadish, D. B. (2019). An expert system-based modeling and optimization of corrugated plate solar air collector for north eastern India. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(7), 1–8.

References

103

31. Reddy, J., Debnath, S., & Jagadish, D. B. (2019). Energy and exergy analysis of wavy plate solar air collector using a novel hybrid expert system. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(10), 1–4. 32. Huang, J. (2008, September). Combining entropy weight and TOPSIS method for information system selection. In 2008 IEEE conference on cybernetics and intelligent systems (pp. 1281–1284). IEEE 33. Mishra, S., & Ray, P.  K. (2016). Power quality improvement using photovoltaic fed DSTATCOM based on JAYA optimization. IEEE Transactions on Sustainable Energy, 7(4), 1672–1680. 34. Warid, W., Hizam, H., Mariun, N., & Abdul-Wahab, N. I. (2016). Optimal power flow using the Jaya algorithm. Energies, 9(9), 678. 35. Rao, R.  V., More, K., Taler, J., & Ocłoń, P. (2016). Dimensional optimization of a micro-­ channel heat sink using Jaya algorithm. Applied Thermal Engineering, 103, 572–582. 36. Rao, R. V., & Saroj, A. (2017). Economic optimization of shell-and-tube heat exchanger using Jaya algorithm with maintenance consideration. Applied Thermal Engineering, 116, 473–487.

Chapter 6

Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR Method

6.1 Introduction For heating, drying, and power generation applications, renewable and clean energy sources are attracting ever-growing attention in both developed and developing countries [1]. This is mostly due to the fast-increasing oil costs and subsequent emission of hazardous gases. Solar energy’s prevalence stands out when considering the most important renewable and clean energy sources [2]. In addition to its immense potential to generate renewable power [3], harnessing the sun’s rays is widely hailed as a game-changing measure in the fight against climate change, reducing reliance on finite fossil fuel supplies and bringing about energy independence for many nations. It is possible to use the sun’s energy for a variety of purposes if it is converted into thermal and electrical energy [4]. Solar photovoltaic (PV) cells absorb sunlight and convert it into usable electricity without emitting any harmful gases into the air [5]. The material used in PV cells is extremely sensitive to sunlight and heats up very rapidly. However, when PV cells are constantly exposed to sunlight, their efficiency at generating electrical power decreases. Commercial PV cells, it has been stated, has an efficiency of 6–16% at 25 °C [6]. An accumulation of waste heat occurs in a PV cell when it is exposed to the sun’s rays for an extended period. Improvements in the PV cell’s electrical performance can be expected when excess heat is removed. The recovered heat has numerous industrial and commercial uses, including space heating and the drying of agricultural products [7, 8]. Thus, a photovoltaic thermal collector (PVTC) generates thermal and electrical energy and enhances the electrical performance of photovoltaic, especially at higher solar insolation. PVTC technology is employed for both cooling and heating [8]. Wolf [9] and Kern and Russell [10] are the pioneers of PVTC technology, since every effort has been made to boost the PVTC’s performance and make solar energy a competitive option.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4_6

105

106

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

Experimentation has been performed with various approaches to increase the electrical efficiency of the PV cell by lowering the temperature. Hegazy et al. [11] used four theoretical models to investigate the phenomenon; the dominant component is the airflow pattern within the photovoltaic thermal air collector (PVTAC). Airflow occurs above and below the absorber plate in the first two models. In the second set of models, airflow occurs on the two sides of the absorber plate. When the airflow was positioned above the heated plate, it was discovered that the thermal efficiency was at its highest possible value. The research that was done and reported by Dubey et al. [12] and Charalambous et al. [13] found that airflow underneath the heated plate led to a more significant gain of energy. In their study, Slimani et al. [14] examined the effects of a single-pass and a double-pass airflow and found that the double-pass PVTAC has an overall thermal efficiency of 74%, but the single-­ pass PVTAC only has a thermal efficiency of 52%. This research is consistent with Sopia et al. [15], which found that the double-pass airflow had the highest overall efficiency due to superior heat extraction compared to the single-pass airflow. The experimental investigation conducted by Jha et al. [16] investigates the efficacy of an air-based photovoltaic thermal (PV/T) collector to produce both thermal and electrical energies. Under the weather conditions of Northeast India, outdoor tests are carried out with variable degrees of photovoltaic (PV) coverage regions (ranging from 25 to 100%), as well as two distinct kinds of absorbers. According to the findings, a high overall energy performance was attained with a PV coverage area of 25%, while a high net electrical energy and overall exergy were seen with a PV coverage area of 100% for both the PV/T collectors. This was the case for both of the PV/T collectors. Gupta et al. [17] conducted research on a hybrid photovoltaic-­ thermal (PVT) sun dryer for drying green chillies. The purpose of this research was to study the performance parameters of the dryer under the climatic conditions of the Northeast Indian region. According to the findings, the rate at which moisture is evaporated during the solar drying process is 130% more than the rate at which it occurs during the natural open sun drying process. The purpose of the experiment that Das et  al. [18] carried out was to explore the performance of a novel sand-­ coated and sand-filled (SCSF) polycarbonate sheet-based solar air collector (SAC) inside controlled indoor circumstances with varying airflow rates and solar inputs. It was discovered that the thermal efficiency of the SAC with storage was 39% and 20% greater, respectively, than that of the black paint-coated aluminum absorber and the sand-coated aluminum absorber. The goal of an MCDM is to provide an efficient framework for categorizing and selecting one or more options from a set of alternatives [19]. It is a methodology for making decisions about complicated problems in a systematic and organized approach [20]. Many real-world issues have at least two competing requirements, and it’s not always possible to find a single answer that satisfies both. Decision-­ makers’ preferences will dictate the compromise that must be reached [21]. Some of the most well-known approaches to making decisions based on multiple criteria are the analytical hierarchical process (AHP), the analytical network process (ANP), the Elimination and Choice Expressing Reality (ELECTRE), the Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE), the

6.1 Introduction

107

Technique for Ordering Preferences Based on Similarity to the Optimal Solution (TOPSIS), the Multi-criteria Optimization and Compromise Solution (VIKOR), and the Decision Site selection [20, 21]. As such, combine two well-known multi-­ criteria decision-making approaches: Saaty’s [22] analytical network process (ANP) and Hwang and Yoon’s [20] TOPSIS (technique for preference by resemblance to ideal solution). Reedy et al. [23] presented a novel hybrid expert system to do an energy and exergy study of a wavy plate solar air collector (WPSAC) using the system. The Sugeno-based subtractive clustering approach is utilized to extract cluster centers, while the multi-criteria ratio analysis method is employed to optimize and predict WPSAC parameter. According to the findings, the optimal values of energy, exergy, and carbon credit for WPSAC are obtained when the parameter values are as follows: mass flow rate 0.00785 kg/s, tilt angle 45°, solar radiation 770 W/m2, and inlet temperature 25 °C. It has been determined that the prediction accuracy is greater than 98.1%. The values of energy efficiency, exergy efficiency, and temperature rise of 37.22%, 11.58%, and 62 °C are found to be the highest possible for WPSAC. Debnath et al. [24] model and optimize a flat plate solar air collector in Northeast India (IFM) using the integrated fuzzy technique. The solar air collector’s accuracy is 97.5%, and the optimal controlling parameters are 0.00785 kg/s mass flow rate, 45° tilt angle, 450 W/m2 solar radiation, and 27 °C temperature rise, and energy and exergy efficiencies are 28.88% and 5.15%, respectively. Research by multiple authors, as summarized above, shows that the nanofluid-­ cooled PVT SAC’s performance is very sensitive to a few key input parameters. Thus, optimizing the input parameters is essential for deriving the system’s peak performance. Conflicting criteria need the use of Multi-attribute Decision Making (MADM) techniques for deciding which input parameters will yield the optimal performance from HPVTS. Methods like the analytic hierarchy process (AHP) [21], the Technique for Order Preference by Simulation of an Ideal Solution (TOPSIS) [22], the VIKOR [23], and the grey relational analysis [25] are frequently used to solve engineering-related problems using MADM. Numerous academics have used these methods to address various decision-making challenges [26–30]. In the research that has been done on solar applications, such as solar collector design and PVT-SAC system optimization, MCDM-based studies have only shown sporadically. Specifically absent from the archival literature is the application that uses entropy-VIKOR for the multi-performance optimization of PVT SAC. Because of this, multi-performance optimization of PVTS through the use of the entropy-­ VIKOR approach makes the work new and worthy of being done. This work aims to determine which input parameters of the nanofluid-cooled entropy-VIKOR will produce the best possible results in terms of the system’s overall performance. Solar irradiation, inlet temperature, mass flow rate, and tilt angle are the four input parameters that are taken into account in this study regarding the PVTS. Entropy-VIKOR calculations are utilized to establish the level of significance each output response possesses. In the final step of the process, entropy-VIKOR is applied to each trial of the experiment to compute the overall performance index values and determine the optimal combination of factor levels.

108

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

6.2 Thermal Modelling and Experimentation 6.2.1 Thermal Modelling The crux of the present work is to examine the thermal behavior of the PVTAC with a flat plate. The performance of the PVTAC flat plate is investigated based on thermal performance coupled with electrical performance at various flow rates. The mathematical modeling of PVTAC is written based on the assumption implemented by Agrawal and Tiwari [31]. The following assumptions have been made: • The PVTAC works in quasi-steady-state condition. • Specific heat of air is assumed constant. • Heat loss is negligible from the side of the PVTAC. The thermal energy yield (Qhourly) from the PVTAC is the quantity of useful heat (J) received in 1 second. It is expressed as [32]:

Qu  ma ca  Tout  T fi 

(6.1)



The daily(Qdaily)thermal energy yield is obtained as: i 1



Qdaily   Qui M

(6.2)



The overall thermal energy is expressed as: Qovther  Qdaily 

Enetdailyel Cf

(6.3)

where Cf is equal to 0.38 which is known as a conversion coefficient for coal-based power plant (thermal) and Enetdailyel is the net generated electrical energy from the PVTAC on a daily basis which can be represented as:



i 1

i 1

M

M

Enetdailyel   Eeli   Pfani



(6.4)

where Eel is the electrical energy generated on an hourly basis, which is expressed as:

Eel  c  A  I  t 



(6.5)

where ηc is referred to electrical efficiency (temperature dependent) of the PV cell, which is expressed as:

6.2  Thermal Modelling and Experimentation



109

c  reffr  1   reffr   Tc  Treffr  



(6.6)

and Pfan is the power consumed by the fan on an hourly basis, which is expressed as: Pfan 

ma  P  a  fan

(6.7)

where ηfan is the efficiency of fan which is taken as 0.9 for the present case. The instantaneous thermal efficiency is expressed as:

th 

Qu b  L  I t 

(6.8)

whereas the overall thermal efficiency achieved from the PVTAC is expressed as [32]:

overallth 

Enetdailyel  Qdaily

(6.9)

i

 I  t  bL



M

Exergy is the useful amount of work that is achieved from a system as it reaches equilibrium with a reference environment. The analysis of exergy uses principles of energy and mass conservation coupled with the second law of thermodynamics. It is expressed on an hourly basis as [33]:



 T  273  Eu  Qhourly 1  amb   Tout  273 

(6.10)

The everyday exergy yield (Edailyex) is expressed as: i 1



Edailyex   Eui M

(6.11)



However, overall exergy output (Eovex) is the summation of thermal exergy output and net electrical energy output, since electrical energy achieved from the PVTAC is a form of exergy. This can be expressed as:

Eovex  Edailyex  Enetdailyel



(6.12)

In 1964, Patela [34] has derived and elaborated estimation method for exergy of radiation also known as inlet exergy or exergy inflow from equilibrium laws of a black body. According to him, it depends on the ambient temperature, the

110

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

temperature of the radiating surface, and the spectral composition of the thermal radiation. The solar radiation has a similar composition as that of the black body. The overall exergy inflow (Einvoex) is expressed as: 4  4 T 1 T   Einvoex  A  I  t   1   amb    amb   3  Ts    3 Ts 



(6.13)

The overall exergetic efficiency can be expressed as:  E ovex   ovex  Einovex



  100 

(6.14)

6.2.2 Experimental Procedure The experimental performance of the PVTAC was evaluated in Silchar, India, located in the country’s northeastern section at coordinates of 24.83° north latitude and 92.7° east longitude. A flat plate-based SAC was used for comparison. A PVTAC with a flat plate, similar to the one shown in Fig. 6.1. A flat plate is positioned on the underside of the duct’s inside surface. The experimentally investigated in terms of temperature at the upper and rear part of the PV module, outlet temperature of air, hourly thermal energy yield, hourly exergy yield, net electrical energy yield, overall yield in energy, exergy, and its corresponding efficiency in June 2018 for six flow rates of air (0.0047–0.0165 kg/s). On each of the days of observation, the experiment was carried out from 9  in the morning to 16  in the evening. Throughout the trials, the data on the average ambient temperature and sun radiation values are recorded and displayed. The experimental systems consist of a single-­ glazed PVTAC that is equipped with a 100  W polycrystalline PV module. This Datalogger

Outlet temperature sensor Solar cell temperature sensor Back surface temperature sensor

Inlet air temperature sensor Flow control valve

Outlet

anel PV p

Air duct

Flat a

Fan

Inlet

er bsorb

plate

ation

Insul

U tubemanometer Metal frame

Fig. 6.1  Schematic diagram of PVTAC setup

6.3  Proposed MCDM Method

111

configuration is depicted in Fig. 6.1. The solar photovoltaic module has a total surface area of 0.648 m2. The photovoltaic (PV) module has been installed on top of the rectangular air channel that has been constructed out of a sheet of PVC. On the steel frame, the air ducts have been installed at a consistent angle of 25° to the horizontal, nearly the same as the latitude of Silchar, India. The aluminum sheet used to make the plate used in the flat plate had a thickness of 0.0002 m, and it was utilized to make the plate used in the flat plate. To prevent air from escaping through the holes in the air duct, a good seal has been created using putty and double-sided tape. A decrease in the electrical efficiency of the PV module is caused by the cell temperature being too high. This issue can be remedied by installing an adequate air bypass for cooling beneath the PV module, which may increase the module’s overall electrical efficiency. Using temperature sensors of the RTD-PT-100 type, readings of the temperature present at the upper and rear parts of the PV module, as well as the temperature of the inlet, outflow, and ambient air, have been detected. The experiment makes use of a total of 12 temperature sensors, each of which is associated with the data logger so that the measurements of temperatures can be reflected at the pre-defined locations. In order to accomplish the forced airflow via the intake and cool down the PV module, a DC fan with 24 W of power is housed inside the rectangular air duct. In order to ensure that there was a consistent flow of air through the inlet, the DC fan was made to run with the assistance of an external DC source. Using the anemometer, the airflow rates were measured and recorded. A pyranometer of the Kipp and Zonen type was utilized to measure the levels of solar radiation that was present throughout the entirety of the experiment.

6.3 Proposed MCDM Method The employment of MCDM strategies is not cutting-edge; such techniques have been employed previously. Researchers have used MCDM to solve optimization problems in many branches of engineering; the following steps illustrate the entropy-VIKOR method. Step 1: Formulation of decision matrix. In this step, a decision matrix is developed done based on the number of criteria of alternatives. The decision matrix includes the performance values of each of the criteria corresponding to the other options. The decision matrix is evaluated using the following expression [35]:   A1  DMij   A2    Am 

C1

C2

X11 X 21  X m1

X12 X 22  Xm2



Cn   X1n  . X 2 n  For  i  1, 2,. m, j  1, 2,. n   . .  .. X mn 

(6.15)

112

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

where DMij represents the response value of ith criteria on jth alternative; X11, X12, X13.... Xmn denotes the performance values of each of the criteria with respect to the corresponding alternative; m represents the number of criteria; and n represents the number of alternatives. Step 2: Determination of precise priority weights using entropy. In this step, precise priority weights for each of the criteria are determined using Eqs. (6.15, 6.16 and 6.17). Here, first, the degree of divergence (dj) for each criterion is calculated using Eqs. (6.15 and 6.16), which measures the distance of each criterion concerning the identical sequence [36]. After that, precise priority weights are determined using Eq. (6.17). i 1



 j  k  Pij ln  Pij  j  1, 2,, n. m

dj  1  j .

j 

dj j 1

 dj n

(6.15)



(6.16)



.

(6.17)

where k is Boltzmann’s constant, [k = 1/ ln m, 0 ≤ dj ≤ 1], and ζj is the precise priority weights for each of the criteria, Ψj. Step 3: Determination of best (B+) and worst (B−) values and values of Ei and Fi. After the criteria weights, best (B+) and worst (B−) values and values of Ei and Fi for each of the criteria are determined using the following expressions:

B   max  Xij 





B   min  Xij 







  Xij    Xij  j 1   max Ei    j   n   X X    ij max  ij min

(6.18) (6.19)     

j 1     Xij max   Xij  Fi  max n   j  n  X  X    ij max  ij min

(6.20)

    

(6.21)

where B+ and B− represent the best and worst criteria from the decision matrix and ζj is the criteria weights. Step 4: Determination of performance index (PI) values.

6.4  Parametric Analysis

113

Next, the determination of overall performance index (PI) values for each of the alternatives is done to assess the optimal criteria. This step converts the multi-­ criteria into a single criteria subjected to certain constraints with consideration of both best/beneficial and worst/non-beneficial criteria. The performance index values for each of the alternatives are calculated using the following expressions:



   Fi  min  Fi    Ei  min  Ei    1  v   PI i  v      max  F   min  F    i i      max  Ei   min  Ei  

(6.22)

where PIi represents the performance index values for ith alternative, Max(Ei) is the maximum value of Ei, and Min(Ei) is the minimum value of Ei, and Max(Fi) is the maximum value of Fi, and Min(Fi) is the minimum value of Fi; v is used as the weight strategy of the majority of criteria, and its value is taken as 0.5, while its value is generally in the range 0–1. At last, a compromised ranking of the alternatives is carried out based on the PIi values. The best alternatives are determined as the ones with the minimum value of PIi in the ranking. The corresponding criteria values are considered as optimal criteria corresponding to the optimal alternatives for the system.

6.4 Parametric Analysis 6.4.1 Variation of Outlet Temperature The PVTAC’s operational efficacy is directly related to the environmental conditions under which it was tested. As the PV cell’s temperature rises, the PVTAC’s electrical conductivity deteriorates; therefore, researchers have looked into how the temperature of the PV cell changes at the top and back of the cell at different airflow rates. In addition, Fig. 6.2 plots the results of an investigation into how the airflow rate affects the air temperature at the exit. The results show that the air temperature at the outflow rises from morning to noon due to amplified sun intensity. All of the experimental facilities’ temperature profiles peak about midday (12  h) and then decrease in the afternoon. These temperatures have been shown to drop at the aforementioned areas as the airflow rate increases; this may be because of improved heat extraction.

6.4.2 Variation of Thermal Energy Yield and Exergy Yield The physical environment in which the PVTAC was tested directly affects the system’s operational performance in that environment. The nature of the changing temperature of the PV cell at its top and the rear surface has been researched for various

114

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

0.0047kg/s 0.007kg/s 0.0094kg/s 0.0128kg/s 0.0141kg/s 0.0165kg/s

48

Outlet temperature (°C)

45

42

39

36

33

30 9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours) Fig. 6.2  Variation of outlet temperature

flow rates of air. As the temperature of the PV cell rises, the electrical conductivity of the PVTAC decreases. In addition, the impact of the flow rate on the air temperature at the outflow was analyzed, and the results are represented in Fig. 6.3a, b. The findings suggest that as the morning progresses through the middle of the day, the temperature of the air at the outlet rises as a result of the intensification of the sun’s rays. At the experimental facilities, every temperature profile reaches its greatest value at noon, and then it drops precipitously in the afternoon and evening. In addition, the findings indicate that an increase in the airflow rate is associated with a decrease in temperature at each of the aforementioned sites, and the researchers speculate that this might be because of improved heat removal.

6.4.3 Variation of Electrical Energy Yield and Electrical Efficiency The primary objective of the current research is to effectively eliminate the surplus heat that is produced by the PV cell with the assistance of air functioning as a heat carrier fluid. The daily net electrical energy yield can be determined with the

6.4  Parametric Analysis

115

120

Thermal energy yield (Wh)

100

0.0047kg/s 0.007kg/s 0.0094kg/s 0.0128kg/s 0.0141kg/s 0.0165kg/s

80

60

40

20 9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

14:30

15:30

16:30

Time (hours)

(a) 4.5

4.0

Exergy yield (Wh)

3.5

0.0047kg/s 0.007kg/s 0.0094kg/s 0.0128kg/s 0.0141kg/s 0.0165kg/s

3.0

2.5

2.0

1.5

1.0 9:30

10:30

11:30

12:30

13:30

Time (hours)

(b) Fig. 6.3 (a, b) Variation of thermal energy and exergy yield

116

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

Eq. (6.4) assistance. Figure 6.4 depicts the daily change in electrical energy yield from the PV cell as well as the daily net electrical energy yield in relation to the airflow rates. However, the magnitude of the increment in the value of net electrical energy yield concerning the increase in airflow rates is less when compared to the electrical energy yield from the PV cell because high flow rates consumed a higher amount of fan power. This is because the PV cell produces more electrical energy. The electrical efficiency of the PVTAC was evaluated using Eq. (6.6) to highlight the significance of the surface temperature of the PV cell on the electrical performance. This was done to explain the relationship between surface temperature and electrical performance. The relationship between the PV cell’s surface temperature and the electrical efficiency fluctuation is seen in Fig. 6.5 for a specific mass transfer rate of 0.0128 kg/s. Because of the rise in temperature at the top surface of the PV cell from morning to noon, the electrical efficiency of the PVTAC demonstrates a decreasing trend from morning to noon. After that, an increase in efficiency is observed.

412

Electrical energy yield from PV cell Net electrical energy yield

Electrical energy yield (Wh)

410 408 406 404 402 400 398 396 0.004

0.006

0.008

0.010

0.012

Mass flow rate (kg/s) Fig. 6.4  Variation of electrical energy yield

0.014

0.016

0.018

6.4  Parametric Analysis

117

64 Top surface temperature of cell Electrical efficiency

62

14.0

Top surface temperature of cell (°C)

58

13.6

56

13.4

54

13.2

52 13.0

50

Electrical efficiency(%)

13.8

60

12.8

48 12.6

46

12.4

44 9:30

10:30

11:30

12:30

13:30

14:30

15:30

16:30

Time (hours)

Fig. 6.5  Variation of electrical efficiency

6.4.4 Modeling of PVT System Using Proposed MCDM Method This section discusses modeling of vertical axis wind turbine in the built environment using proposed MCDM method. The proposed method used is the entropy method with VIKOR. Here, entropy method is used for priority weight calculation of different criteria, while VIKOR is used for obtaining optimal operating conditions of PVTAC in order to get higher thermal energy and electrical energy. In this work, 4 input parameters with 48 number of trials are considered as alternatives and 4 output parameters. In the modeling, first, formulation of the decision matrix is done using Eq. (6.1). In this work, there are 48 number of trials performed by varying the four output parameters such as outlet temperature, thermal energy, thermal exergy efficiency, and electrical energy; input parameters being mass flow rate, solar radiation, and tilt angle are determined; and results are tabulated in Table. 6.1. Second, the entropy method determines priority weights for each of the PVTAC parameters or criteria such as outlet temperature, thermal energy, thermal exergy efficiency, and electrical energy. Here first, the degree of divergence (dj) for each of the PVTAC parameters or criteria is calculated using Eqs. (6.2 and 6.3). The degree of divergence measures the distance of each PVTAC parameter concerning the comparable sequence values. After that, precise priority weights for each PVTAC parameter or criterion are determined using Eq. (6.4), and the results are shown in Table 6.2.

118

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

Table 6.1  Experimental readings of PVTAC

Trial no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Input parameters Solar Mass int (W/ flow m2) (kg/s) 0.004 455 0.004 670 0.004 727 0.004 868 0.004 858 0.004 789 0.004 709 0.004 689 0.007 443 0.007 643 0.007 710 0.007 871 0.007 855 0.007 588 0.007 575 0.007 207 0.0094 450 0.0094 651 0.0094 717 0.0094 869 0.0094 849 0.0094 601 0.0094 570 0.0094 197 0.0128 448 0.0128 643 0.0128 721 0.0128 876 0.0128 830 0.0128 593 0.0128 540 0.0128 190 0.0141 440 0.0141 640 0.0141 730 0.0141 879 0.0141 833 0.0141 580 0.0141 527

Inlet temp (°C) 32.5 35.1 36.4 37.8 37.3 37.2 36.9 36.1 32.3 34.9 36.2 37.6 37.1 37 36.7 35.9 32.6 35.2 36.5 37.9 37.4 37.3 37 36.2 32.4 35 36.3 37.8 37.2 37.1 36.8 36.2 32.4 35 36.3 37.7 37.2 37.1 36.9

Tilt angle(θ) 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25 25

Output parameters output temp Thermal (°C) energy (%) 40 34.481 43 34.953 44 36.370 47 45.345 47 45.345 46 43.456 45 38.260 42 28.341 39 46.431 42 47.838 43 49.948 46 61.908 46 63.315 46 59.797 44 54.169 41 37.989 38 51.013 42 62.350 43 65.184 47 83.133 46 83.133 46 78.410 45 71.797 41 49.124 38 66.892 40 69.465 42 75.8976 46 100.339 45 99.052 44 87.475 43 77.184 41 55.315 37 69.435 40 72.269 42 80.771 45 107.695 45 104.861 44 90.691 42 75.103

Thermal exergy(%) 1.003 1.185 1.158 1.854 1.573 1.591 1.130 0.611 1.235 1.520 1.484 2.364 2.063 1.858 1.689 0.737 1.213 2.000 1.957 3.250 2.734 2.461 2.282 0.968 1.444 1.906 1.950 3.558 2.866 2.263 1.979 0.917 1.476 1.938 2.000 3.687 2.905 2.263 1.806

Electrical energy (Wh) 37.686 53.584 58.223 69.782 67.061 48.846 45.685 16.573 38.000 54.034 58.728 70.357 67.533 49.209 46.016 16.672 38.313 54.427 59.169 70.855 68.078 49.572 46.299 16.772 38.607 54.877 59.611 71.429 68.623 49.962 46.653 16.872 38.862 55.243 59.989 71.889 69.022 50.247 46.890 (continued)

119

6.4  Parametric Analysis Table 6.1 (continued)

Trial no. 40 41 42 43 44 45 46 47 48

Input parameters Solar Mass int (W/ flow m2) (kg/s) 0.0141 200 0.0165 439 0.0165 641 0.0165 717 0.0165 868 0.0165 827 0.0165 570 0.0165 569 0.0165 193

Inlet temp (°C) 36.2 32.5 35.5 36.2 37.8 37.3 37.2 36.9 36.1

Tilt angle(θ) 25 25 25 25 25 25 25 25 25

Output parameters output temp Thermal (°C) energy (%) 40 58.038 37 72.963 40 72.963 41 86.229 45 114.419 44 111.102 43 94.520 42 86.229 40 58.099

Thermal exergy(%) 0.835 1.506 1.912 2.029 3.853 3.014 2.513 1.810 0.945

Electrical energy (Wh) 16.938 39.077 55.580 60.399 72.234 69.458 50.506 47.149 17.096

Table 6.2  Priority weights of the PVT response parameters Priority weights(ζ)

Response parameters Outlet Thermal temperature (°C) energy (%) 0.267 0.288

Thermal exergy(%) 0.165

Electrical energy(Wh) 0.278

In the fourth step, the determination of best (B+) and worst (B−) values and values of Ei and Fi for each of the PVTAC parameters/criteria is done using Eqs. (6.5, 6.6 and 6.7). This measures the separation distance of each PVTAC parameter from the reference values. The normalization of the decision matrix of PVTAC to normalize the various data units into homogeneous units is shown in Table 6.3. The PVTAC parameters or criteria with higher Ei and Fi values indicate the least influence, while the least Ei and Fi values indicate the most influence on the PVTAC performance. The results of Ei and Fi values for each of the PVTAC parameters are shown in Table 6.4. After that, overall performance index (PI) values for PVTAC are determined using Eq. (6.8). This step converts multi-criteria into a single criterion subjected to certain constraints with consideration of both best/beneficial and worst/ non-beneficial criteria of the PVTAC parameters into account. The overall performance index values for the PVTAC are tabulated in Table 6.4. The results generated from the experimental investigations of various parameters are shown in Table 6.1.

6.4.5 Optimization Results of PVTAC Parameters The optimization of PVTAC parameters is discussed in this section. The overall performance index values are used for the selection of optimal operating conditions for PVTAC. Ranking of each performance value for the 48 trials has been carried out, and optimization results are tabulated in Table 6.5.

120

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

Table 6.3  Normalization of PVTAC Output temp (°C) 0.186 0.106 0.080 0 0 0.026 0.053 0.133 0.213 0.133 0.106 0.026 0.026 0.026 0.080 0.160 0.240 0.133 0.106 0 0.026 0.027 0.053 0.160 0.240 0.186 0.133 0.0265 0.053 0.080 0.106 0.160 0.267 0.186 0.133 0.053 0.053 0.080 0.133 0.186 0.267 0.186

Thermal energy (%) 0.267 0.266 0.261 0.232 0.231 0.237 0.255 0.288 0.227 0.223 0.216 0.175 0.171 0.183 0.201 0.256 0.212 0.174 0.165 0.105 0.104 0.120 0.142 0.218 0.159 0.150 0.129 0.047 0.051 0.090 0.124 0.198 0.150 0.141 0.112 0.022 0.032 0.079 0.131 0.188 0.139 0.138

Thermal exergy(%) 0.145 0.136 0.137 0.102 0.116 0.115 0.139 0.165 0.133 0.119 0.121 0.076 0.091 0.101 0.110 0.159 0.134 0.094 0.096 0.030 0.057 0.071 0.080 0.147 0.123 0.099 0.097 0.015 0.050 0.081 0.095 0.149 0.121 0.097 0.094 0.008 0.048 0.081 0.104 0.154 0.119 0.099

Electrical energy (Wh) 0.173 0.093 0.070 0.012 0.025 0.117 0.133 0.278 0.171 0.091 0.067 0.009 0.0235 0.115 0.131 0.278 0.169 0.089 0.065 0.006 0.020 0.113 0.129 0.277 0.168 0.086 0.063 0.004 0.018 0.111 0.128 0.277 0.167 0.085 0.061 0.001 0.016 0.110 0.126 0.277 0.166 0.083 (continued)

6.6  Conclusions and Future Direction

121

Table 6.3 (continued) Output temp (°C) 0.160 0.053 0.080 0.106 0.133 0.186

Thermal energy (%) 0.094 0 0.011 0.066 0.094 0.188

Thermal exergy(%) 0.093 0 0.042 0.068 0.104 0.148

Electrical energy (Wh) 0.059 0 0.013 0.108 0.125 0.276

The optimization results, as depicted in Table 6.5, show that trial no. 8 yields the least PI value among the 48 trials of experiments. The PI value obtained for the optimal setting or optimal trial no. 8 is 1 and shows the highest value among the other experiments. The optimal settings obtained are output parameters for the optimal PVTAC being outlet temperature 42 °C, thermal energy 28.34%, thermal exergy efficiency 0.61%, and electrical energy 16.5 Wh, with input parameters being mass flow rate 0.004 kg/s, solar radiation 689 W/m2, temperature 36.1 °C, and tilt angle 25°. The optimal setting obtained via entropy-VIKOR method provides the PVT SAC’s most optimal response/output parameters. This work also suggests that the proposed hybrid MCDM method can be utilized as a systematic framework model for modeling and optimization of other wind turbines.

6.5 Confirmatory Tests In addition, confirmation tests are carried out to determine the best possible circumstances to validate the findings. The optimization results done with entropy-VIKOR are used to determine the ideal settings for the confirmatory tests. The tabulated findings of the confirmatory tests can be found in Table 6.6. The findings indicate that the outcomes of confirmatory experiments are equivalent to acceptable alongside the experiments’ findings.

6.6 Conclusions and Future Direction Improvements in PVTAC performance in an urban setting are shown as an example. For PVTAC parameter optimization, we propose and employ a hybrid MCDM approach, combining entropy with the VIKOR method. A real-world instance is used to illustrate the efficacy and viability of the proposed strategy. Based on the ideal outcome, the best possible trial combinations for the PVTAC are 8, which produces the lowest performance index values. Upon finding the ideal values for the PVTAC parameters. The optimal settings obtained are output parameters for the optimal PVTAC being outlet temperature 42 °C, thermal energy 28.34%, thermal

122

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

Table 6.4 Ei, Fi, and PIi values for PVTAC parameters Trial no. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

Ei 0.773 0.602 0.549 0.345 0.373 0.497 0.580 0.866 0.746 0.567 0.511 0.288 0.312 0.427 0.523 0.853 0.757 0.491 0.434 0.142 0.209 0.332 0.406 0.804 0.691 0.524 0.423 0.092 0.173 0.363 0.455 0.785 0.706 0.511 0.402 0.086 0.149 0.351 0.496 0.807 0.691 0.508

Fi 0.267 0.266 0.261 0.231 0.231 0.237 0.255 0.288 0.227 0.223 0.216 0.175 0.171 0.183 0.201 0.278 0.240 0.174 0.165 0.104 0.104 0.120 0.142 0.277 0.240 0.186 0.133 0.047 0.053 0.111 0.128 0.277 0.267 0.186 0.133 0.053 0.053 0.110 0.133 0.277 0.267 0.186

PI 0.891 0.722 0.665 0.440 0.468 0.594 0.691 1 0.831 0.651 0.590 0.337 0.358 0.480 0.591 0.979 0.853 0.536 0.472 0.135 0.201 0.335 0.426 0.929 0.787 0.578 0.435 0.038 0.123 0.358 0.462 0.911 0.824 0.566 0.414 0.037 0.100 0.345 0.507 0.932 0.810 0.563 (continued)

6.6  Conclusions and Future Direction

123

Table 6.4 (continued) Trial no. 43 44 45 46 47 48

Ei 0.407 0.053 0.148 0.350 0.458 0.800

Fi 0.160 0.053 0.080 0.108 0.133 0.276

PI 0.441 0.005 0.120 0.343 0.469 0.924

Table 6.5  Performance index values (PI) for PVTAC parameters Expt. no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32

Output temp (°C) 40 43 44 47 47 46 45 42 39 42 43 46 46 46 44 41 38 42 43 47 46 46 45 41 38 40 42 46 45 44 43 41

Thermal energy (%) 34.48 34.95 36.37 45.35 45.35 43.46 38.26 28.34 46.43 47.84 49.95 61.91 63.32 59.80 54.17 37.99 51.01 62.35 65.18 83.13 83.13 78.41 71.80 49.12 66.89 69.47 75.90 100.34 99.05 87.48 77.18 55.32

Thermal exergy(%) 1.00 1.19 1.16 1.85 1.57 1.59 1.13 0.61 1.24 1.52 1.48 2.36 2.06 1.86 1.69 0.74 1.21 2.00 1.96 3.25 2.73 2.46 2.28 0.97 1.44 1.91 1.95 3.56 2.87 2.26 1.98 0.92

Electrical energy (Wh) 37.69 53.58 58.22 69.78 67.06 48.85 45.69 16.57 38.00 54.03 58.73 70.36 67.53 49.21 46.02 16.67 38.31 54.43 59.17 70.86 68.08 49.57 46.30 16.77 38.61 54.88 59.61 71.43 68.62 49.96 46.65 16.87

PI 0.891 0.722 0.665 0.440 0.468 0.594 0.691 1 0.831 0.651 0.590 0.337 0.358 0.480 0.591 0.979 0.853 0.536 0.472 0.135 0.201 0.335 0.426 0.935 0.787 0.578 0.435 0.038 0.123 0.358 0.462 0.911

Rank 7 13 15 31 28 17 14 1 9 16 19 39 35 25 18 2 8 23 26 42 41 40 33 4 12 20 32 46 43 36 29 6 (continued)

124

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

Table 6.5 (continued) Expt. no 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Output temp (°C) 37 40 42 45 45 44 42 40 37 40 41 45 44 43 42 40

Thermal energy (%) 69.44 72.27 80.77 107.70 104.86 90.69 75.10 58.04 72.96 72.96 86.23 114.42 111.10 94.52 86.23 58.10

Thermal exergy(%) 1.48 1.94 2.00 3.69 2.91 2.26 1.81 0.84 1.51 1.91 2.03 3.85 3.01 2.51 1.81 0.95

Electrical energy (Wh) 38.86 55.24 59.99 71.89 69.02 50.25 46.89 16.94 39.08 55.58 60.40 72.23 69.46 50.51 47.15 17.10

PI 0.824 0.566 0.414 0.037 0.100 0.345 0.507 0.932 0.810 0.563 0.441 0.005 0.120 0.343 0.469 0.924

Rank 10 21 34 47 45 37 24 3 11 22 30 48 44 38 27 5

Table 6.6  Confirmatory tests Optimum input parameters Solar Mass int Inlet (W/ flow temp Tilt (kg/s) m2) (°C) angle(θ) Test type Experimental 0.004 689 36.1 25 Results Confirmatory 0.004 689 36.1 25 Result

Output parameters Output temp (°C) 42

Thermal energy (%) 28.34

Thermal exergy(%) 0.61

Electrical energy (Wh) 16.57

43.2

29.52

1.02

15.11

exergy efficiency 0.61%, and electrical energy 16.57  Wh, with input parameters being mass flow rate 0.004 kg/s, solar radiation 689 W/m2, temperature 36.1 °C, and tilt angle 25°. The best response/output parameters for the PVTAC can be found using the entropy-VIKOR method’s optimal setup. Increased thermal and electrical efficiency, as well as enhanced performance and efficiency, is provided by the optimal circumstances for the PVTAC.  In the end, confirmatory tests are run to double-­ check the results with the experimental results, and it is determined that the results are comparable and acceptable. In light of these findings, it is stated that the suggested hybrid MCDM technique can be used as a systematic framework model for modelling and optimization of various wind turbines. Less attention has been paid on research for the development and applications of other MCDM methods, such as TOPSIS, PROMETHEE, OCRA, JAYA, etc., for optimizing wind turbines, even

References

125

though this chapter provided the application of entropy-VIKOR-based MCDM method for modeling and optimizing the performance of PVTAC parameters under built environment.

References 1. Peng, D., Zhang, X., Dong, H., & Kun, L. (2010). Performance study of a novel solar air collector. Applied Thermal Engineering, 30, 2594–2601. 2. Shi, Q., Lv, J., Guo, C., & Zheng, B. (2017). Experimental and simulation analysis of a PV/T system under the pattern of natural circulation. Applied Thermal Engineering, 121, 828–837. 3. Mellor, A., Alvarez, D.  A., Guarracino, I., Ramos, A., Lacasta, A.  R., Llin, L.  F., Murrell, A. J., Paul, D. J., Chemisana, D., Markides, C. N., & Daukes, N. J. E. (2018). Roadmap for the next-generation of hybrid photovoltaic-thermal solar energy collectors. Solar Energy, 174, 386–398. 4. Siecker, J., Kusakana, K., & Numbi, B. P. (2017). A review of solar photovoltaic systems cooling technologies. Renewable and Sustainable Energy Reviews, 79, 192–203. 5. Xondag, H. A. (2008). Flat-plate PV-thermal collectors and systems: A review. Renewable and Sustainable Energy Reviews, 12, 891–959. 6. Hasan, A., Cormack, S., Huang, M., & Norton, B. (2010). Evaluation of phase change materials for thermal regulation enhancement of building integrated photovoltaics. Solar Energy, 84, 1601–1612. 7. Moradi, K., Ebadian, M. A., & Lin, C. X. (2013). A review of PV/T technologies: Effects of control parameters. International Journal of Heat and Mass Transfer, 64, 483–500. 8. Nahar, A., Hasanuzzaman, M., & Rahim, N. A. (2017). Numerical and experimental investigation on the performance of a photovoltaic thermal collector with parallel plate flow channel under different operating conditions in Malaysia. Solar Energy, 144, 517–528. 9. Wolf, M. (1976). Performance analyses of combined heating and photovoltaic power systems for residences. Energy Conversion, 16, 79–90. 10. Kern, E. C., & Russell, M. C. (1978). Combined photovoltaic and thermal hybrid collector systems. Massachusetts Institute of Technology, Lexington, Lincoln Lab. 11. Hegazy, A. A. (2000). Comparative study of the performances of four photovoltaic/thermal solar air collectors. Energy Conversion and Management, 41, 861–881. 12. Dubey, S., Solanki, S. C., & Tiwari, A. (2009). Energy and exergy analysis of PV/T air collectors connected in series. Energy and Buildings, 41, 863–870. 13. Charalambous, P.  G., Maidment, G.  G., & Kalogirou, S.  A. (2007). Photovoltaic thermal (PV/T) collectors: A review. Applied Thermal Engineering, 27, 275–286. 14. Slimani, M., Amirat, M., Kurucz, I., Bahria, S., Hamidat, A., & Chaouch, W.  B. (2017). A detailed thermal-electrical model of three photovoltaic/thermal (PV/T) hybrid air collectors and photovoltaic (PV) module: Comparative study under Algiers climatic conditions. Energy Conversion and Management, 133, 458–476. 15. Sopian, K., Yigit, K. S., Liu, H. T., Kakac, S., & Veziroglu, T. N. (1996). Performance analysis of photovoltaic thermal air heaters. Energy Conversion and Management, 11, 1657–1670. 16. Jha, P., Das, B., & Gupta, R. (2020, November 5). Performance of air-based photovoltaic thermal collector with fully and partially covered photovoltaic module. Applied Thermal Engineering, 180, 115838. 17. Gupta, A., Das, B., & Mondol, J. D. (2022, December 31). Experimental and theoretical performance analysis of a hybrid photovoltaic-thermal (PVT) solar air dryer for green chillies. International Journal of Ambient Energy, 43(1), 2423–2431.

126

6  Optimization of a Photovoltaic Thermal Solar Collector Using Entropy-VIKOR…

18. Das, B., Mondol, J. D., Negi, S., Smyth, M., & Pugsley, A. (2021, February 1). Experimental performance analysis of a novel sand coated and sand filled polycarbonate sheet based solar air collector. Renewable Energy, 164, 990–1004. 19. Wu, C. S., Lin, C. T., & Lee, C. (2010). Optimal marketing strategy: A decision-making with ANP and TOPSIS. International Journal of Production Economics, 127, 190–196. 20. Singh, R.  K., & Benyouce, L. (2011). A fuzzy TOPSIS based approach for e-sourcing. Engineering Applications of Artificial Intelligence, 24, 437–448. 21. Sánchez-Lozano, J. M., Teruel-Solano, J., Soto-Elvira, P. L., & García-Cascales, M. S. (2013). Geographical information systems (GIS) and multi-criteria decision making (MCDM) methods for the evaluation of solar farms locations: Case study in South-Eastern Spain. Renewable and Sustainable Energy Reviews, 24, 544–556. 22. Aragonés-Beltrán, P., Chaparro-González, F., & Pastor-Ferrando, J. P. (2014). An AHP (analytic hierarchy process)/ANP (analytic network process)-based multi-criteria decision approach for the selection of solar-thermal power plant investment projects. Energy, 66, 222–238. 23. Reddy, J., Debnath, S., & Das, B. (2019, October). Energy and exergy analysis of wavy plate solar air collector using a novel hybrid expert system. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41(10), 1–4. 24. Debnath, S., Reddy, J., Das, B., & Jagadish. (2019, July 28). Modeling and optimization of flat plate solar air collectors: An integrated fuzzy method. Journal of Renewable and Sustainable Energy, 11(4), 043706. 25. Yunn, W., & Geng, S. (2014). Multi-criteria decision making on selection of solar–wind hybrid power station location: A case of China. Energy Conversion and Management, 81, 527–533. 26. Yahyaoui, I., Atieh, A., Tadeo, F., & Tina, G. M. (2017). Energetic and economic sensitivity analysis for photovoltaic water pumping systems. Solar Energy, 144, 376–391. 27. Kabalci, Y., & Kabalci, E. (2017). Modeling and analysis of a smart grid monitoring system for renewable energy sources. Solar Energy, 153, 262–275. 28. Saaty, T.  L. (2001). Decision making with dependence and feedback: The analytic network process: The organization and prioritization of complexity. RWS Publications. ISBN: 0962031798. 29. Saaty, T. L. (1980). The analytic hierarchy process. McGraw-Hill. 30. Hwang, C. L., & Yoon, K. (1981). Multiple attribute decision making, a state of the art survey. Springer. 31. Agrawal, S., & Tiwari, G.  N. (2011). Energy and exergy analysis of hybrid micro-channel photovoltaic thermal module. Solar Energy, 85, 356–370. 32. Tiwari, A., & Sodha, M. S. (2006). Performance evaluation of hybrid PV/thermal water/air heating system: A parametric study. Renewable Energy, 31, 2460–2474. 33. Bosonac, M., Sorensen, B., Katic, I., Sorensen, H., Nielsen, B., & Badran, J. (2003). Photovoltaic/thermal solar collector and their potential in Denmark. Final Report, EEP Project 28, 1713-0014. 34. Petela, R. (1964). Exergy of heat radiation. Journal of Heat Transfer, 2, 187–192. 35. Tong, L.  I., Chen, C.  C., & Wang, C.  H. (2007). Optimization of multi-response processes using the VIKOR method. International Journal of Advanced Manufacturing Technology, 31, 1049–1057. 36. Deng, J. L. (1989). Introduction to grey system. Journal of Grey Systems, 1(1), 1–24.

Index

A Artificial neural network (ANN), 7, 9, 10, 14, 23, 41–61, 64, 65, 80 E Energy efficiency, 12–14, 25, 29, 31, 32, 36, 38, 46, 48, 49, 57, 58, 61, 66, 68–72, 74, 78, 79, 81, 85, 88–90, 92–93, 96, 98, 107 Entropy, 25, 64, 79, 80, 83, 85–89, 98, 105–125 Evolutionary techniques, v Exergy efficiency, 13, 24, 26, 27, 29, 31, 33, 34, 36, 38, 44, 46, 48, 50, 51, 57–59, 61, 63, 71, 77–80, 82, 83, 85, 88–90, 92–96, 98, 107, 117, 121, 124 F Fuzzy logic-based expert system (FLES), 12, 13, 63–74, 79 G Grey relational analysis (GRA), 24, 27–28, 33, 38, 107 J JAYA, 80, 85, 87–89, 98, 124

M Multi-criteria decision-making (MCDM), 23–25, 79, 80, 96, 98, 106, 107, 111–113, 117–119, 121, 124, 125 O Optimization, 6–9, 12–15, 25, 33–38, 54, 64–67, 74, 79, 80, 85, 89, 96–98, 105–125 S SAC systems, 13 Sand-coated, 7, 68, 74, 78, 106 Soft computing, 7–15 Solar air collector (SAC), 7, 9, 10, 13, 23–38, 42, 43, 46–48, 50, 52, 55–57, 63–68, 74, 77–98, 100, 101, 106, 107, 110, 121 Solar energy, 1, 2, 4, 10, 11, 15, 23, 25, 43, 63, 71, 77, 81, 105 Solar PVT system, 117–119 Solar thermal collector, 2, 3, 8, 12, 15, 24, 42 Sustainability index (SI), 83–85, 88–90, 92, 96–98 T Thermal efficiency (TE), 2, 7–9, 12, 14, 24, 25, 44, 64, 72, 78, 106, 109 Thermal energy, 2, 4, 10, 11, 25–26, 41, 43, 47, 63, 77, 81, 108, 110, 115, 117, 118, 120, 121, 123, 124

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023 B. Das, Jagadish (eds.), Evolutionary Methods Based Modeling and Analysis of Solar Thermal Systems, Mechanical Engineering Series, https://doi.org/10.1007/978-3-031-27635-4

127

128 Thermal performance, 4, 9, 10, 12, 13, 23, 24, 41–43, 63–74, 78, 79, 81, 108 Trapezoidal absorber plate, 92

Index V Value in Knowledge Organization (VIKOR), 24, 105–125