Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications [1 ed.] 9781620815427, 9781612093796

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Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

MECHANICAL ENGINEERING THEORY AND APPLICATIONS

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COOLING SYSTEMS: ENERGY, ENGINEERING AND APPLICATIONS

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MECHANICAL ENGINEERING THEORY AND APPLICATIONS

COOLING SYSTEMS: ENERGY, ENGINEERING AND APPLICATIONS

AARON I. SHANLEY

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EDITOR

Nova Science Publishers, Inc. New York Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

Copyright © 2011 by Nova Science Publishers, Inc. All rights reserved. No part of this book may be reproduced, stored in a retrieval system or transmitted in any form or by any means: electronic, electrostatic, magnetic, tape, mechanical photocopying, recording or otherwise without the written permission of the Publisher. For permission to use material from this book please contact us: Telephone 631-231-7269; Fax 631-231-8175 Web Site: http://www.novapublishers.com NOTICE TO THE READER The Publisher has taken reasonable care in the preparation of this book, but makes no expressed or implied warranty of any kind and assumes no responsibility for any errors or omissions. No liability is assumed for incidental or consequential damages in connection with or arising out of information contained in this book. The Publisher shall not be liable for any special, consequential, or exemplary damages resulting, in whole or in part, from the readers‘ use of, or reliance upon, this material. Any parts of this book based on government reports are so indicated and copyright is claimed for those parts to the extent applicable to compilations of such works.

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Independent verification should be sought for any data, advice or recommendations contained in this book. In addition, no responsibility is assumed by the publisher for any injury and/or damage to persons or property arising from any methods, products, instructions, ideas or otherwise contained in this publication. This publication is designed to provide accurate and authoritative information with regard to the subject matter covered herein. It is sold with the clear understanding that the Publisher is not engaged in rendering legal or any other professional services. If legal or any other expert assistance is required, the services of a competent person should be sought. FROM A DECLARATION OF PARTICIPANTS JOINTLY ADOPTED BY A COMMITTEE OF THE AMERICAN BAR ASSOCIATION AND A COMMITTEE OF PUBLISHERS. Additional color graphics may be available in the e-book version of this book. LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA Cooling systems : energy, engineering, and applications / editor, Aaron I. Shanley. p. cm. Includes index. ISBN 978-1-62081-542-7 (e-Book) 1. Refrigeration and refrigerating machinery. 2. Cooling. I. Shanley, Aaron I. TP492.C678 2010 621.5'6--dc22 2010051505

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CONTENTS Preface Chapter 1

Radiant Cooling Combined with Ventilation Systems Francesco Causone and Stefano Paolo Corgnati

Chapter 2

Applications of Impingement Jet Cooling Systems Hyung Hee Cho, Kyung Min Kim and Jiwoon Song

Chapter 3

Numerical Discrete Ordinates Method for Radiation Energy Transport Modeling for Thermal Comfort Cooling M. M. Ardehali

69

A Low Neutron Absorbing Coolant for Fast Reactors and Accelerator Driven Systems G. L. Khorasanov and A. I. Blokhin

89

Chapter 4

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vii

Chapter 5

Optimization of Airfoil‘s Cooling Passages Grzegorz Nowak and Iwona Nowak

Chapter 6

Cooling Systems: Retrofit and Thermo-Hydraulic Design for Flexible Operation Martín Picón-Núñez, Lázaro Canizales-Dávalos and Graham T. Polley

Chapter 7

Chapter 8

Study on Adsorption and Thermoelectric Cooling Systems Using Boltzmann Transport Equation Approach Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng and Ibrahim I. El-Sharkawy New Progress in Liquid Desiccant Cooling Systems: Adsorption Dehumidifier and Membrane Regenerator Xiu-Wei Li and Xiao-Song Zhang

Index

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1 37

99

135

145

209 221

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PREFACE This new book examines the energy, engineering and application issues of cooling systems. Topics discussed include radiant cooling combined with ventilation systems; the applications of impingement jet cooling systems; solar cooling systems; liquid desiccant cooling systems and thermoelectric cooling systems using the Boltzmann transport equation approach. Chapter 1 - Radiant heating is currently a widespread technology, while radiant cooling is still often used with hesitation, because of the flaws reported for early applications and the consequent concerns. The use of a proper control and the combination with a ventilation system may avoid nevertheless the common risks associated with this technology, especially condensation. Combining a high temperature radiant cooling system with a ventilation system it is possible to obtain energy savings and a reduction of greenhouse gas emissions, because ventilation airflow rates can be substantially reduced. The combination of radiant cooling with a suitable ventilation strategy can moreover largely increase the cooling capacity of the system. Nevertheless a careful design process is required in order to associate the proper ventilation strategy to the radiant system. The opportunities and threats related to the matched use of radiant cooling and ventilation are reported, highlighting last findings of research. Chapter 2 - This book chapter discussed impingement jet cooling. Jet impingement achieves locally high heat transfer on an interested surface. For these reasons, the impinging jet cooling technique has been widely used in many industrial systems such as gas turbine cooling, rocket launcher cooling and high-density electrical equipment cooling in order to remove a large amount of heat. In this chapter, experimental and numerical investigations are reviewed on flow and heat transfer characteristics of impinging jets. The review included the general single jet and jet impingement; their active controls; high speed jet flows and jet impingement; liquid impinging jet cooling; array jet impingement; array jet impingements on effusion surface. In detail, to enhance the heat transfer in single and array jets, there is discussion on design and control of nozzle geometry, nozzle insertion, jet vibration, secondary injection, and suction flow. In addition, effects of various factors have been concerned with different operating conditions (crossflow, rotation, compressible flow, working fluid, etc.) and combined techniques (rib turbulator, pin fin, dimple, effusion hole, etc.).

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Aaron I. Shanley

Chapter 3 - One of the fundamental necessities that must be accommodated in a habitable environment is thermal comfort. When the associated cost for maintaining adequate comfort condition is to be minimized, the issue of energy transport between the occupant and the surroundings becomes an important factor. Thermal comfort cooling by means of a cooling panel (CP) placed inside a thermal zone utilizes radiative and convective transfer to fully or partially offset the thermal load of the zone. As a result of employing this concept, radiative and convective transfer modes are used for thermal comfort conditioning and, as a result, an increase in energy efficiency is anticipated. This concept also decouples the heat transfer function from the ventilation function of the air in a thermal zone. This decoupling may be beneficial in addressing the indoor air quality (IAQ) requirements. The concept of thermal conditioning by radiation and convection could be employed to reduce energy consumption in commercial office buildings, manufacturing plants, clean rooms, and health-care facilities. For existing office buildings, where newly added office automation equipment and computers result in increased internal cooling loads that were not accounted for in the original design of the air conditioning system, CPs that are cooled could be used to offset the increased thermal load. The utilization of CPs connected to the return line of the existing chilled water system is a viable choice. Thus, the need for required space for installing additional ductwork to handle the increased cooled air flow to offset the cooling load is eliminated. It is of interest to investigate methods of thermal conditioning by a CP where effects of radiation and convection are simultaneously accounted for in the comfort analysis of the occupant and in the efficiency analysis of the cooling system. The objective of this chapter is to present the modeling procedure for radiation energy transport utilizing numerical discrete ordinates method (DOM) for thermal comfort cooling, where the necessary IAQ standards are met. While the focal view of the chapter is on development of DOM for radiation energy transport modeling for thermal comfort cooling, the dependency of thermal comfort model on convection transfer along with its analytical treatment are discussed. The system description and the analysis are presented in Sections 2 and 3. The analysis section includes the models used for the cooling systems, occupant comfort, and radiative and convective heat transfer. Numerical accuracy of DOM is discussed in Section 4. In Sections 5, summary and final remarks are given. Chapter 4 - In the paper one-group cross sections of neutron radiation capture, , by 208Pb, 238U, 99Tc, lead natural, natPb, mix of lead and bismuth, Pb-Bi, averaged over neutron spectra of the critical and subcritical fast reactors are given. It is shown that onegroup cross sections of neutron capture by material of the FR and ADS coolant consisted from lead enriched with the stable lead isotope, 208Pb, are by 4-7 times smaller than for the coolant consisted from natPb or Pb-Bi. The economy of neutrons in the core cooled with 208Pb can be used for reducing reactor‘s initial fuel load, increasing fuel breeding and transmutation of long lived fission products, for example 99Tc. Good neutron and physical features of lead enriched with 208Pb permit to consider it as a perspective low neutron absorbing coolant for fast reactors and accelerator driven systems. Chapter 5 - This chapter discusses issues related to the optimization of the cooling system of the blade of the gas turbine. Systems with both cylindrical cooling passages and with passages with any sections were considered. In the former case the optimization task consisted in finding the location and diameter of the passages; in the latter - as well as finding the location, it also involved the determination of the optimal shape of the cooling holes. To

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Preface

ix

model the shape the Bezier curves, forming closed profiles of the cooling holes, were used. Additionally, in order to match the shape of the passage to the blade profile, a technique was put forward to copy and scale the profile fragments into the component, and build the contour of the passage on the grounds of them. In both cases the task was solved as a multi-objective problem with the use of the Pareto approach. Also, comparative optimization calculations for the scalar objective function were carried out and set up against the non-dominated solutions obtained in the Pareto approach. The evolutionary algorithm was used as the optimization tool, and the testing calculations were made for profile C3X available in reference literature. It was assumed that the cooling agent of the blade was either air or steam. The evaluation of individual configurations was made on the grounds of thermal-strength analyses with the use of the Finite Element Method (FEM). For comparative purposes, the optimization task was also solved by means of conjugate analyses of heat transfer (CHT). The optimization process resulted in configurations of the cooling system that allow a substantial reduction in both the temperature of the blade and its thermal stress, with decreased flow rate of the cooling agent. Chapter 6 - During the operation of cooling systems, many situations may arise. For instance, the cooling demands of a process may increase to such an extent that the cooling capacity is surpassed. The opposite extreme is when the whole cooling system, consisting of a cooling tower, a network of coolers and the pumping system is over designed; in such situations the cooling demand of the process is always supplied; however, the installed surface area and the pumping costs are much higher than they should be. Yet a different situation is when new heat exchangers are placed into the system. The consequence of this action is that the thermal and hydraulic performance of the system changes, therefore effecting the operation of other coolers since the water flow distribution is modified due to the changes in pressure drop induced by the new unit. All these effects have to be analyzed so that measures are taken in order to maintain the operation of the process within the required temperature bounds. The cooling needs of a process may change due to the increase or decrease of the plant throughput. However, most installed cooling systems are also affected by changes in the ambient conditions. An example of this is the change in wet bulb temperature. All of these situations have to be considered when undertaking the design of a cooling system. In the first part of this paper, a practical technique for the retrofit of cooling systems that aims at reducing power consumption due to pumping is presented. The second part introduces a design approach that takes into consideration the need for a flexible operation that seeks to maintain operating costs at a minimum. The kind of cooling systems considered in this study are those composed of a water recycling evaporative cooling tower with counter-current operation. Chapter 7 - In this chapter, the Boltzmann Transport Equations (BTE) is used to formulate the transport laws for equilibrium and irreversible thermodynamics and these BTE equations are suitable for analyzing system performance that are associated with systems ranging from macro to micro dimensions. In this regard, particular attention is paid to analyze the energetic processes in adsorption phenomena as well as in semiconductors from the view point of irreversible thermodynamics. The continuity equations for (i) gaseous flow at adsorption surface, and (ii) electrons, holes and phonons movements in the semiconductor structures are studied. The energy and entropy balances equations of (i) the adsorption system for macro cooling, and (ii) the thermoelectric device for micro cooling are derived that lead to

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expressions for entropy generation and system‘s bottlenecks. The BTE equation is applied to model the adsorption cooling processes for single-stage, multi-stage and multi-bed systems, and the simulated results are compared with experimental data. This chapter also presents a thermodynamic framework for the estimation of the minimum driving heat source temperature of an advanced adsorption cooling device from the rigor of Boltzmann distribution function. From this thermodynamic analysis, an interesting and useful finding has been established that it is possible to develop an adsorption cooling device as a green and sustainable technology that operates with a driving heat source temperature of near ambient. Moreover, the Onsager relations are applied to model the thermoelectric transport equations and, after coupling with Gibbs law and BTE, the temperature-entropy flux derivations are further developed and presented the energetic performances of thermoelectric cooling systems. Chapter 8 - A liquid desiccant cooling system (LDCS) is a new type of air-conditioning system with good energy-saving potential. Its performance is dominated by dehumidification and regeneration processes. At present, few works have been done to propose a general principle for better dehumidifier design and most works about regeneration are only concentrated on the thermal regeneration method. For both aspects, new progress has been made and presented in this paper. On one hand, a new design method has been derived from the experiments: an adsorption dehumidifier, developed by integrating a solid desiccant with liquid dehumidifier, could greatly improve the dehumidification effects. On the other hand, a new regeneration style has been conceived: a membrane regenerator, which consists of many alternatively placed cation- and anion-exchange membranes, would regenerate the liquid desiccant in an electrodialysis way; while a solar photovoltaic generator provides electric power for fueling this process. This new regeneration method is immune from the adverse impact from outside high humidity, and it also has a pretty good performance, as well as the benefit that purified water can be obtained along with the regeneration process. These two developments can make LDCS more practical and competitive in the future market.

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In: Cooling Systems: Energy, Engineering and Applications ISBN 978-1-61209-379-6 Editor: Aaron I. Shanley © 2011 Nova Science Publishers, Inc.

Chapter 1

RADIANT COOLING COMBINED WITH VENTILATION SYSTEMS Francesco Causone1 and Stefano Paolo Corgnati Politecnico di Torino, Department of Energetics, TEBE Gruop Corso Duca degli Abruzzi 24, IT-10129 Torino (Italy)

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ABSTRACT Radiant heating is currently a widespread technology, while radiant cooling is still often used with hesitation, because of the flaws reported for early applications and the consequent concerns. The use of a proper control and the combination with a ventilation system may avoid nevertheless the common risks associated with this technology, especially condensation. Combining a high temperature radiant cooling system with a ventilation system it is possible to obtain energy savings and a reduction of greenhouse gas emissions, because ventilation airflow rates can be substantially reduced. The combination of radiant cooling with a suitable ventilation strategy can moreover largely increase the cooling capacity of the system. Nevertheless a careful design process is required in order to associate the proper ventilation strategy to the radiant system. The opportunities and threats related to the matched use of radiant cooling and ventilation are reported, highlighting last findings of research.

SYMBOLS A [m2] ao [m2] Ar [ - ] ACH [-] AUST [K]

area supply effective area of the jet Archimedes number air change per hour average unheated surface temperature

1 e-mail: [email protected]. web-site: www.polito.it/tebe. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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c [ppm] cp [J/kgK] CC CH Dh [m] DR [%] DV Fε, s-j [-] Fs-j [-] FC FH g [m/s2] hc [W/m2K] hc,h [W/m2K] hr [W/m2K] hr,h [W/m2K] htot [W/m2K] k [-] Ka [-] Ksa [-] m [kg/s] MV NC q [W] qc [W] qr [W] q‖n [W/m2] Ta [K] Tad [K] TD [K] Te [K] Tf [K] Ti [K] Tj [K] Tmr [K] To [K] Top [K] Tp [K] Ts [K] Tsp [K] Tu [%] tx [m] ty [m] uo [m/s] vp [m/s]

contaminant concentration specific heat coefficient ceiling cooling ceiling heating hydraulic diameter draft rate displacement ventilation interchange factor view factor between the studied surface and the j-surface floor cooling floor heating gravitational acceleration coefficient convective heat transfer coefficient human body convective heat transfer coefficient radiant heat transfer coefficient human body radiant heat transfer coefficient total heat transfer coefficient dimensionless temperature of the air at the floor level constant of the specific supply device constant depending on parameters outside the jet (location of thermal load, room dimension, etc.) mass air flow mixing ventilation natural convection heat flux convective heat flux radiant heat flux heat transfer rate in the n direction per unit area air temperature adjusted air temperature effective draft temperature exhaust air temperature air temperature at the floor level room air temperature temperature of the j-surface mean radiant temperature supply air jet temperature operative temperature air temperature at point P surface temperature supply air temperature air turbulence intensity longitudinal throw of the jet vertical throw (drop) of the jet supply air jet velocity air velocity at point P

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Radiant Cooling Combined with Ventilation Systems xs [m] λ [W/mK] λn [W/mK] ∂T /∂n [K/m] dT /dx [K/m] σ [-] Ф [W] ΔT [K] β [1/K]  [-]

3

penetration length of the jet thermal conductivity thermal conductivity in the n direction temperature gradient in the n direction temperature gradient in the x direction Stefan–Boltzmann constant heat flux removed by displacement ventilation characteristic temperature difference thermal expansion coefficient ventilation effectiveness

1. INTRODUCTION Low temperature and high temperature radiant heating have been extensively used to control indoor climate in buildings [1, 2]: mostly low temperature floor heating in dwelling and tertiary buildings [3, 4] and high-intensity infrared equipments in industrial, commercial, and military applications [1]. The major advantages of low temperature radiant heating systems, which represent the lager part of the applications, are the following:  

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

  



comfort levels can be better than those of other conditioning systems because radiant loads are balanced directly and low velocity air motions develop in the space; generating low air movements, and consequently low dust movements, indoor air quality may be further improved; the high level of radiant heat transfer between the radiant surface and the indoor environment makes it possible to reduce the room air temperature still maintaining the required level of operative temperature; ventilation heat losses are then reduced, ensuring energy saving; the entire floor area can be freely used, ensuring an efficient use of space and no limitations on architectural design or occupant use; noise associated with fan-coil or induction units is eliminated; using heat carriers with a very limited convertibility potential, such as water with a temperature close to the room operative temperature, radiant systems may provide a control of indoor thermal environment, with lower energy consumptions compared to other conditioning systems (radiators, fan coils, all-air conditioning systems); heat carriers with moderate temperature encourage the use of renewable energy sources and technologies, such as: ground heat exchangers, heat pumps, solar heating panels, etc., potentially providing further energy savings.

Almost all the same advantages can be achieved by using high temperature radiant cooling [5, 6]. Moreover, a common central air system, coupled to the radiant system, can serve both the interior and perimeter zones and wet surface cooling coils are eliminated from the occupied space, reducing the potential for septic contamination [2].

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Radiant cooling applications are nevertheless still limited: ceiling cooling has been used in some European countries, mainly in office buildings, but is not yet a widespread technology in U.S. [7]; floor cooling applications are instead still a few all over the world, although a remarkable example is the Bangkok airport [4, 8, 9]. As highlighted by Mumma [7], the major concerns regarding radiant cooling are:   

condensation concerns; cooling capacity doubts and concerns; first cost penalty concerns compared to conventional systems.

Many scientists and designers tried to tackle the issue in recent years [6, 7, 10-16]. As resulted in many studies, both floor and ceiling cooling guarantee high levels of thermal comfort, usually better than those of other conditioning systems, while first costs with experienced contractors can reduce, compared to a conventional all-air system [5, 7]. Condensation risk is the main flaw of the system, which should not, actually, be considered unless there is another parallel system in place to decouple the space sensible and latent loads [7, 12]. As underlined in many publications by Mumma [13-16], a dedicated outdoor air system (DOAS) may be a feasible and effective solution combined with radiant cooling, to prevent condensation and to enhance system performance. The major opportunities are to couple mixing or displacement ventilation to ceiling or floor cooling. Both of the alternatives show advantages and limitations, that should be considered in the design phase of the hybrid system and its control.

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2. RADIANT SYSTEMS When talking about radiant systems it is necessary to start form a clear definition and classification, because a lot of different technologies are currently gathered under the general label of radiant systems.

2.1. Definition and Classification The most relevant definition of radiant system is the one reported in the Equipment volume of ASHRAE Handbook [2] and by Watson and Chapman [17]: «a surface from which at least fifty percent of energy transfer is accomplished through radiation». In both of the references it is used referring to radiant panels only, while in the Applications volume of ASHRAE Handbook [1] it is specified that: «radiant heating and cooling applications are classified as panel heating or cooling if the surface temperature is below 150°C and are classified as low-, medium-, or high-intensity if the surface or source temperature range exceeds 150°C». As a matter of fact, in HVAC applications a radiant source is always a surface (floors, ceilings, plates, heaters, strip heaters, etc.), thus the definition reported by Watson and Chapman seems to be the most proper one, focusing on the major characteristic that all

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Radiant Cooling Combined with Ventilation Systems

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radiant systems share: a relevant part of heat transfer accomplished through radiation (at least fifty percent). As pointed out by ASHRAE Handbook [1], radiant heating applications are divided between low temperature and high temperature heating, depending on the radiant surface temperature, while radiant cooling applications only concern high temperature cooling, because the radiant surface temperature cannot drop below room dew-point temperature. It is furthermore common reading about low temperature heating and high temperature cooling, with reference to the temperature of the heat carrier used by the system [4]. However the radiant surface temperature strictly depends on the heat carrier temperature. By referring to the heat carrier, the attention is focused on the heating/cooling generation system, thus on energy issues; by referring to the radiant surface, the attention is focused on the occupied space and on thermal comfort issues [18].

Figure 1. Radiant floor panels - wet system.

Figure 2. Radiant ceiling panels - dry system. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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Within the large family of radiant systems, a relevant place is occupied by radiant panel systems. Their name derived from the definition of ―panel warming‖ given by professor Arthur H. Barker in the 1908: «small hot water pipes embedded in plaster or concrete» [19, 20]. Radiant panel systems include therefore each kind of system built with hydronic piping (currently also electrical resistances) embedded in plaster, concrete or other materials and characterized by a large surface for heat transfer toward the room. They can be prefabricated (dry systems) or built in place (wet systems) (Figure 1 and 2). Currently radiant panels are use both for heating and for cooling, with surface temperatures far below 150°C, as specified by ASHRAE Handbook [1]. Radiant elements, which are characterised by medium and high operating temperatures, are instead used for heating purposes only. They are mostly applied for heating of large spaces such as hangars, industrial buildings, etc. According to ASHRAE, radiant elements can be classified by their operating temperature:   

Low intensity for source temperatures to 650°C Medium intensity for source temperatures to 980°C High intensity for source temperatures to 2800°C

Table 1. Radiant heating and cooling systems classification, part I

ARRAN HEAT GEMENT CARRIER

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The heat carrier used by radiant systems can be water, electricity or gas, therefore they can be classified as hydronic, electrical or gas systems (Table 1). Another relevant issue concerns the position of the radiant surface in the room. Both radiant panels and radiant elements can be positioned at the ceiling level or on the walls (with limitations for radiant elements due to their temperature) and radiant panels can also be installed at the floor level (Table 1).

Hydronic Electrical

SURFACE TEMPERATURE High Temperature Low Temperature Cooling Heating YES YES NO YES

High Temperature Heating NO YES

Gas

NO

NO

YES

Ceiling Wall

YES YES

YES YES

YES NO

Floor

YES

YES

NO

Radiant systems can furthermore be surface-mounted/suspended units or embedded hydronic tubing (currently also electrical resistances) insulated from the building structure. Radiant elements are typically metallic plates, while radiant panels can be made with many different materials: concrete, plasterboard, gypsum board, metallic alloys, plaster (Table 2). The hydronic piping or the electrical resistance is embedded within one of these

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material while the external surface layer can be made with a different material (wood, plastic, ceramic, etc.) Thermally activated building systems (TABS) can also be considered within the large group of radiant systems, because they exchange, in the room, al least fifty percent of energy through radiation. On the other hand they are different than radiant panel systems, because they act directly on the thermal mass of buildings (slabs, walls).

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MATERIAL

APPEARANCE

Table 2. Radiant heating and cooling systems classification, part II

Surface-mounted

ARRANGEMENT Ceiling Wall YES YES

Floor YES

Embedded

YES

YES

YES

Concrete Plasterboard Gypsum board Metallic Plaster

YES YES YES YES YES

YES YES YES YES YES

YES NO NO YES NO

In TABS the hydronic pipes run inside a structural concrete component of the building, usually a slab. Pipes have generally a diameter between 17 and 20 mm, while the inter-axis between them is usually in the range between 150 and 200 mm. This kind of systems can work by using the floor or the ceiling as the heat transfer surface toward the room, or a combination of both [4]. When TABS are used, there is always a large delay between the thermal stress and its effect on the mechanical plant, due to the influence of the thermal mass of the building. The slab where pipes are embedded collects thermal energy brought by the warm water in the heating season and releases it after a time lag into the room, when heat losses are higher. During the cooling season the slab is cooled down by the water running in the pipes, and it is able to accumulate heat due to peak loads in the room. The accumulated heat is removed by the fluid after a time lag, when thermal loads are lower. Due to the high thermal mass, the control of the system cannot be instantaneous, and thus the temperature in the room fluctuates during the day, requiring the occupants to adapt to it [4].

2.2. Fundamental of Heat Transfer The aim of any heating/cooling system is to provide a comfortable thermal environment for occupants, in order to improve their performance and well-being [4]. The best systems should guarantee it with the minimum energy consumptions and greenhouse gas emissions.

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In order to correctly design and compare different systems it is fundamental to understand the way they exchange heat within the occupied space, with occupants and boundary surfaces. In this section a brief overview of the topic is given, recalling the fundamental of heat transfer related to radiant systems and necessary to understand the following sections. Further detailed analyses can be found in the major manuals about the topic [21, 22].

2.2.1. Conduction Conduction concerns energy transfer through solids, liquids or gases due to molecular or atomic interactions. However the macroscopic approach based on Fourier‘s law is adequate to the purpose of this work. The basic equation for the analysis of conductive heat transfer is Fourier‘s law:

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qn  n

T n

(1)

where the heat flux q‖n is the heat transfer rate in the n direction per unit area perpendicular to the direction of the heat flow (W/m2), λn is the thermal conductivity in the direction n (W/mK), and ∂T /∂n is the temperature gradient in the n direction (K/m). The thermal conductivity is a parameter depending on the material, the temperature and the direction. In isotropic materials such as metals, the thermal conductivity is equal in each direction, while in anisotropic materials such as wood and laminated materials, it varies depending on the direction. Metals show the highest values of thermal conductivity, while insulating materials and gases show the lowest values. In the case of the built environment, conduction is especially relevant to heat transfer through walls, ceilings, floors, and other solid objects subjected to a temperature gradient in a specific direction. The analysis of conductive heat transfer can hence be reduced to the case of one-dimension only. When applied to steady-state conditions, the thermal conductivity can furthermore be considered constant, because independent of the temperature. The Fourier‘s law in one-dimensional form can thus be expressed as: q  A 

dT dx

(2)

where q is the heat flux (W), λ is the thermal conductivity of the medium (W/mK), A is the cross-sectional area for heat flow (m2), and dT/dx is the temperature gradient in x direction (K/m). Inside a radiant panel, the conductive heat transfer occurs through the pipe section (hollow cylinder), through the concrete, gypsum or plasterboard layer (plane wall), through the finishing material (plane wall) and through the backward insulating board (plane wall).

2.2.2. Convection The convective heat transfer describes the exchange of energy between a solid surface and an adjacent fluid at different temperatures. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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Convection can be either natural or forced. Natural convection occurs because of the buoyant forces brought about by temperature gradients; forced convection occurs when a blower, a fan a pump or the wind moves a fluid over a surface. In the case of natural convection, the solid surface increases or decreases the temperature of the adjacent fluid. The fluid volume close to the surface becomes thus more dense or less dense than the remaining part of the fluid. The fluid with higher density tends to move downward, while the fluid with lower density tends to move upward: fluid movements are hence generated. The convective heat transfer depends on several parameters and extensive studies were conducted on it [21, 22]. The convective heat flux exchanged between a solid surface and the surrounding air can, nevertheless, be expressed through Newton‘s law:

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qc  A  hc  Ts  Ta 

(3)

where A is the solid surface area (m2), hc is the convective heat transfer coefficient (W/m2K), qc is the convective heat flux (W), Ta is the room air temperature (K) and Ts is the solid surface temperature (K). The convective heat transfer coefficient expresses the convective heat exchange between the solid surface and the surrounding fluid, due to the temperature difference of one Kelvin degree between the surface temperature and the adjacent fluid temperature. This coefficient depends on several parameters, and, as consequence of it, it is extremely difficult to evaluate its value. The fluid velocity, the fluid properties and the orientation of the surface to the fluid are some of the most important parameters. In the case of forced convection the fluid velocity is the most important parameter, while in the case of natural convection the orientation of the surface to the fluid and the temperature difference between the surface and the fluid are the most important parameters. The equations commonly used for the evaluation of the convective heat transfer coefficient result from experimental measurements. Inside a built environment, convention occurs between the radiant surface and the room air. It is natural convection brought about by temperature gradients. The value of the heat transfer varies a lot depending on the orientation of the surface to the fluid and on the temperature difference between the surface and the fluid. Floor heating and ceiling cooling generate relevant air movements and thus convective heat transfer, while floor cooling and ceiling heating can hardly generate a substantial convective heat transfer, due to the low buoyant forces. High temperature heating elements, due to the high temperature difference with the surrounding air, generate relevant air movements, nevertheless their heating effect is mostly carried out through direct radiant heat transfer with occupants.

2.2.3. Radiation Radiant heat transfer describes the exchange of energy between bodies at different temperatures by means of electromagnetic waves. Thermal radiation can be transferred by solids, fluids or gases, although in the case of the built environment only the radiant heat exchange between solids is accounted. Air is considered not to participate to the heat transfer. Thermal radiation does not need a medium to be exchanged, because electromagnetic waves can move also in the vacuum [21, 22]. As conduction and convection it depends on

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temperature differences between bodies, although thermal radiation is not linearly dependent on the temperature differences, but it tends to be proportional to differences in the fourth power of temperature. Many other parameters influence thermal radiation: wave direction, spatial location (x, y, z), wavelength and time. While analysing the built environment some simplifications are required. In the case of radiant heating and cooling, do not considering solar radiation [23], the radiant heat transfer between surfaces occurs through infrared radiation (IR) with wavelengths higher than 2500 nm. It is important to point out that each surface inside the control volume affects the radiation fields in the control volume, exchanging thermal radiation with the surrounding surfaces. Radiant systems may nevertheless provide a better control of the thermal radiation field compared to other HVAC systems. In the most general conditions, the radiant heat flux exchanged between a surface and the other surfaces in the room can be expressed by the following equation:



n

q r  σ Fε s  j Ts  Tj j1

4

4



(4)

where σ is the Stefan–Boltzmann constant (-), Fε, s-j is the interchange factor (-), Ts is the surface temperature of the studied body (K) and Tj is the temperature of the j-surface (K). The use of the fourth degree is nevertheless uncomfortable for calculations, thus the problem is generally solved through a linearization of the phenomenon. This is possible, introducing the linear radiant heat transfer coefficient:

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n

hr 



σ Fε s  j Ts  Tj j1

4

4



(5)

Ts  AUST

where σ is the Stefan–Boltzmann constant (-), Fε, s-j is the interchange factor (-), Ts is the analysed surface temperature of the studied body (K), Tj is the temperature of the j-surface (K) and AUST is the average unheated surfaces temperature (K). The reference temperature for the calculation of the radiant heat transfer coefficient, is the average unheated surface temperature (AUST) calculated taking into account the view factors between surfaces:

AUST  4

 F n

j 1

s j

Tj

4

 (6)

where Fs-j is the view factor between the studied surface and the j-surface (-), and Tj is the temperature of the j-surface (K). The linear radiant heat transfer coefficient expresses the radiant heat exchange between a specific surface and all the other surfaces in the room, due to the temperature difference of one Kelvin degree between the specific surface temperature and the AUST. The actual radiant

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heat flux exchanged between the radiant surface and the surrounding surfaces in the room can therefore be expressed through the following equation:

q r  A  hr  Ts  AUST 

(7)

where qr is the radiant heat flux (W), hr is the linear radiant heat transfer coefficient (W/m2K), Ts is the analysed surface temperature of the studied body (K) and AUST is the average unheated surfaces temperature (K).

2.2.4. Multimode Heat Transfer In actual environments, the radiant heat transfer and the convective heat transfer occur at the same time. The total heat transfer due to the multimode heat exchange can be calculated as the sum of the radiant heat transfer and the convective heat transfer, and it is commonly expressed as surface heat transfer:

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qtot q q  r  c A A A

(8)

where qtot is the total heat flux (W), qr is the radiant heat flux (W), qc is the convective heat flux (W) and A is the area of the studied body (m2). In order to simplify calculations, the total heat transfer is commonly expressed as a function of a total heat transfer coefficient and the temperature difference between the radiant surface and a reference temperature. The most suitable reference temperature is the operative temperature, because it depends both on the air temperature and on the mean radiant temperature in the room [24]. The operative temperature would be a convenient solution as reference, because it is already used as reference for thermal comfort analyses and its use is suggested also for heat load calculations in EN Standard 12831 [25]: qtot  htot  Ts  Top  A

(9)

where htot is the total heat transfer coefficient (W/m2K), Ts is the surface temperature of the studied body (K), Top is the operative temperature (K) and A is the area of the studied body (m2). The operative temperature, for comfort analyses, is express by the equation: Top 

h

c ,h

 Ta   hr , h  Tmr  hc , h  hr , h

(10)

where hc,h and hr,h are respectively the human body convective and radiant heat transfer coefficients (W/m2K), Ta is the air temperature (K) and Tmr is the mean radiant temperature (K). Standards on thermal comfort indicate that in rooms with air velocity lower than 0.2 m/s, and differences between mean radiant temperature and air temperature less than 4 K, the operative temperature can be calculated as the adjusted air temperature:

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Francesco Causone and Stefano Paolo Corgnati Top  Tad 

Ta  Tmr 2

(11)

where Tad is the adjusted air temperature (K), Ta is the air temperature (K) and Tmr is the mean radiant temperature (K). The total heat transfer coefficient expresses the radiant and convective heat transfer between a specific surface and the room, due to the temperature difference of one Kelvin degree between the specific surface temperature and the room operative temperature. This coefficient cannot nevertheless be calculated as the sum of the radiant heat transfer coefficient and the convective heat transfer coefficient, because they refer to different physical phenomena, and therefore they have different reference temperatures (AUST and air temperature) [18, 24]. While the convective heat transfer coefficient is physically defined as the surface conductance between a surface and the air boundary layer, the linear radiant heat transfer coefficient is just a theoretical parameter, created to compare radiant heat transfer to convective heat transfer in multimode heat transfer calculations, but it does not have a physical definition, since radiation does not follow a linear model.

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2.3. Heating and Cooling Capacity of Radiant Systems Heating and cooling capacity of radiant systems depends on thermal comfort limits [2628], which impose mandatory limitations to the radiant surface temperature and to heat transfer coefficient values. Some relevant researches about radiant systems showed that the radiant heat transfer coefficient of low temperature radiant heating and high temperature radiant cooling systems can be assumed nearly constant (5.5 W/m2K), when the radiant surface is a grey-body [24, 29]. The convective heat transfer coefficient is instead a function of many parameters, and especially of the radiant surface temperature and of the air temperature and velocity. Its value can vary a lot [24]. The total heat transfer coefficient, depending both on radiation and on convection cannot be constant as well, however its fluctuations are lower than the convective coefficient. Some values of the total heat transfer coefficient can be found in the literature under steady-state conditions and natural convection (no forced flow in the room) [24]. These values are valid at design conditions. Slightly lower values may be experienced when temperature differences between the radiant surface and the operative temperature in the room are smaller. Radiant floor surface temperature is definitely limited in the standards [26, 27], while ceiling and wall surface temperature limits are derived from radiant asymmetries limits, supposing typical boundary conditions in the room. That is why radiant floor shows only a temperature as limit, while ceiling and wall show a range of temperature (Table 3). In the case of cooling, ceiling and wall surface temperature limits are not derived from radiant asymmetries limits, but they depend on the condensation risk (Table 3). The radiant surface temperature should not be lower than the dew-point temperature in order to avoid condensation. The temperature of 17°C is the dew-point temperature in a room with air temperature 26°C and relative humidity 58%. However it should not be considered as a

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constant value, because the dew-point temperatures within buildings vary noticeably worldwide and through the year, when a mechanical ventilation system is not operated. Table 3. Maximum heating/cooling capacity of radiant systems as a function of total heat transfer coefficients and temperature limits in rooms Total heat transfer coefficient [W m-2 K-1]

Surface temperature limits [°C]

Operative temperature limits [°C]

Maximum capacity

Heating

Cooling

Maximum Minimum (heating) (cooling)

Minimum (heating)

Maximum (cooling)

Heating

Cooling

Ceiling

6

11-13*

27-35

~17**

20

26

42-90

99-117

Wall Floor occupied zone Floor perimeter zone

8

8

27-35

~17**

20

26

56-120

72

11

7

29

19

20

26

99

49

11

7

35

19

20

26

165

49

[W m-2]

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* Many literature publications report a safety value of 11 W m-2 K-1, nevertheless recent measurements (Causone et al. 2009) showed values up to 13 W m-2 K-1, assuming operative temperature as reference. ** Dew-point temperature in a room with air temperature 26°C and relative humidity 58%.

What is mostly evident is that thermal comfort and condensation risk are the actual aspects which impose performance limits to radiant panel systems. Since these are mandatory issues, it is evident that buildings with relevant heat losses or gains cannot be climatically controlled by radiant panel systems if heat losses or gains are not formerly reduced (a different case is the one involving solar radiation [23]). The building envelope design is thus strictly connected to the final performance of the radiant system: a radiant panel system cannot be designed without definitely knowing the building envelope characteristics. Another relevant consideration concerns heat transfer actuated by radiant systems in the room. Whether the radiant heat transfer coefficient is constant (5.5 W/m2K), it is evident that for ceiling heating and floor cooling, more than 78% of the heat transfer is accomplished through radiation and only a low convective heat transfer is activated in the room. Since warm air moves upward, in the case of heating ceiling the warmer air stays close to the ceiling producing just low horizontal movements. Under these conditions a very feeble convective heat transfer may be activated. In the case of floor cooling, the cool air stays close to the floor, because cool air move downward. Also under these conditions a very feeble convective heat transfer may be activated. In order to improve the system performance the convective heat transfer should be enhanced.

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3. COMMON VENTILATION STRATEGIES

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3.1. Ventilation Aims: Indoor Air Quality and Cooling The primary objective of ventilation is to ensure a satisfactory level of indoor air quality. This goal can be coupled with a secondary objective: to maintain the desired air temperature in the indoor environment. The concept of ventilation is therefore directly linked to the issue of indoor air quality (IAQ). The objectives of ventilation, natural or mechanical, can be obtained by adopting different strategies in terms of air distribution, as explained in the following paragraphs. Ventilation and infiltration are terms commonly used and sometimes confused, but they are substantially different. Ventilation means the intentional supply of an air flow in an indoor environment: the ventilation is then linked to the desire to supply a certain amount of air in a room. On the contrary, infiltration is defined as the un-intentional introduction of air within a space: for example, through windows, according to their properties of air permeability, external climatic conditions and internal microclimate parameters, an air flow rate may result even if not linked to the specific will of the occupants. Ventilation and indoor air quality are inextricably linked, but, when does an indoor environment show a good air quality? Or, in a room, when does the air quality is considered acceptable? A general definition, derived from more medical than engineering field, establish that the air quality is acceptable when in the air there are not pollutants in dangerous concentrations, according to the health criteria established by competent authorities. A definition closer to the engineering approach used for thermal comfort evaluations, defines the air quality acceptable when at least 80% of the occupants expressed satisfaction about it [26]. This definition reveals a key feature: all aspects related to environmental comfort (thermo-hygrometric, visual, noise and air quality) introduce the subjectivity of perception and, consequently, subjectivity in the expression of a judgment about the satisfaction addressed to certain microclimatic aspects. Field investigations show that the perception of IAQ not only can vary significantly from person to person, but also people tend to rapidly lose their ability to clearly judge IAQ due to the very short time addiction of persons. The indoor air, contaminated and of poor quality, should be renewed by outdoor air, which is supposed to have higher quality. Moreover, in this process of air exchange, the outside air is typically mixed with indoor air. Therefore, indoor air quality is controlled through the general dilution of pollutants in the environment.

3.2. Mixing Ventilation The limitation to contaminants exposure and the extraction of cooling loads are obtained, in a mixing ventilation system, by acting basically on the supply jet characteristics: the air

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flow path in the room is led by the momentum flow of the jet entering from the supply opening, which creates the desired air mixing in the ventilated space. In fact, the first objective is achieved in mixing ventilation by a high velocity device that supplies air outside the occupied zone. The supply air should possess a sufficiently high momentum to guarantee a well mixing flow inside the room. The second goal, which refers to cooling conditions, is obtained by supplying air at a temperature lower than the room temperature: in this case the supply air jet is defined nonisothermal. As a consequence, designing a mixing ventilation system means mainly to design the air jet, in particular to define its thermal and fluid-dynamic properties in order to obtain the desired air distribution within the indoor environment. The air flow is supplied through a terminal device, and the jet spreads from the terminal device. The occupied zone can be ventilated either by direct drop of the jet into the occupied zone, or by the reverse flow created by the jet itself. In the ideal case of perfect mixing, both the concentration level of contaminants and the air temperature and relative humidity are uniform in the whole room (Figure 3).

Figure 3. A room with mixing ventilation.

The attitude of the ventilation strategy to remove contaminants from the room can be expressed by the ―ventilation effectiveness‖. The mean ventilation effectiveness  is define through the equation: ε

cR  co c co

(12)

where c , co and cR are respectively the mean contaminant concentration in the room and the contaminant concentration of the supplied and removed air (-). Moreover, the ventilation effectiveness in the occupied zone  oc is: ε oc 

cR  co c oc  c o

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(13)

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Francesco Causone and Stefano Paolo Corgnati

where coc is the mean contaminant concentration in the occupied zone (-). With mixing ventilation (see also Figure 3) cR is equal to coc and, as a consequence,    oc  1 .

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The prediction of the air flow in the occupied zone is very important to prevent discomfort for occupants due to draft risk. In fact, considering the jet supplied at ceiling level, short penetration lengths, defined as the distance at which the jet separates from the ceiling, should be avoided, because the jet could enter prematurely the occupied zone by high speeds or low temperatures, causing discomfort. This situation typically occurs when high thermal loads have to be removed and consequently the jet is supplied with a high temperature difference compared to the room. When mixing ventilation is designed, two basic parameters should be clearly evaluated: the air jet throw, defined as the distance from the supply device where the jet velocity (ux, in Figure 4) shows a fixed value, and the maximum value of the jet velocity acceptable in the occupied zone to avoid draft risk for occupants.

Figure 4. Air jet throw.

These two parameters can be calculated by the designer through analytical formulas, or obtained by tests performed on the supply terminal devices. The study of the air flow inside the room and the evaluation of the position where the jet enters the occupied zone are necessary in order to find out where and to what extent draft risk may occur. With reference to the analytical formulas, the thermal and fluid dynamic characteristics of the supply air jet can be expressed by the jet Archimedes number that is the ratio of thermal buoyancy forces to inertial force: Ar 

β  g  a o  Ti  To  u o2

(14)

where in particular ao ,To and uo define the supply jet properties (see also ―Symbols‖).

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The supply jet is also characterised in the more usual terms of penetration length and throw. The jet penetration length xs is defined as the distance from the supply terminal device where a wall jet separates from the ceiling and starts dropping down toward the occupied zone. It may be expressed as a function of the jet Archimedes number Ar, by means of the formula valid for three-dimensional wall jets [30]: xs ao

 1   0.19  K sa  K a     Ar 

0.5

(15)

where Ksa and Ka are constants defined for the specific supply device. The jet throw is defined as the horizontal (tx) or vertical (ty) axial distance from the supply device where the maximum velocity in the stream cross section is reduced to a predefined terminal velocity, typically ranging from 0.25 to 1 m/s [31]. The air jet flow pattern inside the room has a direct influence on thermal comfort perceived by occupants. In order to evaluate the Draft Rate (DR), i.e. the percentage of dissatisfied people due to draft into the occupied zone [27], the following equation may be used:

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DR = (34-Tp) (vp-0.05)0.62 (0.37 vp Tu + 3.14)

(16)

where Tp (K), vp (m/s) and Tu (%) are respectively the temperature, the velocity and the turbulence intensity of the air at the point P. The part of the room up to 1.8 m above the floor was assumed as the occupied zone. In addition to this ―field‖ approach, a concise index, the Air Diffusion Performance Index (ADPI) [31], is usually used. It represents the volume fraction (and not, as usual, the percentage of locations) of the occupied zone where the following conditions are simultaneously verified:  

air speed less than 0.35 m/s effective draft temperature -1.5 K < TD < 1 K

TD  Tp  Ti   8  Vp  0.15

(17)

where TD is the effective draft temperature (K). Moreover, another related index named ADPIDR (Air Diffusion Performance Index referred to Draft Rate) can be used, defined as the volume fraction of the occupied zone where DR  15%, as required by standard ISO 7730 [27].

3.3. Displacement Ventilation Displacement ventilation was developed as a new strategy to overcome threats remarked for mixing ventilation: bothering for cold air draft and consequent local discomfort, low

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Francesco Causone and Stefano Paolo Corgnati

ventilation effectiveness (much lower than the theoretical value) and the excessive use of transport energy for all-air systems [6]. The early applications of displacement ventilation were made in Scandinavian countries, but later other countries showed interest in the new strategy, e.g. Germany, England, Japan and U.S.A. [32], and currently some applications have been installed also in Mediterranean countries such as Spain, Italy and Greece and in Asiatic countries. As underlined by Skistad [33]: «ventilation in the Nordic countries has always been displacement ventilation driven by buoyancy, with more or less thermal stratification inside the rooms. In non-industrial premises, this was so until the modern ventilation techniques entered the stage and made ventilation synonymous with mixing the air in the room. In industrial premises, natural ventilation with displacement effects remained in parallel with mechanically driven ventilation and various ventilation principles». Displacement ventilation was scientifically studied first for industrial applications from the 1940‘s to the 1970‘s [34] and later, in the 1980‘s, its application was investigated further for non-industrial premises. The basic idea of displacement ventilation is to keep fresh supply air and stale room air separated, and it involves introducing the air at low speed directly into the occupied zone at a temperature usually slightly lower than the room air temperature. When displacement ventilation is used, vertical air movements generated by heat sources in the room are enhanced and a thermal stratification is definitely produced. The fresh supply air spreads all over the floor until it meets a heat source. If the heat source is also a contaminant source, the supply air, while raising up exploiting the heat plum, removes the contaminant exactly where it is produced and takes it in the upper part of the room, far away from occupants‘ breathing zone. Displacement ventilation exploits the thermal stratification to develop a contaminant stratification in the room: the contaminant is concentrated in the upper part of the room above the breathing level, while in the lower part of the room fresh and clean air is spreading (Figure 5). In the upper part of the room it is therefore typical to register very low ventilation effectiveness values, while in the lower part it is common to register ventilation effectiveness values above 1. The global effect on IAQ is therefore much better than mixing ventilation.

Figure 5. Displacement ventilation: the fresh supply air at the floor level and the contaminated air (due to occupants, furniture or other sources) above the breathing level. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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As a matter of fact, displacement ventilation cannot be used for heating purpose, because warm supply air would not spread along the floor, but rise up in the room, providing a mixing effect. Usually supply air is between 1 and 4 K colder than the room air (up to 8 K when high induction terminal devices are used) and the supply air velocity in the occupied zone should be very low, in order to respect thermal comfort limits [26, 27]. Under these conditions, it is evident that the cooling capacity of the system is limited by thermal comfort requirements. The major risk connected to the use of displacement ventilation is draft at ankle level, when supply air is too cold and air velocity too high. That is why standards impose limitations for temperature and air velocity. Displacement ventilation may therefore provide good performance:     

when contaminant sources are heat sources as well; where occupants are the major contaminant sources and have quite stable positions (restaurants, classrooms, conference rooms, theatres, cinemas, etc.); where air quality is the major purpose (not extreme cooling loads); in tall rooms, where to better exploit thermal stratification; where disturbance to room air flow is not substantial.

The major advantages resulting from displacement ventilation are:  

improved air quality at breathing level; longer periods when to exploit free running ventilation (no pre-heating).

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The major risks related to the improper use of displacement ventilation are:   

draft risk at ankle level; not effective thermal and contaminant stratification, and consequent reduction of the indoor air quality; extremely high ventilation flow rate.

The correct design is therefore fundamental to reach good system performance, and a clear vision of what principles drive displacement ventilation is the basic step where to start. If displacement ventilation is used, the flow pattern in the room substantially depends on the convection flows from the heat sources. Horizontal contaminant and air layers in the upper part of the room are a peculiar feature of displacement ventilation. While air and contaminants can easily move within the horizontal layer, movements between different layer require relevant forces. It is therefore useful to install the exhaust air terminal device at the layer in which contaminants are mostly concentrated, which usually is where the highest temperature occurs (Figure 6). Typically the exhaust is installed in the upper part of the room. As already mentioned, the supply air should be at a lower temperature with respect to the room air. The temperature of the supply air at the floor level rises because of the induction with the room air and because of the convective heat transfer with the floor surface.

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Francesco Causone and Stefano Paolo Corgnati

Figure 6. The exhaust air terminal device should be installed at the layer in which contaminants are mostly concentrated.

As described by Elisabeth Mundt [35], the warm ceiling exchanges heat by means of radiation with the cooler floor, which transfers it to the air at floor level by convection. This process is fundamental to stabilize thermal stratification in the room. The dimensionless temperature of the air at the floor level is described by the following equation:

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k

Tf  Tsp Te  Tsp

(18)

where k is the dimensionless temperature of the air at the floor level (-), Tf is the air temperature at the floor level (K), Tsp is the supply air temperature (K) and Te is the exhaust air temperature (K). Typically, in rooms equipped with displacement ventilation the ―50%-rule‖ is used as a first approximation to describe the vertical air temperature distribution. The model known as the ―50%-rule‖ was proposed by Skistad [33]. It postulates that the air temperature at floor level is half-way between the supply air temperature and the extract air temperature and that the air temperature gradient from floor to ceiling level can be considered linear: 0.5 

Tf  Tsp Te  Tsp

(19)

The ―50% rule‖ states that the supply air is heated for 50% by room air induction and convective heat transfer with the floor and for 50% by heat sources in the room. This is obviously an average value, observed under typical non-industrial conditions. On the other hand, it has been shown that if heat sources in the room are mostly point heat sources, the dimensionless temperature of the air at the floor level is typically 0.3 [34]. As well in tall building, i.e. rooms with ceiling heights larger than usual, the ―50% rule‖ is not verified, and it is much proper to use a ―33% rule‖ [34].

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Once established the temperature of the supply air, the airflow rate should be evaluated in order to provide a required level of indoor air quality (following indications in standards) and to guarantee a defined stratification of contaminants in the room. In order to reach these objectives it is fundamental to provide a supply flow rate nearly equal to the flow rate generated by all the heat sources in the room (heat plumes). If the supply flow rate is substantially lower than the heat plumes, the boundary layer between contaminated and fresh air is low, and it could reach the occupants‘ breathing level. On the other hand, if the ventilation flow rate is largely higher than the heat plumes, the flow equilibrium in the room could break, producing mixing conditions. Guidelines [34] may be used to verify the value of heat flows generated by different heat sources, in order to correctly evaluate the supply flow rate. If displacement ventilation has also a cooling function, it is furthermore necessary to check if the calculated supply flow rate is enough to cover the cooling load. The heat flux removed by displacement ventilation can be calculated as follow

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  c p  Te  Tsp  m

(20)

where Φ is the heat flux (W), m is the mass air flow (kg/s), cp is the specific heat coefficient (J/kg K), Tsp is the supply air temperature (K) and Te is the exhaust air temperature (K). Laboratory tests indicate that, under a equal contaminant concentration in the occupied zone, displacement ventilation may work with lower renovation flow rates than mixing ventilation [34], and this because it definitely exploits the thermal stratification in the room. However, when very low ventilation rates and large under-temperature are used, mixing ventilation is in most cases preferable [34]. In actual applications it was found that the flow rates used by displacement and mixing ventilation were quite the same. The major energy saving potential related to the use of displacement ventilation concerns the higher potential of free cooling and the reduced needs for cooling. Diffusers for displacement ventilation need furthermore less pressure drop than diffusers for mixing ventilation, and thus less fan power [33].

4. RADIANT COOLING AND VENTILATION 4.1. Opportunities and Threats So far the advantages and limitations of radiant systems and ventilation systems have been shown separately. The question which then arise is: «why one should use two systems together?». The answer to this question may not be univocal, nevertheless the main purpose is to obtain an hybrid system providing performance which the two systems alone could not provide. Comfort levels obtained by using radiant systems proved to be better than those of other conditioning systems, nevertheless radiant systems cannot provide control of the latent heat load and this issue is particularly relevant for radiant cooling, because condensation should be prevented. A ventilation system should therefore always be operated together with a radiant

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cooling system. Windows and doors of a building can be operated to supply fresh air to the indoor environment, but mechanical ventilation should definitely be used to always guarantee an energy efficient air exchange rate [36] and to decouple the space sensible and latent loads. Additionally, minimum ventilation rates for air renewal and indoor air quality are mandatory for commercial and industrial buildings and necessary in new airtight residential buildings. If the systems proved so far to have peculiar benefits working alone, the combination of two systems together does not necessary result in a combination of advantages. Many benefits of a system may in fact influence negatively the other system. A more accurate analysis should be made when considering hybrid systems, by assessing at the same time both indoor air quality and thermal comfort. Energy issues may be analysed further, ones provided the effectiveness of the hybrid systems. The practical options are to couple ceiling or floor cooling to mixing ventilation or to displacement ventilation. Other ventilation strategies are not considered because they are not so relevant among current applications. Wall cooling is not considered as well because of the same reasons.

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4.2. Radiant Cooling and Mixing Ventilation Radiant cooling panels represent a successful solution to combine with mixing ventilation systems when high cooling loads need to be removed. In such situations, the combination of the ventilation system with a ceiling cooling permits both to remove the thermal load and to guarantee the respect of the comfort standards. Both radiant floors and ceilings can be applied. The use of floor cooling does not modify significantly the air flow path of the air jet, because there is not a direct interference between the two elements: the air jet is in fact supplied outside the occupied zone. In the design stage, being known the maximum floor cooling capacity limited by the minimum acceptable surface temperature, the supply air flow rate and temperature of the jet have to be designed according to the residual cooling load. As a consequence, when cooled floors are used, the cooling contribution of the air jet is significant if high thermal loads are reported. On the contrary, ceiling cooling does not simply extract heat loads but it also influences significantly the air flow in the room. In particular, with high thermal loads significant improvements can be obtained applying ceiling cooling with mixing ventilation, reducing the risks due to the drop of the jet into the occupied zone. When only a mixing ventilation system is used to cool a room, an enhancement of heat loads could involve an unacceptable drop of the jet, entering the occupied zone with low temperature and high velocity. Under these conditions, one solution that can be chosen is to extract part or the total amount of the heat loads through radiant cooling panels, in order to restore acceptable jet supply conditions. The ceiling panel solution is more profitable than the floor one for cooling purpose, due to the higher efficiency provided by the enhancement of the convective heat exchange between the air and a cooled surface.

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When applying a cooled ceiling, a thin cool surface layer of air forms under the panel, creating a source of negative buoyancy forces which highly interact with the jet flow if the supply takes place at ceiling level. A typical and interesting application is represented by a wall-mounted diffuser, located below the ceiling. In this configuration, when the jet enters the room it attaches to the ceiling due to the Coanda-effect [37]. Hence, a high interaction between the ventilation air and the cooling element is established. On one hand the jet exchanges heat with the ceiling, on the other hand the rise of the air velocity near the ceiling determines an increase of the convective heat exchange coefficient. The air is supplied isothermally if the whole thermal load is removed by the ceiling, or non-isothermally, if a fraction of the thermal load is extracted by the ventilation air. Results from Corgnati et al. [38] show that, for the coupled mixing ventilation and ceiling cooling systems (MV/CC) with side wall diffusers located at ceiling level, the Archimedes number Ar, previously defined, can be calculated using as supply air temperature To, the average value between the supply air jet temperature and the mean ceiling temperature. By using this equation, the influence of the cooled ceiling on the jet drop is also taken into account. As a rule, for these systems, the cooled ceiling extracts thermal loads up to its maximum cooling capacity while the supply air removes the exceeding thermal load. In Figure 7, the results of jet throws tx and ty for a terminal velocity of 0.5 m/s are presented for both all-air mixing ventilation systems (MV) and coupled mixing ventilation and ceiling cooling systems (MV/CC). The results confirms that the longitudinal jet throw tx decreases with the increase of Ar, and ty increases with Ar. As a consequence, the cold jet tends to enter sooner and more deeply into the occupied zone when high Ar are achieved. The use of coupled MV/CC systems allows to improve significantly the horizontal throw and to reduce the jet vertical drop: therefore, the jet can be supplied at lower Archimedes numbers, as part of the heat load is extracted by the cooled ceiling.

Figure 7. tx and ty as function of Ar.

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Francesco Causone and Stefano Paolo Corgnati

Figure 8. DR as function of Ar.

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In Figure 8 and 9, the percentage of dissatisfied people due to draft (the maximum DR that occur in the occupied zone) and the indexes ADPI and ADPIDR are plotted as a function of Ar. Figure 8 clearly confirms that, according to the Ar shown in Figure 7, the use of a MV all-air system produces a significantly high percentage of dissatisfied people due to draft, as the air jet drops prematurely into the occupied zone. This is due to the high Archimedes numbers characterizing the jets. On the contrary, with MV/CC coupled systems, characterized by low Ar numbers, the draft risk is sensibly reduced. The results about the ADPI and ADPIDR are presented in Figure 9. With low Ar numbers (MV/CC coupled systems), ADPI reaches values up to 90% and ADPIDR values up to 80%.

Figure 9. ADPI and ADPIDR as function of Ar.

The results show that the use of a primary air mixing and ceiling cooling panels coupled systems, characterized by air jet supplied with low Archimedes numbers, will lead to:

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Radiant Cooling Combined with Ventilation Systems   

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an increase of the jet longitudinal throw and smaller vertical drop; a significant decrease of the draft risk due to the jet direct drop; an increase of both the ADPI index and ADPIDR index.

4.3. Radiant Cooling and Displacement Ventilation

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Floor cooling and ceiling cooling when operated with a displacement ventilation system produce substantially different effects in the room, and different potential negative interactions may also occur. It is therefore necessity to discuss about the two combinations separately.

4.3.1. Ceiling Cooling and Displacement Ventilation (CC/DV) Ceiling cooling applications became quite common in European countries during last years [14, 15, 36], mostly because of the thermal comfort benefits they may provide: homogeneous temperature in the occupied zone, low air motion and turbulence intensity (i.e. low draft rate), direct effect on occupants‘ thermal sensation. Displacement ventilation, may guarantee high level of indoor air quality, better than mixing ventilation, by exploiting thermal stratification in the room. Nevertheless the vertical temperature differences between the head and the ankle level should not exceed limits suggested by standards (< 3K) [26, 27]. Therefore the temperature difference between the supply and the room air should be relatively small, which limits DV cooling capacity [39]. In order to increase DV cooling capacity is not, on the other hand, possible to increase much the airflow rate because this should be proportional to the heat plums in the room [34] in order to establish a defined contaminant stratification, otherwise the stratified flow could turn into a mixing pattern. Moreover, larger airflow rates would require larger DV diffusers in order to control the air velocity at floor level and prevent draught at ankle level, and larger ductwork and air handling units, with consequent higher installation costs and energy consumptions for fan operation [40]. An effective solution may be indeed to combine ceiling cooling with displacement ventilation, charging them with separate tasks. For such a configuration a typical design strategy is to size the CC to cover the major part of the sensible load, while DV should cover the exceeding sensible heat load and the entire latent load, while providing the required indoor air quality [38]. Particular attention should be paid in the design phase to the sensible load distribution between CC and DV. A proper equilibrium should be found because where the cooling load removed by CC is considerably larger than that removed by DV, downward air motions from the CC panel could destroy the stratified displacement airflow pattern, causing a relative uniform temperature and contaminant distribution. The uniform temperature distribution provides better thermal comfort but worst air quality [36], and mixing ventilation conditions could occur in the room. It is therefore fundamental, for the proper behaviour of the hybrid system, to achieve an appropriate vertical temperature stratification, within the limits suggested for thermal comfort [26, 27]. Practical applications showed that the temperature gradient between head and ankles should be between 1 and 2.5 K [36, 41].

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Francesco Causone and Stefano Paolo Corgnati

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Since the temperature gradient depends on several boundary conditions such as cooling load, ventilation rate, supply air temperature and CC temperature, its value fluctuate along the time. During the operation of the combined CC/DV system, the control strategy has therefore an important impact on thermal comfort, air quality and energy consumption. A typical control strategy includes a constant airflow DV system with a fixed air temperature, and variable CC temperature [39]. The DV system will cover part of the sensible heat load and the entire latent load, while providing the necessary renovation air. When the sensible cooling load is lower than the design value, CC temperature will increase and the percentage of the total cooling load removed by CC will decrease. Since the radiant heat transfer coefficient of the CC is nearly constant while the convective heat transfer is a function of the temperature difference between room air and the radiant surface [24], the CC convective heat transfer will suffer the larger reduction. Under these conditions, the downward air movement contrasting heat plums reduces, and the thermal gradient in the room slightly increase (Figure 10, left side). When the CC removes the major part of the cooling load, the vertical temperature distribution will be more uniform [36], and the stratified boundary layer that separates the stale contaminated air, from the fresh supply air in the room will lower, reducing the ventilation effectiveness of the system (Figure 10, right side). A well-designed CC/DV system should always have both zones characteristic for DV, adapting to fluctuations of cooling load.

Figure 10. Thermal and contaminant stratification fluctuations as function of load distribution in a combined CC/DV system.

Rooms with the combined CC/DV system usually have slightly the same mean radiant temperature as the room air temperature, because the entire enclosure is cooled by radiation [39]. The high level of radiant heat transfer between the radiant surface and the indoor environment, makes it possible to increase the room air temperature still maintaining the required level of operative temperature; ventilation heat gains are then reduced, ensuring energy saving compared to an all-air system. The difference in total energy consumption between CC/DV and all-air systems is nevertheless the function of several parameters: supply air temperature, outdoor airflow rates and cooling loads besides the climate conditions. A useful comparison is possible only when the studied systems assure equivalent thermal comfort levels. This does not mean that the air

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temperature should always be strictly equal between the systems, but conditions which allows a comparison should be found [42]. As a general consideration, Novoselac [39] observed that with the increase of peak cooling loads, the combined CC/DV system become more economical than an all-air VAV system. On the other hand when cooling loads are low a VAV seems to be more energy efficient. Sodec [43] calculated instead that the energy consumption required by a CC/DV system are 17% lager than the one of a CC/MV system. The reason for this lager energy consumption is the higher air supply temperature with DV. To keep the air dew point temperature below CC temperature, the outdoor air is firstly cooled and dehumidified, and then heated to the supply temperature for DV. This process considerably increases the annual energy consumption for heating [39]. To avoid condensation, it is fundamental to control CC temperature. Conroy and Mumma [5] suggest an additional central dew-point temperature control. With this control, the supply water flow for CC increases when the room air dew point temperature is close to the water supply temperature. Another solution is to switch off the cooled water supply as soon as the relative humidity reaches ―dangerous‖ levels [39]. However, as remarked by Novoselac [39], risk from condensation is always present during the start-up of the system, after night or weekend breaks. For the outdoor air conditions when outside humidity is higher than the inside one, and during the periods when the system is turned off, there is a certain infiltration of humidity in the room at the system start-up time. A possible solution is an earlier start of the DV system and a gradual start of CC system. The design of a hybrid CC/DV system is therefore a challenge because of the substantial interaction between the two systems. The design guidelines for CC and DV as stand alone systems cannot be used for the design of the combined CC/DV system, if indoor air quality and thermal comfort levels want to be achieved and energy saving is regarded as well.

Figure 11. Redraw from Behne (1999); design diagram to determine the combination of CC with MV or DV.

New useful guidelines are reported in Novoseleac and Behne recent works (Figure 11 and 12). Alamdari [44] reports 60 W/m2 as maximum cooling capacity for CC/DV systems, with Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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Francesco Causone and Stefano Paolo Corgnati

a cooled panel area covering the 75-85% of the ceiling. Nevertheless charts drawn by Behne show values up to 100 W/m2 (Figure 11). It is on the other hand a good design rule to reduce the percentage of cooling load covered by the CC, to values below 50%, in order to prevent substantial interactions with the stratified displacement airflow pattern.

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Figure 12. Redraw from Novoselac and Srebic (2002); design diagrams for CC/DV hybrid systems.

4.3.2. Floor Cooling and Displacement Ventilation (FC/DV) If relevant researches have been reported for ceiling cooling combined with displacement ventilation, it is not the same for floor cooling and displacement ventilation. Few studies on this topic were in fact found in the literature [18, 45-47]. However a large and important building that applies this technology has already been constructed, i.e. the Bangkok airport, whose design is reported in some papers [4, 8, 9]. As for CC and DV, when combining FC and DV together, some attentions should be paid in order not to invalidate the performance of the hybrid system. The use of FC with DV could in fact exacerbate the typical problems encountered with displacement ventilation: draft risk at ankle level and discomfort due to the extreme vertical air temperature differences. A major limitation resides in the low cooling capacity of FC. Thermal comfort standards impose that the floor surface cannot be lower than 19°C. Since the convective heat transfer of FC is limited, due to the feeble air motion generated by the cooled surface, the maximum cooling capacity of FC is about 50 W/m2 (Table 3), half of the value achievable with CC. As previously mentioned, also the cooling capacity of DV is limited because the temperature difference between the supply and the room air should be relatively small, in order to respect thermal comfort standards and to maintain thermal and contaminant stratification [39]. Combing FC and DV, the cooling capacity of both FC and DV is therefore much improved; however it cannot be compared to the cooling capacity of a combined CC/DV system. Also for FC/DV systems a typical design strategy is to size the FC to cover the major part of the sensible load, while DV should cover the exceeding sensible heat load and the entire latent load, while providing the required indoor air quality [38].

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Recent studies [45] showed that, under typical boundary conditions, in an office room, when a FC/DV system is installed, the ―50% rule‖ is very unlikely to be respected. Nevertheless when airflow rates are increased and thus for higher floor surface temperature, the vertical air temperature profiles tend to decrease, coming closer to the theoretical profile predicted by applying the ―50% rule‖. The large vertical gradients reported during experimental tests, probably depend on the fact that with floor cooling the heat transmitted by radiation from the warmer ceiling to the floor is not then transmitted to the supply air at floor level by convection, as was the case in Elisabeth Mundt‘s experiments [32, 35], but it is directly removed by the radiant floor. Under these conditions the temperature of the supply air at floor level does not increase due to convective heat transfer from the floor, as in the case of displacement ventilation and the uncooled floor. Higher vertical air temperature differences therefore occur [45]. The vertical temperature differences measured between head and ankles during the mentioned tests, were generally higher than the limits imposed by standards, on the other hand, comfort evaluations made using a thermal manikin did not indicate any particular problem of local thermal discomfort [45]. The thermal gradients, although slightly higher than limitations, seem to be acceptable for occupants, and thus the combined FC/DV system appears to be effective. During floor cooling tests reported by Causone et al. [45], draft rate at ankle level, in the occupied zone, was always below 15%, for airflow rates in the ranged between 35 and 80 l/s, while ventilation effectiveness was always very high: an average value of 2.2 is reported for an airflow rate of 50 l/s, and an average value of 5.7 is reported for an airflow rate of 80 l/s. Although the limitations shown above, the combined FC/DV system showed good performance and it is a valid application when cooling load does not assume extreme values. Considering the maximum cooling capacity of 30 W/m2 for DV reported by Behne [36] and the maximum cooling capacity of 50 W/m2 for FC [24], the maximum cooling capacity of the combined FC/DV system should be close to 80 W/m2. Since cooling loads in an office building are usually between 35 and 70 W/m2 [39], the hybrid FC/DV system could be applied in most of the conditions. In the literature is on the other hand reported that, if FC is positioned under the effect of direct solar radiation its cooling capacity substantially increases, and it can exceed 100 W/m2 [12, 48]. Condensation is again the major risk to be avoided when installing FC/DV systems. The control and operation strategies suggested for CC/DV system can be applied as well to FC/DV systems. Nevertheless a particular attention should be given to the control, because floor cooling systems typically have a higher inertia than ceiling cooling, and thus they answer with delay to thermal stresses. On the other hand, since the ―dry‖ supply airflow spreads along the floor, when using combined FC/DV systems, a major benefit is provided to prevent condensation on the cooled surface, compared to CC/DV, FC/MV and CC/MV systems. At the moment updated guidelines and graphs for the design of combined FC/DV systems are not available, as for the case of CC/DV systems (Figure 11 and 12) or the case of FH/DV systems [45, 48]. Professionals should therefore address this issue carefully [4, 8, 9], while research should further improve knowledge about this topic.

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Francesco Causone and Stefano Paolo Corgnati

5. HEAT TRANSFER COEFFICIENT ENHANCEMENT When a ventilation system is operated together with a radiant system, a further interaction should be investigated, because the air motion generated has an impact on the heating/cooling capacity of the radiant surface. The ventilation system, under certain conditions, may improve the performance of the radiant system, because, by increasing the air velocity and turbulence in the room, it creates a forced convective heat exchange which increases the natural convective heat exchange. Some algorithms for the calculation of the enhanced convective heat transfer coefficient of a heated/cooled surface are given in the literature, for the case of mixing and displacement ventilation (Table 4) [49-51]. On the basis of these algorithms the possible enhancement of the convective heating/cooling capacity of radiant floors and ceilings can be calculated. Jeong evaluated that radiant ceiling cooling capacity, when considering mixing ventilation, is enhanced from 5% to 35% [48, 49]. However when the diffuser discharged air velocity is less than 2 m/s, the impact of mixed convection on the panel cooling capacity is small and the correlation for the natural convection heat transfer can be used to estimate panel cooling capacity [48, 49]. Table 4. Literature convection correlations for radiant panel systems and DV or MV

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Surface

Ventilation

Convection correlation

FH

NC

hc  2.175  ΔT

FH

DV

h c  (2.175  ΔT 

FC

NC

h c  0.704  ΔT

FC

DV

h c  (0.704  ΔT 

CH

NC

h c  0.704  ΔT

CH

MV

h c  f(v, ΔT)  0.704  ΔT

CC

NC

h c  2.13  ΔT

CC

MV

h c  f(v, ΔT)  2.13  ΔT

0.308

0.133

Dh

Dh

0.308

0.706

6 0.8 6 )  (( Ts  Tsupply ΔT )  0.48  ACH )  

0.133

0.601

Dh

0.706

Dh

Awbi and Hatton (1999)

0.601

6 0.8 6 )  (( Ts  Tsupply ΔT )  0.48  ACH )  

0.133

Dh

1/6

0.31

1/6

Novoselac et al. (2006) Awbi and Hatton (1999)

0.601

0.133

Reference Awbi and Hatton (1999) Novoselac et al. (2006)

Dh

0.601

Derived from Jeong and Mumma (2003) Jeong and Mumma (2003)

0.31

Jeong and Mumma (2003)

where: CC Ceiling cooling CH Ceiling heating FC Floor cooling FH Floor heating DV Displacement ventilation MV Mixing ventilations NC Natural convection Dh Hydraulic diameter [m] ACH Air change per hour ΔT Characteristic temperature difference [°C]; the temperature difference between the heated/cooled surface and the air

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The highest improvements are reported for ceiling heating and floor cooling, because these systems have very low natural heat transfer coefficients. Hence, the activation of a forced convection results in a considerable enhancement of their convective heating/cooling capacity, even with low air velocity or low air changes per hour. Improvements are nonetheless reported also for floor heating and ceiling cooling [18].

6. DEDICATED OUTDOOR AIR SYSTEMS (DOAS) Despite the ventilation strategy, it is worth noting that the radiant system can be operated together with a dedicated outdoor air system (DOAS), considering the benefits that can derive form this application. The concept is not new [14], nevertheless the use of DOAS increased significantly in the last few years [16], especially as consequence of the high performances required by current standards. As underlined by Mumma [14, 15], a separated dedicated outdoor air ventilation system may, in fact, be the only reliable method of meeting ANSI/ASHRAE 62 requirements [52]. Dedicated outdoor air systems are based on the following basic tenets:  

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

decouple the space latent and sensible loads; cover all the latent load through the DOAS, by providing at the same time the required ventilation flow rate for indoor air quality; remove the sensible load, primarily independent of the DOAS, with a parallel system.

The parallel mechanical system balancing the sensible load may include: a parallel all-air VAV system, fan coil units, packaged unitary water source heat pumps, packaged unitary equipment, ceiling cooling, floor cooling. Conroy and Mumma [5] advise ceiling cooling as the most viable application combined with a DOAS. The small ventilation air ductwork and parallel radiant cooling panel terminal equipments offer, in fact, a significant opportunity to reduce the required floor-to-floor dimension. Furthermore, as mentioned also in previous paragraphs, radiant cooling provides better comfort levels than other conditioning systems, while assuring energy saving, because of the moderate temperature of the heat carrier used. In addition to the decrease of operating costs, also first costs may results lower with respect to a conventional all-air system [7]. Floor cooling can provide analogous benefits, when combined with DOAS, as ceiling cooling. However the cooling capacity of floor is lower and this can limit its application to buildings with relevant cooling loads. A DOAS can be both constant volume or variable volume, although for most situations constant volume is used [16]. Dehumidification can be accomplished by using either active desiccants or coiling coils. Typically cooling coils are better when the dew-point temperature is above 4°C, while active desiccants are better when the dew-point temperature is below 4°C [15]. Therefore in most of the non-industrial applications, cooling coils are preferable.

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Francesco Causone and Stefano Paolo Corgnati

Major advantages are achieved when an enthalpy wheel is used to precondition the outdoor air ahead the of the cooling coil. The enthalpy wheel cools and dehumidifies the outdoor air in the summer, lowering the load on the cooling coil. In the winter it can instead be used to heat and humidify the outdoor air. As underlined by Mumma [16], the keys to success are perhaps the proper control of the enthalpy wheel and the control of the cooling equipment to ensure that the space latent load is completely handle by the ventilation air. When designing a hybrid system which combines radiant cooling and ventilation, a DOAS should always be applied. Decoupling the space latent and sensible loads is in fact mandatory to prevent condensation on the cooled surface, while many other benefits can be achieved: better thermal comfort and indoor air quality, energy saving, reduction of operating and first costs.

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7. CONCLUSION A general overview on radiant systems was given, focusing on their potentialities and limitations in terms of heating and cooling capacity. Wider considerations followed on the performance advantages and disadvantages deriving from the combination of radiant cooling with different ventilation strategies. Both mixing and displacement ventilation have been analysed. Professionals should pay particular care to the design phase of the hybrid system, due to the interactions deriving from the combination of the two systems. Peculiar design tools and procedures have been reported to help exploiting positive interactions while preventing negative ones. To obtain good performance it is nevertheless extremely important the operation and management of the hybrid systems, which should be handled since the early stage of the project. In particular, when coupled with mixing ventilation, ceiling cooling performance can be enhanced by the ventilation air jet at ceiling level, increasing the convective cooling capacity of the radiant system. While, when displacement ventilation is used, the ceiling cooling can be applied successfully in order to extract part of the cooling load, provided that the downward air motion does not destroy the stratified displacement airflow pattern. Applications of floor cooling with displacement ventilation are possible and showed good performance under experimental conditions, however they should be chosen only when cooling load does not assume extreme values. The main flaw of radiant cooling is the condensation risk, that may be prevented by operating the radiant system together with a dedicate outdoor air system and by assuring the correct control logic. When designing a radiant cooling system a parallel system should always be considered to decuple space sensible and latent loads. In conclusion, the combination of radiant cooling with a suitable ventilation strategy can provide better performance compared to a conventional all-air system, both in terms of thermal comfort and of indoor air quality, while assuring substantial opportunities to reduce the operational energy demand.

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ASHRAE, 2007, Applications volume of ASHRAE Handbook, Chapter 53: Radiant Heating and Cooling, American Society of Heating, Refrigerating and Air-Conditioning Engineers, USA. ASHRAE, 2008, HVAC Systems and Equipment volume of ASHRAE Handbook, Chapter 6: Panel Heating and Cooling, American Society of Heating, Refrigerating and Air-Conditioning Engineers, USA. B.W. Olesen, 2002, Radiant floor heating in theory and practice, ASHRAE Journal 7, 19–24. J. Babiak, B.W. Olesen, D. Petras, 2007, Low temperature heating and high temperature cooling, Rehva, Brussels. C.L. Conroy, S.A. Mumma, 2001, Ceiling radiant cooling panels as a viable distributed parallel sensible cooling technology integrated with dedicated outdoor-air systems, ASHRAE Transactions 107 (1). H.E. Feustel, C. Stetiu, 1995, Hydronic radiant cooling - preliminary assessment, Energy and Buildings 22, 193–205. S.A. Mumma, 2002, Chilled Ceilings in Parallel with Dedicated Outdoor Air Systems: Addressing the Concerns of Condensation, Capacity, and Cost, ASHRAE Transactions 108 (2). P. Simmonds, S. Holst, S. Reuss, W. Gaw, 1999, Comfort conditioning for large spaces, ASHRAE Transactions 105 (1) 1037–1048. W. Kessling, S. Holst, M. Schuler, 2004, Innovative design concept for the new Bangkok international airport, NBIA, Symposium on Improving Building Systems in Hot and Humid Climates, Richardson, 17-19 May 2004. J.L. Niu, J.v.d. Kooi, 1994, Thermal climate in rooms with cool ceiling systems, Building and Environment 29, 283-290. J.L. Niu, J.v.d. Kooi, H.v.d. Ree, 1995, Energy saving possibilities with cooled-ceiling systems, Energy and Buildings 23, 147-158. B.W. Olesen, 1997, Possibilities and limitations of radiant floor cooling, ASHRAE Transactions 103 (1) 42–48. J-W. Jeong, S.A. Mumma, W.P. Bahnfleth, 2003, Energy conservation benefits of a dedicated outdoor air system with parallel sensible cooling by ceiling radiant panels, ASHRAE Transactions 109 (2) 627–636. S.A. Mumma, 2001, Overview of integrating dedicated outdoor air systems with parallel terminal systems, ASHRAE Transactions 107 (1). S.A. Mumma, 2001, Designing dedicated outdoor air systems, ASHRAE Journal, May 2001, 28-31. S.A. Mumma, J-W. Jeong, 2005, Field experience controlling a dedicated outdoor air system, ASHRAE Transactions 111 (2). R.D. Watson, K.S. Chapman, 2002, Radiant heating and cooling handbook, McGrawHill, New York. F. Causone, 2009, Radiant Heating and Cooling: Limitations and Possibilities of Improvement, Ph.D Thesis, Department of Energetics, Politecnico di Torino.

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[19] R. Bean, B.W. Olesen, K.W. Kim, 2010, History of Radiant Heating and Cooling Systems, Part 1, ASHRAE journal 52 (1), 40-47. [20] R. Bean, B.W. Olesen, K.W. Kim, 2010, History of Radiant Heating and Cooling Systems, Part 2, ASHRAE journal 52 (2), 50-55. [21] F.P. Incropera, D.P. DeWitt, T.L. Bergman, A.S. Lavine, 2007, Fundamentals of heat transfer, Wiley, New York. [22] J.P. Holman, 1992, Heat transfer, McGrow-Hill, London. [23] F. Causone, S.P. Corgnati, M. Filippi, B.W. Olesen, 2010, Solar radiation and cooling load calculation for radiant systems: definition and evaluation of the Direct Solar Load, Energy and Buildings 42 (3), 305–314. [24] F. Causone, S.P. Corgnati, M. Filippi, B.W. Olesen, 2009, Experimental evaluation of heat transfer coefficients between radiant ceiling and room, Energy and Buildings 41 (6), 622–628. [25] CEN, 2003, Heating systems in buildings - Method for calculation of the design heat load. EN Standard 12831. Bruxelles: Comité Européen de Normalisation. [26] ANSI/ASHRAE, 2004, Thermal environment conditions for human occupancy. ASHRAE Standard 55. Atlanta: America Society of Heating, Refrigerating, and Air Conditioning Engineers. [27] CEN, 2005, Ergonimics of the thermal environment – Analytical determination and interpretation of thermal comfort using calculation of the PMV and PPD indices and local thermal comfort criteria. Standard EN ISO 7730. Bruxelles: Comité Européen de Normalisation. [28] CEN, 2007, Indoor environmental input parameters for desing and assessment of energy performace of buildings addressing indoor air quality, thermal environment, lighting and acoustics. Standard EN 15251. Bruxelles: Comité Européen de Normalisation. [29] B.W. Olesen, F. Bonnefoi, E. Michel, M. De Carli, 2000, Heat exchange coefficient between floor surface and space by floor cooling - Theory or a question of definition, ASHRAE Transactions: Symposia DA-00-8-2, 684–694. [30] S.P. Corgnati, G.V. Fracastoro, M. Perino, 2000, Sistemi radianti per il raffrescamento estivo: dinamiche di asportazione dei carichi termici, in Proceeding of: ATI 2000, September 2000 (Italian text). [31] D. Etheridge, M. Sandberg, 1996, Building Ventilation – Theory and Measurement, John Wiley and Sons. [32] E. Mundt, 1995, Displacement ventilation systems – Convection flows and temperature gradients, Building and Environment 30 (1), 129-133. [33] H. Skistad, 1994, Displacement ventilation. Somerset: Research Studies Press, Ltd. Wiley, New York. [34] H. Skistad, E. Mundt, P.V. Nielsen, K. Hagstrom, J. Ralio, 2002, Displacement ventilation in non-industrial premises, Rehva, Brussels. [35] E. Mundt, 1996, The performance of displacement ventilation system – Experimental and theoretical studies, Ph.d Thesis, Bulletin n. 38, Building Services Engineering, KTH, Stockholm. [36] M. Behne, 1999, Indoor air quality in rooms with cooled ceilings. Mixing ventilation or rather displacement ventilation?, Energy and Buildings 30, 155–166.

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[37] B. Tripathi, S.G. Moulic, 2007, Investigation of the buoyancy affected airflow patterns in the enclosure subjected at the different wall temperatures, Energy and Buildings 39 (8), 906-912. [38] S.P. Corgnati, M. Perino, G.V. Fracastoro, P. Nielsen, 2009, Experimental and numerical analysis of air and radiant cooling systems in offices, Building and Environment 44, 801–806. [39] A. Novoselac, J. Srebic, 2002, A critical review on the performance and design of combined cooled ceiling and displacement ventilation systems, Energy and Buildings 34, 497-509. [40] S. Hu, Q. Chen, L.R. Glicksmann, 1999, Comparison of energy consumption between displacement and mixing ventilation for different US building and climate, ASHRAE Transaction 105 (2) 453-464. [41] H. Tan, T. Murata, K. Aoki, T. Kurabuchi, 1998, Cooled ceiling/Displacement ventilation hybrid air conditioning system – design criteria, in: Proceeding of Roomvent ‘98. [42] E. Fabrizio, S.P. Corgnati, F. Causone, M. Filippi, L. Schiavio, 2010, Contrasting the energy and comfort performance of radiant heating and cooling system vs. all air systems by numerical simulation, in: Proceeding of CLIMA 2010 Sustainable Energy Use in Buildings, Antalya, 9-12 May 2010. [43] F. Sodec, 1999, Economic viability of cooling ceiling systems, Energy and Buildings 30, 195-201. [44] F. Alamdari, 1998, Displacement Ventilation and Cooling Ceiling, in: Proceeding of ROOMVENT‘98, vol. 1, Stockholm, 197-204. [45] F. Causone, F. Baldin, B.W. Olesen, S.P. Corgnati, 2010, Floor heating and cooling combined with displacement ventilation: possibilities and limitations, Energy and Buildings 42 (12), 2338–2352. [46] Y. Ren, D. Li, Y. Zhang, 2006, Experimental Study of the Floor Radiant Cooling System Combined with Displacement Ventilation, in: Proceeding of ICEBO 2006, Shenzhen, China. [47] H. Skistad, 2003, Floor heating and displacement ventilation, in: Proceedings of Cold Climate HVAC 2003, Trondheim, 15-18. [48] F. Causone, B.W. Olesen, S.P. Corgnati, 2010, Floor heating with displacement ventilation: an experimental and numerical analysis, HVACandR Research 16 (2), 139– 160. [49] J-W. Jeong, S.A. Mumma, 2003, Ceiling radiant cooling panel capacity enhanced by mixed convection in mechanically ventilated spaces, Applied Thermal Engineering 23, 2293–2306. [50] J-W. Jeong, S.A. Mumma, 2003, Impact of mixed convention on ceiling radiant cooling panel capacity, HVACandR Research 9 (3), 251-257. [51] A. Novoselac, B.J. Burley, J. Srebric, 2006, Development of new and validation of existing convection correlations for rooms with displacement ventilation systems, Energy and Buildings 38, 163–173. [52] ANSI/ASHRAE, 2007, Ventilation for Acceptable Indoor Air Quality ASHRAE Standard 62.1-61.2. [53] Awbi, H.B. Hatton, A, 1999, Natural convention from heated room surfaces, Energy and Buildings 30, 233–244.

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Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

In: Cooling Systems: Energy, Engineering and Applications ISBN 978-1-61209-379-6 Editor: Aaron I. Shanley © 2011 Nova Science Publishers, Inc.

Chapter 2

APPLICATIONS OF IMPINGEMENT JET COOLING SYSTEMS Hyung Hee Cho1, Kyung Min Kim and Jiwoon Song Department of Mechanical Engineering, Yonsei University, Seoul, 120-749, Korea

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ABSTRACT This book chapter discussed impingement jet cooling. Jet impingement achieves locally high heat transfer on an interested surface. For these reasons, the impinging jet cooling technique has been widely used in many industrial systems such as gas turbine cooling, rocket launcher cooling and high-density electrical equipment cooling in order to remove a large amount of heat. In this chapter, experimental and numerical investigations are reviewed on flow and heat transfer characteristics of impinging jets. The review included the general single jet and jet impingement; their active controls; high speed jet flows and jet impingement; liquid impinging jet cooling; array jet impingement; array jet impingements on effusion surface. In detail, to enhance the heat transfer in single and array jets, there is discussion on design and control of nozzle geometry, nozzle insertion, jet vibration, secondary injection, and suction flow. In addition, effects of various factors have been concerned with different operating conditions (crossflow, rotation, compressible flow, working fluid, etc.) and combined techniques (rib turbulator, pin fin, dimple, effusion hole, etc.).

1. INTRODUCTION Impinging jets, which are used in many applications, can produce high heat/mass transfer rates. It is easy to adjust the location of interest and to remove a large amount of heat on the impingement surface. For these reasons, the impinging jet technique has been widely used in cooling, heating, and drying systems for many engineering applications such as gas turbine 1

Corresponding author. Tel.: +82 2 2123 2828, Fax.: +82 2 312 2159. E-mail address: [email protected].

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Hyung Hee Cho, Kyung Min Kim and Jiwoon Song

cooling, drying of paper or textiles, processing of steel or glass, high-density electrical equipment cooling, freezing of cryogenic tissue among others. In addition to their applications, jet-impingement cooling has been of interest to many fields of fluid dynamics and thermal engineering Figure 1.

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Figure 1. Various applications of impinging jets.

Numerous experimental and numerical investigations have been conducted on heat transfer and cooling of impinging jets in order to control heat transfer and improve cooling performance in single and array jets with subsonic to supersonic jet velocities. Many researchers have performed a multitude of experiments by considering the nozzle geometry, impinging surface, and active methods such as jet vibration, secondary injection, and suction flow. In addition, various factors concerned with operating conditions (crossflow, rotation, mass flow rate, jet velocity, working fluid, etc.) and combined techniques (rib turbulator, pin fin, dimple, effusion hole, etc.) have been investigated in order to identify the optimum condition and geometry. A large number of experimental methods including the liquid crystal method, IR camera technique, and naphthalene sublimation method have been used to obtain detailed heat transfer distributions. Given the improvements in computational performance, many numerical calculations have been performed to obtain local heat transfer distributions in complex geometries, because the numerical results are still disagreement with the experimental result in local distribution. There have been many studies and literature reviews on impinging jets. Martin [1] reviewed investigations on the hydrodynamics of impinging flow along with the variables and boundary conditions of heat and mass transfer, local variations in transfer coefficients for single nozzles and nozzle arrays, integral mean transfer coefficients, and the influence of outlet flow conditions on transfer coefficients for nozzle arrays. Viskanta [2] reviewed heattransfer characteristics of single and multiple isothermal turbulent air and flame jets impinging on surfaces. The review focused on applications to materials or comparisons of theory and experiments. The stagnation point heat transfer in this paper was described in a similar way, despite the many differences in the jet characteristics (i.e., axial velocity and

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Applications of Impingement Jet Cooling Systems

39

turbulence intensity) of isothermal and flame jets. Han and Goldstein [3] presented a review of jet-impingement heat transfer in gas turbine systems. They reviewed characteristics of the different flow regions for submerged jets such as the free jet, stagnation flow, and wall-jet regions. In addition, they discussed heat-transfer characteristics of both single and multiple jets considering the effects of parameters important to gas turbine systems including the curvature of surfaces, crossflow, angle of impact, and rotation. Weigand and Spring [4] summarized relevant experimental and numerical results on multi-jet-impingement heat transfer including the latest developments in the literature. They provided profound knowledge on the design of such configurations complemented by a structured listing of factors influential for heat transfer. This paper included the physics of multiple jet configurations; an introduction to the characteristics of flow field and heat transfer in multiple jets with regard to the effects of jet pattern, jet diameter, or open area; crossflow effects, separation distance, jet-to-jet spacing, and optimization of impingement arrays. In this chapter, recent research trends on impinging jets are reviewed. We focus on summarizing single impingement jets and impingement jet arrays in which air/liquid will be issued into air/liquid. We also consider the effects of air jet velocities of low to high Reynolds number on flow and heat-transfer characteristics in a single air jet.

2. HEAT TRANSFER VARIABLES IN IMPINGING JETS The Nusselt number is widely used in the heat transfer as a dimensionless form of heat transfer coefficient. The variable is defined as

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Nu =

ℎ𝐷 𝑘

(1)

where h is the heat transfer coefficient, D is the nozzle diameter, and k is the thermal conductivity of the fluid. Here, ℎ=𝑇

𝑞𝑤

𝑤 −𝑇 𝑟𝑒𝑓

(2)

where qw is the wall heat flux, Tw is the wall temperature, and Tref is a reference temperature. Normally, Tref is either the total temperature of jet flow (Tf) or the adiabatic wall temperature (Taw). The latter is obtained from a recovery factor (r) defined by a non-dimensional form. 𝑟=

𝑇𝑎𝑤 −𝑇𝑓 𝑈𝑓2 /2𝐶𝑝

(3)

where Uf is the jet velocity and Cp is the specific heat of the fluid at constant pressure. The Nusselt number changes depending on whether Tf or Taw is chosen as the Tref. For a low Reynolds number flow, two results are the same. However, the results show discrepancy for high Reynolds numbers. Therefore, the reference temperature must be carefully chosen. Detailed explanations are provided by Goldstein et al. [5-6].

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3. SINGLE JET FLOW AND JET IMPINGEMENT In general, the flow structure of an impinging jet consists of the free jet, stagnation flow, and the wall-jet regions as illustrated in Figure 2. The free jet region is divided into the flow development and fully developed regions. A potential core in the flow development region is observed when the height (H) to nozzle diameter (d) is less than about 6. The width of the potential core in free jet flow is reduced moving downstream by the shear flow. In the fully developed jet flow, the velocity profile is approximated as a Gaussian distribution. The jet flow impinging on a surface forms the stagnation flow region in which the radial velocity increases rapidly as the surface is approached. Subsequently, the outward radial flow generates the wall-jet region. The heat transfer distributions are non-uniform due to these complex flow patterns, such as flow deceleration, acceleration, transition, and etc. ―Energy separation‖ of temperature field appears in the impinging jet due to a strong coherent structure of ring vortices around the jet [3]. Basic to advanced experiments and simulations have been conducted to understand the heat transfer characteristics on impinging jets. Liquid

Nozzle

d

V Free jet region

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H

Potential core

Boundary layer

Stagnation region

y

Wall jet region

x or r

Impingement surface (target surface) Figure 2. Schematic diagram of flow region around an impinging jet.

Hwang [7] showed the effect of jet spacing on the radial distribution of the Nusselt numbers. For small nozzle-to-plate spacings of 2 and 4, there are two peaks in the Nusselt number distribution as shown in Figure 3. The first peak at an r/D of less than 0.5 is generated by the effect of stagnating flow acceleration. This acceleration reduces the boundary layer thickness, resulting in an increase in heat transfer. The secondary peak appears at an r/D of approximately 2. Generally, it is thought that the secondary peak in the Nusselt number is induced by the flow transition from laminar to turbulent and by secondary vortices. The vortices near the wall disturb the boundary layer flow and enhance the mixing of ambient fluids, creating the peak in the Nusselt number. As the gap distance increases and the location of the impingement plate moves outside of the potential core, there is only one peak at the stagnation point. The reason is that the jet flow is fully developed and the

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Applications of Impingement Jet Cooling Systems

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turbulence intensity at the stagnation region is sufficiently high. In addition, Lee and Lee [8] measured local heat transfer in a stagnation region on a heated flat plate for an axisymmetric impinging jet. They reported the Nusselt number correlation at the stagnation point consisted of Reynolds numbers and nozzle-to-plate spacings. 170

x/ D=2 x/ D=4 x/ D=6 x/ D=8 x/ D=12 x/ D=16

150

Nu

130

110

90

70

50 0

1

2

3

4

5

r /D

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Figure 3. Local heat transfer distributions in different impinging jet spacing [7]. (D=nozzle exit diameter, r=radial direction, x=nozzle-to-plate distance).

Measurements of the velocity and turbulence distributions are important in the design of impinging jets because local heat-transfer distributions change with the velocity and the turbulence of the impinging jet. Gardon and Akfirat [9] concluded that heat-transfer phenomena can be explained as effects of the intense and spatially varying turbulence in jets. Popiel and Trass [10] showed ring-shaped wall eddies induced by large-scale toroidal vortices from an impinging round jet using the smoke-wire flow-visualization technique. They reported that these wall eddies for low nozzle-to-plate separations, induced consecutively at a transition zone, were responsible for the additional enhancement of local momentum and heat or mass transfer. Jambunathan et al. [11] investigated the parameters affecting flow and heattransfer characteristics of impinging jets. They reported that heat transfer by jet flow on an impinged surface is affected by nozzle geometry, flow confinement, turbulence intensity, recovery factor, and dissipation of jet temperature, as well as many other parameters (Re, Pr, non-dimensional nozzle-to-plate spacing, and non-dimensional displacement from the stagnation point). Chung and Luo [12] and O‘Donovan and Murray [13] have studied unsteady heat-transfer characteristics using transient measurements and calculations of flow velocity and intensity. Many researchers who study heat-transfer improvement in impinging jets have used an effective passive-control technique. For example, Hwang and Cho [14] installed multi-tube insertion in the nozzle and examined the vortex flow interaction between inserted multi-tube jet flows (Figure 4). Bilen et al. [15] studied differences about the round jets with different swirling inserts. Lee and Lee [16] studied heat-transfer enhancement using an elliptic jet for

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Hyung Hee Cho, Kyung Min Kim and Jiwoon Song

engineering applications having a small nozzle-to-surface spacing less than the potential core length. They reported that the heat transfer rate was larger than that for the axisymmetric jet (AR = 1) in the stagnation region at smaller nozzle-to-surface spacings (H/D> τ, τr, local thermal equilibrium can be applied over space and time, leading to macroscopic transport laws.

In the FTT analysis, the processes of heat transfer (from and to the heat reservoir) are time dependent but all other processes (not involving heat transfers) are assumed reversible. Take for example, an endo-reversible chiller that has been commonly modelled [12]. Invariably, they assumed reversibility for the flow processes of its working fluid but irreversible processes are arbitrary applied and restricted to the heat interactions with the environment or heat reservoirs. Owing to the arbitrary assumption of reversibility for the flow processes of working fluid within the chiller cycle, the FTT faces an ―uncertain treatment‖ [13] and hence, it renders itself totally impractical in the real world. On the other hand, there has been an excellent development in the general argument of equilibrium and irreversible that applies to macro systems. It is built upon an approach following the method of de Groot and Mazur [10]. They proposed the theory of fluctuations that describes non-equilibrium (irreversible) phenomena, based on the basic reciprocity relations [14], and relied on the microscopic as well as drawing phenomenon about macroscopic behavior. Most non-equilibrium thermodynamics assumes linear processes occurring close to an equilibrium thermodynamic state and assumes that the phenomenological coefficients are constant [15]. For the microscopic and sub-microscopic domains, the transport equations are developed from the rudiments of the Boltzmann Transport Equation (BTE) but conforming to the First and Second Laws of Thermodynamics. In the sections to follow, the main objective is to

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Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al.

discuss and formulate the basic conservation laws (mass, momentum and energy balances) for the thin films and based on the specific dissipative losses encountered in these layers, the entropy generation with respect to the electrons, holes and phonons fluxes will be formulated. The organization of this chapter is as follows: Section 2 describes the general form of conservation equations. The equations to be discussed are the mass, momentum and energy conservation and the properties of the collision operator. In section 3, the mathematical rigor of the BTE with respect to irreversible production of entropy is presented. Following the Gibbs expression on entropy, the entropy balance equation is established in relation with the conservation equations, which comprise a source term or entropy source strength term. Section 3 tabulates a list of the common entropy generation mechanisms and demonstrates the manner the terms are deployed in the BTE formulation. For application examples of this demonstration presented in the previous sections, section 4 demonstrates the mathematical modeling and the performance analysis of adsorption cooling systems. Based on the conservation laws and the entropy balance equations, section 5 develops the temperatureentropy formulations of a solid state thermoelectric cooling device, a pulsed thermoelectric cooler and a micro-scale thermoelectric cooler. The thermodynamic performances of these solid state coolers are discussed graphically with T-s diagrams. In this section, the mathematical modelling of the thin film superlattice thermoelectric element is developed from the basic Boltzmann Transport Equation where the collision terms are included. This chapter finally ends with a conclusion.

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2. GENERAL FORM OF BALANCE EQUATIONS In this section, the transport processes involving the mass, momentum, and energy are described from the basic conservation laws, developed together with the transport of heat or energy by molecular fluxes such as electrons, holes and phonons within the micro layers in a system.

2.1. Derivation of the Thermodynamic Framework Figure 2 shows a schematic of an ensemble or a group of molecular particles, such as an electrons, holes or phonons, represented initially at a time t where their positions and velocities are expressed in the range d 3r  , d 3 v near r and v , respectively. The operator, d 3 indicates the three dimensional spaces of the variables r and v . At an infinitesimally small time dt later, the molecular particles move, under the presence and influence of an external force F (r, v) , to a new position r  r  rdt and attaining a velocity v  v  v  dt . Owing to collisions of molecular particles, the number of molecules in the range d 3r d 3 v could be also changed where particles or molecules originally outside

the range d 3r  d 3 v can be scattered into the domain under consideration. Conversely, molecules originally inside the domain range could be scattered out. Following the framework of Reif, F. [16], the generic form of the conservation laws is additive and is given by,

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Study on Adsorption and Thermoelectric Cooling Systems… Molecules_ at _(t ' ),( r ' )&v '

Molecules_ at _(t ),( r )&v

153

Molecules_ at _(r ' )&v"

    ' ' ' 3 ' 3 ' f (r , v , t ) d (r )d ( v )  f (r , v " , t ) d 3 (r )d 3 ( v " )  f colli (r , v " )d 3 (r ' )d 3 ( v") (1) where t’= t + dt, the range r  r  rdt  and v  v  v  dt . f r, v, t  is the statistical distribution function of an ensemble particle, which varies with time t, particle position vector r, and velocity vector v.

Figure 2. The motion of a particle specified by the particle position r and its velocity v''.

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For convenience, we drop the implied 3-D operator, d3, the equation reduces to a more readable form, i.e.,

f r  rdt , v   v  dt , t  dt   f r, v , t   f colli r, v , t  dt or the collision term is f colli r, v , t dt  f r  rdt , v   v  dt , t  dt   f r, v , t  By invoking the partial derivatives, the basic Boltzmann transport equation is now expressed for a situation that handles the molecular flux over a thin layer of materials, i.e.,  f r f v "  f colli f      " t t  r t v t  rearranging f t

f  f      colli t  t  drift

and the subscript ―drift‖ refers to the flow of flux through space (r) and convective velocity (v) and the second term is the effect of collisions with time. It is noted that the term ―drift‖ is a non-equilibrium transport mechanism that associates with the external force F (r, v) , i.e.,

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f dr f dv  f  ,      t  Drift r dt v dt where r is the position vector, v is the velocity vector, i.e.,

v is

dv F ,  dt m *

(2)

v 

dr dt

, and the rate of change of

where m* is the mass of a single molecular particle.

The physical meanings of velocity and electric field are described in the drift term of equation (2) is now fully elaborated as, f F f f f ,  f   v   v  F   r m * v r p  t  Drift

where the momentum p  m * v , is that associated with a molecular particle. Substituting back into equation (2), the general form of the transport equation with respect to r, p and t becomes

f f f f   v  F  colli . t r p t

(3)

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Having formulated the basic form of the Boltzmann transport equation or BTE in short, and two other functions will be used along the BTE and they are: Firstly, the carrier density of the molecular flux is now incorporated by defining the carrier density as the integral of the product between the molecular particles and the change in their momentum [7], i.e.,

n   fdp .

(4)

Secondly, the substantive derive of any variable, , that varies both in time and in space can be expressed in vector notation as d     .v =   (v.  ) , or simply can be written dt t t d  as   v   . The following conservation equations can now be formulated with the BTE dt t

format and they are elaborated here below.

2.2. Mass Balance Equation For a given space and time domain, the basic Boltzman transport equation (3) is now invoked to give

f f f f   v  F  colli t r p t

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where the partials of f to the momentum and space in 3-dimensions can be represented by applying the ―Del‖ operator, i.e.,  p f  f , f  f . Thus, integrating on both sides of p r equation (3) with respect to the momentum space, and noting the definition of the carrier density n (equation 4), yields:

n n  vn  F   p f dp  colli t t

(5)

Should dp be small in the space, the second term of right hand side of equation (5) can be omitted and equation (5) reduces to a familiar expression of the form;

n n  (vn)  colli , t t

(6)

where the collision effects from molecular particles are still retained. Defining the effective density as   m * n , where m* is the mass of single molecular particle. For simplicity, assuming the particles move with an average velocity, then v  v , and rearranging gives the mass conservation as

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   (v )  t t

.

(7)

colli

The advantage of equation (7) is that it is perfectly valid for describing electrons or phonons flow within submicron semiconductor devices and the collision term takes them into account. In the case of a macro-scale domain, the mass balance omits the collision term, i.e.,

  .( v) . t

(8)

The form of equation (8) can also be derived using the Gauss theorem within a control volume method [16]. For example, the rectangular coordinates nomenclature for the

ˆ would yield the continuity equation as component velocities for v  uˆi  vˆj  wk

 u  v  w    0. t x y z

(9)

Only when steady state is considered, i.e.,   0 ; and a case of constant-fluid density, t

the following simplified continuity equation reduces to

u v w   0 x y z Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

(10)

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Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al.

In vector notation, the mass conservation for a macro domain and constant density situation is simply expressed as     v  t . d     v dt

(11)

2.3. Momentum Balance Equation Starting from the basic transport equation, f   v f  F f  f colli , and multiply the t r p t momentum, p, on both sides before integrating over the momentum space yields;

f  pf dp   pv.f dp   pF. p f  dp   p colli dp  t t

(12)

Invoking the definition of the carrier density, n. and the left hand term of equation (12)

 np nm * v  v  whilst the first term on the pf dp     t t t t right hand side of equation (12) is reduced to  pv.f  dp  . vpf  dp  .J p , where can be expanded as,

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J p is a tensor. This flux density of momentum can further be transformed to





.J p  . vp  f dp  . v v  . vv  P , where according to Reif, F. [16], the velocity vector v v  U consists of a mean velocity v and a peculiar velocity U, and the pressure tensor is given by, P   U U   UU . The second term on the right hand side of equation (12) is given by,

 p F. f  dp  F   .p f  dp  F  f  p

p

p

.p dp  Φ , known as the source of

momentum, and the last term on the right hand side refers to as the collision integral, v   f   p t colli dp  t colli .Combining these expressions from above, equation (7) is now summarized in terms of the physical variables (  , v, p) as

  v    v   .P   v v   Φ  . t t colli

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(13)

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The vector product vv, is also known as the Dyadic product which is given by a set of matrix functions with respect to the component velocities. Detailed manipulation of the Dyadic product can be found in many mathematics texts. In general, two kinds of external forces may act on a fluid: (i) the body forces which are proportional to the volume such as the gravitational, centrifugal, magnetic, and/or electric fields, and (ii) the surface forces which are proportional to area, for example, the static pressure drop due to viscous stresses. From a microscopic viewpoint, the pressure tensor, P, is a related to short-range interaction between the particles of system, whereas the body forces, Φ, pertains to the external forces in the system. Equation (13) describes a balance for the momentum density (  v ), the momentum flow,

P   v v

with a convective portion  v v , and Φ, is a source of momentum.

Some examples of the type of source terms employed in two different application scenarios are outlined in Table 1. Table 1. Examples of the source term, Φ, for two common applications Field

Φ

 .τ  g , the first term indicates the viscous force per Fluid mechanics [18]

unit volume where τ is the stress tensor. The second term shows the gravitational force.

zE , where z is the total electric charge per unit mass in

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Electric flow [10]

the control volume and E is the electric field acting on the conductor.

For a macro scale flow situation, the collision term is omitted and equation (13) reduces to the conventional form as   v   .P   v v   Φ . t dv     P  Φ dt

(14)

It is noted that the total pressure tensor can be further divided into a scalar hydrostatic part p, and a tensor part, .

2.4. Energy Balance Equation Associated with the flow of a carrier density, n, there is a corresponding energy flow, w, such as the thermal energy and the drift energy term. By multiplying both sides of the basic BTE, i.e., equation (3), by w and integrating over the momentum space (product of mass and velocity) yields

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Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al.

f  wf dp   wv.f  dp   wF. p f  dp   w colli dp  t t

(15)

Expanding the left hand side of equation (15),  wf dp  wn  nm * e   e , where e is t  the total energy per unit mass and e  1 v 2    u . On the right hand side of equation (2.15), 2

the spatial gradient (i.e., the first term) can be placed outside the integral to give,  wv.f dp  . vwf dp  .J w , where J w represents the energy flux, defined here as n

J w   vwf dp   e v  P.v   k J k  J q , and

ev is a convective term, ( P.v ) is the

k 1

mechanical work in the system,

n

 k 1

k

J k equals to a potential energy flux due to diffusion, J q

is the heat flow. The second term on the right hand side of equation (15) can be expanded as:

 wF. f dp  F. w p

p

f dp 

 vF m*

 Φ.v

The collision term can also be expressed in terms of the energy dissipated Y, i.e.,

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w

f colli nw  Y . dp   t t colli t colli

Combining the above expressions, the energy balance equation is now summarized that includes the collision terms as; e Y  .J w  Φ.v  t t

(16) colli

To further understand the usage of the energy balance equation (i.e., equation 16), a minor digression is needed to demonstrate the presence of kinetic and potential energy terms. Multiplying the equation of motion [equation (13)] by v, a balance equation for the kinetic energy can be obtained, i.e.,   v  .v  . vv  P .v  .v t

1    v 2  2    t

1   .  v 2 v  P.v   P : v  .v 2 

(17)

which is commonly known as the mechanical energy term. Note that the vector reduction could be performed on equation (14), as given by de Groot, [10] 

3

  vv  v     i 1

  vi v j v j xi 

n

i, j  1,, n   i 1

 1 vi v 2j xi 2

1      v 2 v  2  

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159

and n

    P  v   P : v    i 1

 xi

 n  n n    Pij v j    Pij vj    xi j  1 i  1 j  1  

n n   n n       v j Pij  Pij v j    Pij vj xi xi  i 1 j 1 xi i 1 j 1 

i, j  1,2,3,, n

n n      v j   Pij     P   v j 1 i 1  xi 

Similar simplifications can also be made on the rate of change of potential energy density, as shown below; n n r      n  .  v   k J k    J k Fk   k v kj J j t k 1 k 1 j 1   k 1

(18)

    . v   J   JF t

The above results indicate that should

n

 k 1

k

v kj  0

 j  1,r  ,

potential energy is conserved into the chemical reaction situation.

this implies that the n

J k 1

k

Fk  JF which is

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referred to the source term where the particles interact with a force field such as the gravitational field or the electric charge experienced within an electric field. Adding equations (17) and (18), the combined effects become 1   v 2  2        . 1 v 2 v  P.v   P : v  .v  .v  J   JF   t t 2  1    v 2    2   . 1 v 2 v  P.v  v  J   P : v  JF  .v   t 2 

From the energy balance equation (16) and substituting for these derived functions, one obtains working form of the energy equation which gives in terms of the internal energy, u, heat flux, Jq, and the associated source and collision terms;  e   e   .J w  .v  t t colli 

 u  Y  .uv  J q   P : v  JF  t t

(19) colli

It is noted that uv + Jq is the energy flow due to convection and thermal energy transfers which contributes to the internal energy change, while the vectors P:v + JF is deemed as the source term associated with the internal energy. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al.

Further simplification of the energy balance equation (19) leads to its concise form of having only 4 terms and it is applicable to micro or thin layer flow of electrons or phonons;  u     uv  J q   P : v  JF  Y t t du Y     J q  Ψ  dt t

colli

(20)

colli

It is noted that the last term of the right hand side indicates the rate of change of energy as a result of collisions of the molecular particles such as electrons or phonons. Collision occurs by four processes in the micro-sublayer, i.e., (i) the increase in carrier kinetic energy due to interactions between electrons and holes or phonons, (ii) the heat dissipation arising from electrons or phonons interaction with the lattice vibrations, (iii) the heat dissipation by the electrons to the holes and vice versa, and (iv) the heat generation arising from the recombination and generation of the molecular particles. Equation (20) could be extended to macro analysis (adsorption cooling systems) by simply dropping the collision term which has its form known conventionally as the energy balance equation;

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

du    J q  Ψ dt

(21)

Another name for equation (20) is the equation of internal energy, as it is known in some texts [10, 17]. At this juncture, it is perhaps appropriate to elaborate these terms in terms of some common application examples. For example, the source term Ψ, in equilibrium and irreversible thermodynamics has two parts: (i) One aspect is the reversible rate of the internal energy attributed by effects of compression and (ii) the other is the irreversible rate of internal energy contributed by any dissipative effect. For most engineering applications involving real gasses, the internal energy is expressed in terms of the fluid temperature and the heat capacity. In such cases, the internal energy u may be considered as a function of  and T, and assuming constant specific heats, i.e.,

  u   u   p   du    d    dT   p  T    d  cv dT   T  T   T    and the substantial derivative term becomes



du  dT  dT  p   d  p     p  T      cv   p  T   .v  cv dt  dt  dt  T   dt  T  

Invoking the energy balance equation (21), it becomes

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dT  p     J q  T   .v   JF dt  T Vˆ

cv

161 (22)

Should the gas be assumed ideal, then  p   p and the second term of right hand side  T Vˆ T equation (22) becomes zero, i.e.,

dT    J q  JF . dt

cv

(23)

In another example, the internal energy u is considered to be a function of p and T, as in a real gas. Hence,

h  u  p 

dh du d dp  p  . dt dt dt dt

Invoking the constant pressure assumption, it can be shown that  dh   c p dT . dt dt

dh du d dh dT  p   c p dt dt dt dt dt

(24)

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From equation (24) and substituting for the energy balance equation for  du , it can be

dt dT demonstrated that the substantial derivative for the enthalpy, c , comprise only two p dt

terms, i.e.,

dT du d  p dt dt dt dT d c p    J q  p  v  JF   p dt dt

c p

(25)

From the continuity equation (11) we show that

p

d  p  v dt

Equation (25) is written as,

c p

dT    J q  JF dt

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(26)

162

Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al. The right hand side of equation (26) comprises (i) the heat flux term, J q and (ii) the

energy source term JF. Table 2 tabulates three scenarios where the source energy could be elaborated. For example, in the study of adsorption, where many chapters of the thesis are devoted, the source energy is derived by considering adsorbate mass and the isosteric heat of  H ads . Other examples in fluid mechanics and electrically powered semiadsorption, i.e., q conductors are also explained. It should be emphasized that equations (21-26) are valid for macro-scale devices simulation. However, for the analysis of sub-micron devices, the collision terms, which are provided in equation (20), must be included. Table 2. Explanation of energy source in different fields. Field

Source of energy JF

 : v ; This term indicates the irreversible internal energy increase due to viscous dissipation. ρelectJ2; this is the Joulean heat.

Fluid mechanics Electrical Chemical/Adsorption

 H ads , where q is the adsorption or desorption rate and q H ads is the isosteric enthalpy of adsorption.

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2.5. Summary of Section 2 In section 2, the conservation laws, i.e., mass, momentum and energy are derived from the transportation of molecules using the Boltzmann Transport Equation (BTE). The thermodynamic framework for describing the conservation laws is applicable to both the macro-scale and micro-scale systems. This approach differs from the control volume approach of de Groot and Mazur [10] Bird, R. B. [18], etc., where the Gauss theorem was employed. The latter approach could not embrace the collision terms, as what has been shown here using the BTE approach. For thin films or micro-scale systems, the collisions of electrons with electrons, electrons with holes, holes with holes are deemed to have significant dissipative effects, a source of irreversibility as quantified in the next section.

3. CONSERVATION OF ENTROPY The change of entropy of a system relates not only to the entropy (s) crossing the boundary between the system and its surroundings, but also to the entropy produced or generated by processes taking place within the system. Processes inside the system may be either reversible or irreversible [19]. The reversible process may occur during the transfer of entropy from one portion to another of the interior without entropy generation. On the other hand the irreversible process invariably leads to entropy generation inside the system.

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The entropy per unit mass is a function of the internal energy u, the specific volume 

and the mass fractions ck i.e. s  s(u, , ck ) . In equilibrium the total differential of s is given by the Gibbs relation [10] n

Tds  du  pd    k dck , where p is the equilibrium pressure and k is the k 1

thermodynamic or chemical potential of component k.

T

dc ds du d n  p   k k dt dt dt k 1 dt

(27)

From mass balance we get

P d T dt



P P   v  T T t

colli

The mass balance equation, equation (7), is written as,

d k    k   v    J k  k dt t

colli

where Jk   k v k  v  is the diffusion flow of component k defined with respect to the

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‗barycentric motion‘. Defining the component mass fractions ck as

ck 

k 

n

so that  ck  1 , k 1

and equation (7) can be simplified as

d k   k   v    J k  k dt t



colli

dck    J k dt

From equation (27) we have,

dc ds du d n  p   k k dt dt dt k 1 dt n  dc ds  du p d     k k dt T dt T dt k 1 T dt

T

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164

Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al. n J  k J k  q k 1     T  

  1   1 1 n 1 Y P      2 J q  T   J k   T  k   JF  k  1 T T T T  t  T t T    colli 

(28) colli

where Jk  k v k  v is the diffusion flow of component k defined with respect to the ‗barycentric motion‘. From equation (28), one observes that the entropy flow is given by two terms:

Js 

n 1   J q   k J k  , T k 1 

(29)

and the entropy source strength by

  1 1 1 n 1 Y  J q  T   J k   T k   JF  2 T k 1 T  T T t T      irreversible   collision

 

 colli

P  T t

colli

(30)

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The expression of entropy generation (equation 30) provides the key to irreversible thermodynamics. The first two terms indicate entropy generation as a result of irreversible transport processes whilst the third term represents entropy increase due to source applied to the system. The last two terms on the right hand side entropy increase due to (1) heat transfers from the other systems via collision processes, (2) free energy changes associated with recombination and generation of electron-hole pairs. Table 3. Example of processes leading to the irreversible production of entropy. Entropy generation    dS 

 dt  irr

Mechanical energy (due to friction or viscosity) Dissipation Electrical energy (by the passage of electric current through a resistance)

Irreversible heat flow in a conducting medium

Equations 1  dF  (Richard et. al., 1948), where dF is the   dt T  dt  rate at which work is done against force or viscous force.

I 2 R , where I is the flow of current through a T resistance R in conductor or semiconductor at temperature T.  1 . q.  T 

Here

q KT  is the vector which

expresses the rate of heat flow. The final expression is  dS  kTT .     dt  irr

T2

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165

Table 3. (Continued). Entropy generation    dS 

Equations

Free expansion of gas without absorbing heat [19]

The approximate expression for the irreversible increase in entropy accompanying the transfer of any particle element of the gas , consisting of dN moles, from pressure P1 to P2 is

 dt  irr

 P1  dS irr  RdN log  P    2 

 fc c fD d ...  dx  dS     R log K p  log a b  , where Kp fA fB ...  dt  dt  irr  is equilibrium constant at temperature T, R is the gas constant, fAfB…fcfd…etc., are the actual instantaneous values of the fugacities, a. b, …, c, d, … are the number of moles and dx is a factor.

Chemical reaction [19]

dt

Collisions (electron and hole transport in submicron semiconductor or thin film devices)

1 Y P   dS  , where the first      dt  colli T t colli T t colli term of right hand side indicates the collision due to change of energy between electrons-electrons, electrons-holes, holes-holes interactions, and the second term defines the collision because of change of carrier density.

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From equation (28) the general form of entropy balance equation is written as,

dS  .J s   dt

(31)

It is noted here that equation (31) has a similar form to the expression for total entropy, i.e.,

dS  dS   dS      , dt  dt  rev  dt  irr

(32)

Comparing the first term of the right hand side of both equations, the reversible entropy flux is  dS  

 dt  rev

  .J s  . This is the net sum of quantities carried into the system by transfers 

of matter, plus the net sum of quantities of entropy carried in by the transfer of heat. The second term yields  dS     , which is the entropy generation rate produced by irreversible    dt  irr

 

processes taking place inside the system. Table 3 shows some common examples of the irreversible processes (hence the internal entropy generation) of common engineering processes.

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  .XdV   X.nd   X.d

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V





Boltzmann Transport Equation approach

f f  f      colli t t  t  drift

Mass

  .( v) t

      v   t t

Momentum

v    vv  P    t

v  v   .P  vv     t t colli

Energy



Entropy

n    J q  k J k  ds k 1         dt T     n   1 1   2 J q  T   J k   T  k  T k 1 T  T  1  JF T

du    J q  Ψ dt



colli

du Y    J q  Ψ  dt t colli

n    J q  k J k  ds k 1   1 J  T        T2 q dt T     k  1 n    J k   T  T k 1 T   1 1 Y P   JF   T T t colli T t colli

The details of the BTE for analyzing the mass, momentum, energy and entropy conservation equations in macro and micro scales have been discussed in this section. This section concludes with the summary of all conservation equations as shown in Table 4 using Gauss and BTE approaches so that these two methods could be compared. This section is followed by the detailed thermodynamic modeling of adsorption cooling system (section 4), bulk thermoelectric module as examples of macro scale device, and thin film superlattice thermoelectric for micro scale system (section 5) to understand their thermal transport phenomena.

4. ADSORPTION COOLING The physical adsorption process occurs mainly within the pores of adsorbent and at the external adsorbent surface, and is determined by its adsorption isotherms, thermodynamic property surfaces of energy and entropy, heats of adsorption and adsorption kinetics. In a physisorption, the adsorbed phase is held near to the pores of the adsorbent by the existence of van der Waals forces as shown in Figure 3. The development of adsorption cooling system is based on the thermodynamic property surfaces of adsorbent-refrigerant system and the thermal compression of natural working refrigerants like water or alcohols and lies in its ability to operate with motive energy derived from fairly low temperature sources such as waste heat in process industries or sun light

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which indicates the adsorption process as an avenue for avoiding the use of ozone depleting substances [20]. The principal advantage of adsorption chillers (ADC) is that it is amenable to regenerative use of adsorption heat. Adsorption system incorporates no mechanical moving parts and generates no noise or vibration. A certain number of adsorbent-adsorbate pairs have been tested theoretically and experimentally for evaluating the performances of ADCs. These are silica gel-water, zeolite-water, silica gel-methanol, activated carbon-methanol, activated charcoal-NH3, zeolite-CO2, etc. Recently, a new family of composite sorbents called Selective Water Sorbents (SWSs) has been presented for sorption cooling and heat pumping [21].

Figure 3. The schematic diagram of a single component adsorbent + adsorbate system for any uptake, x as a function of pressure, P and temperature, T. The effects of gaseous phase are also shown here.

It is based on a porous host matrix (silica, alumina, etc.) and an inorganic salt (CaCl2, LiBr, MgCl2, MgSO4, Ca(NO3)2, etc.) impregnated inside pores [22, 23]. Building from the previous works, this article presents both the steady-state and dynamic behaviors of SWS-1L in a two-bed solid sorption cooling system using a transient distributed model. These results are compared with those of commercial adsorption cooler based on Fuji RD type silica gel such that a device for new generation of cooling can be enlightened. Both the heat and mass transfer resistances of the adsorption heat exchanger as well as the temporal energetic behavior in the evaporator and condenser are also taken into account in the present model. In this section, we also elucidated the effects of the isosteric cooling and heating times as well as the total cycle time on the system performances, and demonstrate that the current cooler design tends at optimum conditions.

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4.1. Description of Adsorption Cooling Model

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The adsorption cooling system which utilizes the adsorbent-adsorbate characteristics and produces the useful cooling effects at the evaporator by the amalgamation of ―adsorptiontriggered-evaporation‖ and ―desorption-resulted-condensation‖ was described elsewhere [2426]. Figure 4 shows the schematic layout of the adsorption chiller. It comprises the evaporator, the condenser and the reactors or adsorbent beds. For continuous cooling operation, firstly a low-pressure refrigerant (hence water) is evaporated at the evaporator due to external cooling load (or chilled water) and is adsorbed into the solid adsorbent located in the adsorber.

Figure 4. Schematic of a two-bed adsorption chiller.

The process of adsorption results in the liberation of heat of adsorption at the adsorber providing a useful heat energy output and a cooling effect in the condenser/evaporator heat exchanger. Secondly, the adsorbed bed is heated by the external heat source and the refrigerant is desorbed from the adsorbent and goes to the condenser for condensation by pumping heat through the environment. The condensate (refrigerant) is refluxed back to the evaporator via a pressure reducing valve for maintaining the pressure difference between the condenser and the evaporator. Pool boiling is affected in the evaporator by the vapor uptake at the adsorber, and thus completing the refrigeration close loop or cycle. These phenomena are expressed mathematically using the mass and energy balances between major components of the adsorption chiller system.

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Evaporator The energy balance becomes evap (  c p )eff

2 2 T evap  d evap,o  d evap,i t  4

2 2 evap  2  d  d evap ,i   evap  T  evap,o 2   4  z  

   d evap,i hevap T rvap  T chill (33)  





evap ( McP )eff where is the sum of all mass capacities of the evaporator. The first term on the right hand side defines the latent heat of evaporation that goes to adsorption bed, the second term is the enthalpy of liquid condensate and the last term denotes the cooling capacity of evaporator, which rises from the cooling of chilled water. Temperature boundary conditions

evap are T z

z 0

T evap  0 and z

 0 , respectively. zL

cond

The energy balance equation on the chilled water control volume is written as

 chill c chill f p, f

T chill T chill  2T chill UAchill chill  u chill  chill c chill  chill  chill T  T evap f f p, f f t z z 2 Vf



Hence the terms,

bed dxads dt

and

bed dxdes dt



(34)

indicate the adsorption rate and the desorption rate. The

boundary conditions of the chilled water tube are

T chill z  0,t   T chill,in and

T chill z  Ltube ,t  0 . z

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



Adsorption Isotherms and Kinetics The adsorption/desorption rate is calculated from the knowledge of adsorption equilibrium and kinetics and is given by the conventional linear driving force (LDF) equation [27] dx 15Dso e  dt R p2

E  a RT

x

*



x ,

(35)

where Dso defines a pre-exponential factor of the efficient water diffusivity in the adsorbent, Ea represents the activation energy, R is the universal gas constant and Rp is the average radius of the adsorbent grains. Kinetic data were taken from [28, 29]. Hence the adsorption uptake at equilibrium condition is expressed as a function of pressure (P) and temperature (T). The authors have measured the isotherms of water adsorption on silica gel of type RD, type A [30] and on SWS-1L [31, 32]. These experimentally measured data are fitted using the Tóth‘s equation [33], i.e.,

x* 

xm K o  expH ads R T  P

1  K

1 0  expH ads ( R T )  P

t



1 t1

,

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(36)

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where x* is the adsorbed adsorbate at equilibrium conditions, xm denotes the monolayer capacity,

H ads the isosteric enthalpies of adsorption, Ko the pre-exponential constant, and t1

is the dimensionless Tóth‘s constant. These values are furnished in Table 4. The most significant difference between these two adsorbents (silica type RD and SWS1L) lies in their water vapor uptake characteristics. From Table 4, one could observe that the water vapor uptake capacity of SWS-1L is higher than that of type RD. On the other hand, the adsorption uptake of water vapor on SWS-1L is expressed in terms of mole/mole by the polynomial equation, i.e., x*  exp a  bF  cF 2 [28, 32], where F indicates the





Polanyi adsorption potential and is represented by

F   RT lnP Ps  . The values of the

adjustable coefficients a, b and c that provide the best approximation of the two segments of the temperature-independent curve of sorption of water by SWS-1L composite [28, 32] are also furnished in Table 4. It should also be noted here that the values of Dso , E a and R p are found same for both RD silica gel-water and SWS-1L-water systems, i.e., the adsorption/desorption rate for both systems are nearly same but the difference between the two systems are occurred due to their different uptake capacities. Table 4. Adsorption isotherms of silica gel-water systems Ko (Pa-1)

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Type

-13

H ads (kJ/kg)

xm (kg kg-1)

t1

2800

0.4

8

RD (Tóth isotherm)

7.3 × 10

SWS-1L (Tóth isotherm)

2 × 10-12

2760

0.8

1.1

Type SWS-1L (polynomial equation)

a 2.83378 5.80313

b -3.0133×10-4 -0.00119

c × 109 7.46702 69.9054

ΔF kJ/mol 1-5 5-9

Bed As the evaporated refrigerant is associated onto the solid adsorbent by the flow of cooling fluid at ambient conditions during adsorption period, and the desorbed refrigerant is dissociated from the solid adsorbent by the flow of heating fluid during desorption period. The heat energy is exchanged between cooling/heating fluid and the adsorption bed. A schematic of the adsorption bed with heat exchanger is shown in Figure 1. The energy balance for the heat transfer fluid is given by

T f j t

 u fj

T f j z



 jf  c j f

 2T f j j p,f

z

2



h fj m A fj

 c Vf j f

j p,f

j

T

j f



 Tm ,

(37)

where u defines the flow rate of cooling/heating fluid, j indicates heating or cooling for j

desorption or adsorption, h f  m represents the heat transfer coefficient. The boundary condition for fluid flow becomes Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

Study on Adsorption and Thermoelectric Cooling Systems… during adsorption: T f z  0,t   T f

and

during desorption: T f z  0,t   T f

and

j

cool,in

j

hot,in

T f j z T f j z

z  L

tube

z  L

tube

171



,t  0 ,



,t  0 .

The energy balance of the metal tube that contains heat transfer fluid is written as h fj m Atube hm s Atube T tube tube  2T tube tube j  tube tube  T  T  T tube  T sg f tube tube t  cp z 2  tubec tube  tubec tube p V p V









(38)

A T  fin tube r c V tube





fin

tube tube p

Here the value of  is equal to 1 when any fin is attached with the tube, otherwise

  0 . The boundary conditions of the heat exchanger tube inside the adsorber are tube T tube z  0,t   0 and T z  Ltube ,t  0 , respectively. z z The fin thickness is very small and the heat transfer in the fin is assumed to be one dimensional in the radial direction. The energy balance equation of the fin is given by



T   fin fin t  cp Copyright © 2011. Nova Science Publishers, Incorporated. All rights reserved.

fin

fin

 T fin   r rr



 r  fin   h fin s A T fin  T sg .  fin c pfinV fin





(39)

fin The boundary conditions are T fin r  ro   T tube and T r  r fin   0 .

r

The energy balance of the adsorbent control volume can be written as (heat flow is considered both in r and z direction)

T sg dx h fin s A  c   xc  . eff T sg   sg H ads  t dt V fin h Atube  m stube T tube  T sg V



sg

sg p

g

a p









where

fin

T

fin

 T sg





(40)

the

specific heat capacity of the adsorbed phase is given by [34]  1 1 v g  H ads  . The first term in the right hand side indicates the c ap  c lp  H ads  sg  g  v T sg  T sg T

specific heat capacity at liquid phase, and the other terms occur due to the non ideality of gaseous phase, which incorporate two additional inputs from the properties of adsorbent + adsorbate system, namely the H ads and the isotherms (P-T-x) data [35]. On the other hand,

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g  the effective thermal conductivity of the adsorbed phase is eff  g    2 / 3 sg   

  [36], 

where  indicates the porosity of bed. Here eff is defined as the total thermal conductivity of adsorbent particles stacked together in the adsorber. The boundary condition at radial sg direction becomes  eff T r

T sg  hm s T tube  T sg and r



r  ro



0. r  r fin

Condenser After desorption, the desorbed refrigerant is delivered to the condenser as latent heat and this amount of heat is pumped to the environment by the flow of external cooling fluid. In the modelling, we assume that the condenser tube bank surface is able to hold a certain maximum amount of condensate. Beyond this the condensate would flow into the evaporator via a Ubend tube. This ensures that the condenser and the desorber are always maintained at the saturated pressure of the refrigerant. The energy balance of the condenser is expressed as cond (  c p )eff

T cond  d con,o  d con,i  t  4 2

cond

where ( Mc P )eff

2

2 2  cond  2T cond  d con  ,o  d con,i     d con,i hcon,i T cond  T cool 2    4  z   





(41)

is the sum of all mass capacities of the condenser. The first term on the

right hand side defines the latent heat of condensation, the second term is the enthalpy of liquid condensate and the last term denotes the sensible cooling of the condenser.

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cond Temperature boundary conditions are T z

z 0

T cond  0 and z

0. zL

cond

The energy balance equation of the cooling water control volume is written as

 cool c cool f p,f

T fcool t

 u cool  cool c cool f f p,f

T cool  2T cool UA  cool  f z z 2 V fcool

cool

The boundary conditions of the cooled water tube are T

T

cool

cool

 T cond



(42)

z  0,t   T cool,in

and

T cool z  Ltube ,t  0 . z





Mass Balance The mass balance of refrigerant in the adsorption chiller is expressed by dM ref  dx bed dx bed    M sg  des  ads  , dt dt   dt

(43)

where Msg is the mass of adsorbents packed in each of the two adsorbent beds, and Mref is the mass of refrigerant in liquid phase.

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The roles of the beds (containing the adsorbent) are refreshed by switching which is performed by reversing the direction of the cooling and the heating fluids to the designated sorption beds and similarly, the evaporator and condenser are also switched to the respective adsorber and desorber. It is noted that during switching interval, no mass transfers occur between the hot bed and the condenser or the cold bed and the evaporator. The cycle average cooling capacity Qchill, heating capacity Qheating and COP are, respectively calculated as tcycle

T fchill,in  T fchill,out

0

t cycle

,chill chill Q chill   chill u chill Atube c p,f  f f f

dt ,

tcycle

T fheating,in  T fheating,out

0

t cycle

,bed heating Q heating   heating u heating Atube c p,f  f f f

(44)

dt ,

(45)

and

Q chill COP  heating . Q

(46)

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4.2. Discussion The adsorption bed design incorporates a circular finned tube heat exchanger. The values for the parameters used in the present model are furnished in Table 5. Figure. 5. features the temperature histories at the outlets of the type RD silica gel (red lines in Figure 3) and SWS1L based chiller system (thick black lines in Figure 5) and these are compared with experimental data (thick blue lines and circles) of RD silica gel and water based adsorption chiller. Due to the positioning of the temperature sensors, the experimentally measured outlet temperatures are affected by the time constant of downstream mixing valves in the pipeline. It is evident that our present simulation results exhibit a sufficiently good agreement with the experimental data stemming from a distributed parameter model. Figure 5 also shows the temperature histories at the outlets of the condenser and chilled water. It should be noted here that the delivered chilled water temperature is slightly lower for adsorption chiller employing SWS-1L as can be seen in Figure 5. Figure 6 (a) presents the simulated Dühring diagram of the cyclic steady state condition of an entire bed comprising SWS-1L, from which one observes that during cold-to-hot thermal swing of the bed, momentary adsorption takes place although heating source has already been applied to heat up the bed in pre-heating mode. The entire bed is observed to be essentially following an isosteric path (constant x) during switching. In contrast, the local spatial points in the bed are not evolving in an isosteric manner, which is confirmed by the present analysis. This shows that while some parts of the bed may continue to adsorb, other parts desorb, resulting in the entire bed following an isosteric path. At the end of hot-to-cold

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thermal swing, there is a pressure drop in the bed. This causes the adsorbate in the cool bed to desorb momentarily and condense into the evaporator. The P-T-x diagram for adsorption bed employing RD type silica gel during steady state is also imposed in Figure 6 (b) for comparison. Table 5. Values adopted for adsorption chiller simulation used in the present model [37] Dso

2.54 × 10-4 m2/s for SWS-1L and RD silica gel

Ea

4.2 × 104 J/mol for SWS-1L and RD silica gel

Rp

1.7 × 10-4 m for type RD and 1.74 × 10-4 m for SWS-1L 924 J(/kg K)

c sg p hm s

36 W/(m2 K) [16]

h fins

36 W/(m2 K) [16]

UAchill UAcond

(2557 W/(m2 K) × 1.37 m2) (4115 W/(m2 K) × 3.71 m2)

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Mc  Mc 

evap p eff

(8.9 kg × 386 J/(kg K) + 40 kg× cp,water J/(kg K))

cond p eff

(24 kg × 386 J/(kg K) + 5 kg× cp,water J/(kg K))

ri

7.94 mm

Atube  2ro Ltube

ro = 8.64 mm, Ltube = 1 m

V fchill  ro2 Levap

Levap = 2.1 m

V fcool  ro2 Lcond



2 V fin  Nh r fin  ro2



Lcond = 2.34 m N = 100, h = 0.1 mm, rfin = 22 mm

u chill f

0.18 m/s

u cool f

0.198 m/s

u heating f

0.14 m/s

M sg T fcool,in

20 kg

T fhot,in

85 ºC

T fchill,in

14.8 ºC

31 ºC

Figure 7 presents the effects of cycle time on COP and cycle average chiller cooling capacity for type RD and SWS-1L based adsorption chiller systems. It is clearly seen that the Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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COP increases monotonically with the cycle time. The reason is that with a longer cycle time, the relative time frame occupied bed switching which involves a significant sensible heat exchange is reduced vis-à-vis that of a shorter cycle time. This will lead to a favorable effect on the COP.

Figure 5. Simulated (black for SWS-1L-water system; red line for type RD silica gel-water system) and experimental (blue circles for type RD silica gel-water based adsorption system) heating fluid and cooling fluid outlet temperatures from the adsorption chiller system. Simulated and experimentally (for type RD silica gel only) measured fluid outlet temperatures from the condenser and evaporator are also shown here.

The variation of cooling capacity is not monotonic. For SWS-1L based adsorption chiller, the cooling power increases steeply up to 500 s, and it begins to decrease with a similar slope at the cycle time of over 500 s. Lower cooling capacity under a relative shorter cycle time is caused by a reduced extent of adsorption, which is also related to a reduced extent of desorption due to the insufficient heating of the desorber. At a certain cycle time, the maximum adsorption/ desorption capacity is achieved at the prevailing heating and cooling source temperatures. Extending the cycle time further brings forth unfavorable effect on useful cooling as the cycle average cooling capacity decreases. For the SWS-1L - water based pair, cycle times longer than 300 s can be realized with the higher cooling power and COP as compared to the adsorption cooling system based on RD silica gel-water pair. The system performance at different driving heat source temperatures in case of optimum conditions [(i) cycle time 420 s, switching time 30 s for type RD silica gel-water system, and (ii) cycle time 630 s, switching time 30 s for SWS-1L – water system] is shown in Figure 8 for the same heat sink temperature of 31 ºC.

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b)

Figure 6. Dühring diagram of the whole bed under cyclic steady state condition for (a) SWS-1L and water based adsorption chiller, (b) type RD silica gel and water based adsorption cooling cycle. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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For type RD silica gel-water system the COP reaches the maximum value of 0.35 at T = 75-80 oC. For SWS-1L - water system at this temperature range the COP is larger (0.42-0.45) and remains almost constant at higher T. The COP of SWS-1L - water system is higher than that of RD-water system because of high cooling and less driving heat generation powers, which may occur due to larger x for the same heat source and heat sink temperatures. This much larger COP shows significant advantage of the new working pair as compared with the conventional unit. Thus, from the present simulation results, it is found that the newly SWS-1L based adsorption chiller provides a promising unit for cooling applications. This theoretical conclusion should be confirmed practical testing of the new adsorbent in the optimized ADC configuration.

Figure 7. Effect of cycle time on COP and cycle average cooling capacity.

Figure 8. Influence of driving heat source temperature on cyclic average cooling capacity and COP. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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4.3. Summary of Section 4 We have successfully modeled and predicted the performances of SWS-1L and water based adsorption chiller using a simplified distributed approach such that both the transient and steady state behaviors of ADC can be captured. It is found that the performances of ADC incorporating SWS-1L as adsorbents, in terms of cooling capacity, coefficient of performance and peak chilled water temperature, are better than those of the commercial available silica gel-water based adsorption chiller. An optimum switching time of 30 s is obtained for both cycles and the cycle performance improves with increasing hot water inlet temperature.

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5. MACRO AND MICRO THERMOELECTRIC COOLERS The reversible thermoelectric effects are the Seebeck, Peltier and Thomson effects [38]. These are related to the transformation of thermal into electrical energy, and vice versa. The physical nature of the thermoelectric effects is not well explained in the literature, as well as the dependence of Seebeck coefficient on temperature and materials. From the electron theory, the absorption of Thomson heat in the interior of a thermally non-uniform conductor has been reported to be the additive superposition of two effects: Firstly, a part of Thomson effect is the internal Peltier effect which is caused by the non-equilibrium electron distribution functions in a thermally non-uniform conductor. Secondly, the other part is heat absorbed due to current flow against the drift potential difference. These effects are assumed to be reversible and hence, the sign of the Thomson heat changes with the reversal of current direction. The thermoelectric effects in semi-conductors are stronger than those found in metals. This is attributed to the fact that electron gas in semi-conductors is far from being degenerated and obeys the classical Boltzmann statistics. The non-equilibrium changes in the distribution function are more noticeable than in a degenerated gas and this affects the magnitude of the thermoelectric effects. The magnitude of non-equilibrium change in the distribution function (and consequently the magnitudes of the thermoelectric effects) depends on the relative importance of the factors (such as electric field, thermal non-uniformity) that are responsible for the departure from equilibrium, as well as the mechanism for reestablishing the equilibrium. When an electric field is applied to a thermoelectric device, the following irreversible processes are deemed to occur in each elemental volume: (i).Electric conduction (electric current due to an electric potential gradient). (ii).Heat conduction (heat flow due to a temperature gradient). (iii).A cross effect (electric current due to a temperature gradient) (iv).The appropriate reciprocal effect (heat flow due to an electric potential gradient). The last two belongs to a new class of irreversible process [14]. The organization of this section is as follows: Section 5.1 describes the thermodynamic modelling of the bulk thermoelectric cooler and in addition, the entropy analysis of a transient thermoelectric cooler is also discussed. The thermodynamic behavior of a pulse thermoelectric cooler is investigated in section 5.2. The

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governing equations employed in this section are derived from the Boltzmann Transport Equation (BTE) that is reported in the previous section.

5.1. Thermoelectric Cooling

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The refrigeration capability of a semiconductor material depends on parameters such as the Peltier effect, Joule heat, Thomson heat and material‘s physical properties over the operational temperatures between the hot and cold ends. A thermoelectric device is composed of p-type and n-type thermoelements such as Bi2Te3 and they are connected electrically in series and thermally in parallel. These thermoelectric elements are sandwiched between two ceramic substrates. As shown in Figure 9, thermoelectric cooling is generated by passing a direct current through one or more pairs of n and p-type thermoelements, the temperature of cold reservoir decreases because the electrons and holes pass from the low energy level in ptype material through the interconnecting conductor to the higher energy level in the n-type material. Similarly, the arrival of electrons and holes in the opposite end results in an increase in the local temperature forming the hot junction. When a temperature differential is established between the hot and cold junctions, a Seebeck voltage is generated and the voltage is directly proportional to the temperature differential. The amount of heat absorbed at the cold-end and dissipated at the hot end depends on the product of Peltier coefficient (  ), Fourier effect (λte) and the current (I) flowing through the semiconductor material, whilst the heat generation due to the Thomson effect occurs along the thermoelectric element. Thermoelectric effects are caused by coupling between charge transport and heat transport and from which the basic mass, energy and entropy equations can be formulated to form a thermodynamic framework.

Figure 9. The schematic view of a thermoelectric cooler.

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5.1.1. Energy Balance Analysis The Peltier and the Thomson effects enhance the cooling effect in thermoelectric materials. The Thomson effect is a function of the gradients from the Seebeck coefficient and the temperature in an operating thermoelectric pallet or element. The energy balance equation of the thermoelectric cooler, as shown in Figure 9, follows the methodology of the Boltzmann transport equation which has been discussed in the previous section, namely: u  u  ,  .uv  J q   P : v  JE  t t colli

(47)

where u is the internal energy per unit mass, ρ is the density, v defines velocity, Jq indicates the heat flow, P represents the pressure and JE is the energy field term. For the bulk thermoelectric material analysis, the contributions from the collision terms are deemed negligible and can be neglected;

teu   .teuv  J q   P : v  JE . t

(48)

Hence the subscript te indicates the thermoelectric cooler. As there is no velocity and pressure fields in a thermoelectric device, u (49)  te  .J q  JE t

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Invoking the definition of enthalpy;

h u  pV  u    t t t t

h  u  pV



h  hT , p  

T h  h  Tte  h  p        c p ,te te t  Tte  p t  p Tte t t

where the pressure gradient term is zero. The first term of right hand side of equation (3.1) is the heat current density, J q (in W/m2), and the second term is the electric current field, JE J   (in W/m3). Using the thermodynamic-phenomenological treatment [39], the heat current density

Jq  

Qo J  teT , F

(50)

where J (in amp/m2) denotes the electric current density, Qo indicates the heat transport of electrons/ holes, te defines the thermal conductivity of the bulk thermoelectric element and F is the Faraday constant and the electric current density can be expanded as

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J   te   where

 te Qo FTte

Tte ,

181 (51)

 te defines the electrical conductance and  is the electrical potential.

Equation (51) is re-arranged as,  

J



 te

Qo Tte FTte

(52)

Hence,  .J q  JE  .te Tte  

Q J2 J  Tte    te F  Tte 

where  Q  is equivalent to the entropy term. T   te 

Now, substitute all these relations into equation (49), the expression becomes [40]

 te c p ,te

Tte J 2 JTte  ste    Tte ,  .te Tte    t  te F  Tte  p

(53)

where ste introduces the transported entropy of the bulk thermoelectric arms. Defining the Thomson coefficient   as [41],

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 

Tte  ste  ,   F  Tte  p

the governing thermal transport in the bulk semiconductor arms is given by

 te c p ,te

Tte J2  .te Tte    JTte t  te

(54)

Using the Kelvin relations [17],



     , where   Tte  Tte 



  T  is the Peltier coefficient.

Equation (54) can now be written as (derivations are shown in Appendix),

 te c p ,te

Tte J2     te  2Tte   JT  T  JT  Tte te t  te  T 

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(55)

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5.1.2. Entropy Balance Analysis The basic entropy balance equation has been introduced in the previous chapter, as shown below: ds    J s   dt   s   .J s   sv    t



(56)

Introducing the phenomenological relations:

J s ,te   te ste v  

te Tte

Tte 

 Tte

J,

(57)

and invoking the Kelvin laws, one could observe

T   .

(58)

Assuming only the bulk thermoelectric materials, the collision terms are usually neglected and the entropy source strength is given by (as discussed in the previous sections);

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 

  1 1 1 n  J   T  J k   T k   J  E  q 2 T k 1 T  T T 

Hence, the entropy generation of thermoelectric arm can now be modified into a form that is inclusive of the Peltier coefficient and the local temperature as [17]

 

1     1   Tte  J   Tte  J  Tte  J /  te  Tte  Tte Tte  Tte

Finally, the entropy balance equation (56) becomes;

 te ste    te Tte  J J2    t Tte Tte Tte te

(59)

The first term on the right-hand side of equation (59) represents the change of entropy due to heat conduction; the second term indicates the entropy flux due to Seebeck effect and the last term is the entropy generation due to Joule heat. A more elegant method of writing the entropy fluxes of thermoelectric arm is to express them in terms of (i) the heat and carrier fluxes, (ii) the internal dissipation, and (iii) the entropy generation that comes from conduction and Joulean heat transfer:

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Study on Adsorption and Thermoelectric Cooling Systems… entropy source strength  ernal dissipation flux entropy     int  Jouleanheat    T  1    te ste  J   J2     te te     te Tte .   t Tte   Tte te  Tte  Tte   

due to

183

      

(60)

where the units of entropy flux is in W/m2 K and it is given by, S flux 

te Tte Tte



J ,

(61)

Tte

and entropy generation per unit volume is in W/m3 K which is expressed as:

 1  J2 . S gen  te Tte .    Tte  Tte te

(62)

Equation (62) is always a positive term.

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5.1.3. Temperature-Entropy Plots of Bulk Thermoelectric Cooling Device From the work of Carnot and Clasius, Kelvin deduced that the reversible heat flow discovered by Peltier must have entropy associated with it. It has been shown that the coefficient discovered by Seebeck was a measure of entropy associated with electric current [41]. A temperature-entropy (T-s) has been proven to be a pedagogical tool in analyzing the performance of thermoelectrics undergoing both reversible and irreversible processes. The parameters used in the computation are listed in Table 6. Table 6. Physical parameters of a single thermoelectric couple. Property Hot junction temperature, TH Cold junction temperature, TL Thermoelectric element length, L Cross-sectional area, A Electrical conductivity, σ' Seebeck coefficient α (V/K) α (T) = αo + α1 ln (T/To) Thermal conductivity, λ

value 300 K 270 K 1.15 × 10 -3 m * 1.96 × 10-6 m2 * 97087.38 ohm-1.m-1 * αo = 210 × 10-6 V/K, α1 = 120 × 10-6 V/K To = 300 K (Seifert et al., 2002) 1.70 W/m K *

*Melcor thermoelectric catalogue, Melcor Corporation, 1040 Spruce Street, Trenton, NJ 08648, USA. Web site: www.melcor.com.

For an ideal thermoelectric device, the Seebeck () coefficient is constant and the heat flux at the hot and cold junctions are given by JTi where the subscript i refers either to the hot or cold junction. Thus, the temperature Seebeck coefficient (T-) plot is simply a simple rectangle. However, the temperature effect on the Seebeck () coefficient induces the dissipative losses along the p and n legs of thermoelectrics and an indication of these losses

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are shown by the shaded area on the T- plot, as shown in Figure 10, in which the physical properties of the Bismuth Telluride thermoelectric pairs are used.

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Figure 10. T-α diagram of a thermoelectric pair. The shaded areas indicate dissipative losses along p and n legs.

Figure 11. Temperature-entropy flux diagram for the thermoelectric cooler at the maximum coefficient of performance identifies the principal energy flows.

The two isotherms are the hot and cold junctions whilst the inclined lines indicate the effect of temperature on the  values when the current (I) travels along the p- and n-legs. For thermodynamic consistency, the temperature-entropy (or temperature-entropy flux) diagram is. In an optimum current operation of the thermoelectric cooler, the presence of entropy loss (due to conduction heat transfer and Joule heat) along the p-n legs is given by KT /Ti and they are manifested by enclosed areas ―k-i-u-r-d-c-k‖ and ―j-i-n-q-a-b-j‖ of

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Figure 11. Both mentioned dissipative losses have the consequence of reducing the cooling effect, represented by area ―a-d-r-q‖. Within the internal framework (adiabatic chiller), the cycle ―a-b-c-d‖ operates in an anti-clockwise manner with process with two isotherms b-c and d-a, as well as two non-adiabats a-b and c-d. Details of these processes are described in Table 7. Thus, the T-s diagram provides an effective means of analyzing how the real chiller cycle of thermoelectrics is inferior to the ideal Carnot cycle by capturing the key losses and useful effects in the cycle.

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Table 7. Description of close loop a-b-c-d-a (Figure 11) Process

Description

a--b

This process is developed along P-arm of the thermoelectric pair. Points a and b are the states at the ends of the thermoelement of which the temperatures are TL and TH respectively (as current J flows from P-arm to N-arm). The process a-b cannot be adiabatic because it absorbs heat due to the Thomson effect which depends on the Seebeck coefficient of the thermoelectric element. The areas beneath the a-b process represent dissipation due to heat conduction, and heat absorbed by the Thomson effect. Area 2-i-j represents the energy dissipation due to Seebeck coefficient, which varies along the thermoelectric p-arm.

b--c

This process represents the heat exchange between system and medium (environment) which occurs at the union between P-arm and N-arm at temperature TH.

c--d

The process c-d is developed along N-arm, where points c and d are at the ends of the thermo-element whose temperature are TH and TL. The areas beneath c-d process indicate heat losses due to dissipation. If this process is adiabatic, the Thomson effect would be null. Area 1-l-k indicates the energy losses due to Seebeck effect along the n-arm.

d--a

This process represents the heat exchange between the system and the heat load at isothermal condition; however it occurs in the physic union between thermoelectric elements at temperature TL.

From temperature-entropy flux diagram, the thermodynamic performance variables can be easily tallied with the enclosed rectangles. The heat fluxes at the cold (process d-a) and hot (process b-c) reservoirs are as follows (for details please see Appendix)  AT cj    IT  AT QL  Area adrq   TL J S , pn  TL  I  L cj   TL ,   Joulean_ heat

Peltier _ cooling



  IT L



 1 2 I R 2



conduction  _ heat

KT

T hom son _ heat



 1 IT 2

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(63)

186

Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al.  AT hj    IT  AT QH  Area bcto   TH J S , pn  TH  I  H hj   hj TH   Joulea_ heat

Peltier _ heat



 ITH



 1 2 I R 2



Conduction  _ loss

KT

(64)

T hom son _ heat

 1 IT 2



where T is the temperature difference across the hot and cold junctions. The first term of right hand side of both equations (63) and (64) indicates Peltier cooling and heating, the second term is the Joulean heat, the third term represents heat conduction between hot and cold junctions and the heat absorbed by the Thomson effect. The Thomson heat is transmitted by thermal conduction across the thermo-element and this effect is not reversible. From the first law of thermodynamics, the required electrical power input is given by, P  Area bcto   Area adrq   TH J S , pn QH

hot

 TL J S , pn

cold

QL

  1 1 1 1  ITH  I 2 R  KT  IT  ITL  I 2 R  KT  IT 2 2 2 2

(65)

P  I TH  TL   I 2 R  IT

11),

The equivalent cycle at the same TH and TL is denoted by a rectangle 1-2-j-k (see Figure for which or COPcarnot  Area1vm2 Areakvmj   Area1vm2

COPcarnot  Area1vm2 Area12 jk   TL T .

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The irreversibility is the heat dissipation, which is shown in Figure 11, occurs due to the Joule heat and to the heat conduction along the thermoelectric arm.

5.2. Transient Behavior of Thermoelectric Cooler The performance of a Peltier or thermoelectric cooler can be enhanced by utilizing the transient response of a current pulse [42-45]. At fast transient, a high but short-period (4 seconds) current pulse is injected so that additional Petlier cooling is developed instantly at the cold junction: The joule heating developed in the thermoelectric element is a slow phenomenon as heat travels slowly over the materials and could not reached the cold junction in the short transient. Hence, the cold junction temperature is at the lowest possible value and heat flows only from the source to the cold junction. An example of such an application of the short transient cooling is an infrared detector operating in a ‗winking mode, which needs to be super cold only during the wink. Figure 12 shows the schematic diagram of a current ―pulse train‖ thermoelectric cooler with the p- and n- doped semiconductor elements are electrically connected in series and are thermally in parallel. The hot side of the device is mounted directly onto a substrate to reject heat to the environment and the thermal contact between the cold junction of thermoelectric device and the cold substrate (load) is made periodically. There are two periods of operation: Firstly, an ―open contact‖ period with tno and current flow Jnp to maintain the lowest temperature Tmin at the cold junction but the cold substrate (load) is not connected with the cold junction. Secondly, a large current pulse Jp (where Jp=MJnp, M >

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1) is applied for a duration tp and concomitantly, the cold substrate makes contact with the cold junction. Intense Peltier cooling is achieved during tp, which reduces the cold junction temperature below Tmin. However, Joule and Thomson heating are developed in the bulk thermoelectric module and diffuse towards the hot and cold ends of the device. Thermal contact of the cold substrate with the cold end of the thermoelectric module is maintained over the short current pulse period but these surface break contact before the cooling could be degraded by the conduction heat. In the open contact manner, the cold substrate temperature could reach below that of the cold junction temperature under the normal thermoelectric operation. The total operation consists of two periods; one is the normal thermoelectric operation and the other is the pulse or effective operation. The cycle of (normal operation + pulse operation) is repeated such that the device is continuously produced cooling. This section formulates a non-equilibrium thermodynamic model to demonstrate the energy and entropy balances of a transient thermoelectric cooler. In analyzing the fast transient cycle in the classical T-s plane, one distinguishes the entropy fluxes of the working fluid (which is the current flux J) from the external entropy fluxes in the hot and cold reservoirs and at the interface with the reservoirs. The T-s relation is formulated that identifies the key heat and work flows, the heat conduction and electrical resistive dissipative losses.

Figure 12. Schematic diagram of the first transient thermoelectric cooler. (a) indicates the normal operation and cold substrate is out of contact, (b) defines the thermoelectric pulse operation and cold substrate is in contact with the cold junction, (c) shows the thermoelectric couple consisting of p and n arms, (d) indicates that the pulse current is applied to the device.

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5.2.1. Derivation of the T-S Relation The methodology of energy and entropy balances of the commercial available thermoelectric device has been discussed briefly in the previous sections. Starting from the general entropy balance equation, it can be expressed in terms of the key parameters such as Peltier effect   , electrical conductivity   , current density (J) and Fourier effect (λ), as shown below [46]: entropy generation entropy flux       p T p J p    1    p s p  J p2      ,       p T p .   T  T  T    t T p ,te   p p p    p

(66)

hence the subscript p defines the pulsed thermoelectric cooler, the first term of the right hand side indicates the entropy flux in a given control volume and the second terms represent the total entropy generation. The total entropy flux density (in W/m2 K) is expressed by

J s ,tot

p



 p Tp Tp

 J p ,

(67)

and the entropy generation (in W/m3 K) is written as

 p ,tot

 1   p T p . T  p

 J2  p .  T  p p 

(68)

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The energy conservation equation is as follows

 pc p

  J p2   p Tp   J pT p ,te  T  J pT p   T p t  p  p

T p

2

 T p .  

(69)

To solve the problem, two boundary conditions are defined: Firstly, during the normal (open-contact) operation, there is only Peltier cooling at the cold junction T p x

 at cj

JTcj , p

and at hot junction, a hot side heat sink is represented by, T p

(70)

at hj

 Thj . But during the pulse

(close-contact) operation, at the cold junction the boundary condition becomes

T p x

 at cj

. JTcj q subs ,  p p

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(71)

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. where qsubs is the cooling load of the cold substrate.

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5.2.2. Discussion Figure 13 shows the transient behavior of the pulsed thermoelectric cooler where the hot junction is assumed to be constant at Thj = 308 K. Based on the physical properties of a thermoelectric cooler, as tabulated in Table 6, the simulations with an initial current density of Jnp = 0.675 A/mm2 yield an exponential decrease of the cold junction temperature to Tc,A‘ = 240 K (denoted by point A´), and beyond which a pulsed current density of Jp = 2.025 A/mm2 for a duration of 4 s is applied for the pulsed or contact mode.

Figure 13. The transient temperature-time trace of cold reservoir temperature of a pulsed thermoelectric cooler. Point ―A‖ indicates the beginning of pulse period, ―B‖ denotes the lowest temperature reached by the cooler and ―C‖ represents the end of pulse period, ―C‘ ― shows the beginning of non-contact period, ―B‘ ― indicates maximum temperature rise due to energy balance between the residual heat from the pulsed period and the steady state cooling.

The high pulsed current in the thermoelectrics produces instantaneous Peltier cooling, as shown by the decrease in the cold junction temperature to point B. Concomitantly, the pulsed current generates the Joule and Thomson heating within the p-n legs and this is reflected by the rise of cold junction temperature from point B to C. As no cooling could be achieved by the cold substrate, the cold junction breaks contact with it at point C. However, the residual heat transfer from the mentioned effects is generally a slower phenomenon as compared to Peltier cooling, the temperature of the cold junction continues to rise until the cooling by Jnp overcomes the residual heat within the legs, culminating in a maxima for the temperature of the cold junction, as depicted by point B‘. For the non-contact duration, the energy flows in the thermoelectric device can best be followed by tracking the temperature versus entropy fluxes along the p-leg in a anti-clockwise direction, i.e., points ―a‖ to ―g‖ of Figure 14: Point ―a‖ denotes the cold junction temperature and the entropy flux here is taken to be zero or the datum. As holes migrates along the p-leg, both entropy flux and temperature increase with the spatial length until point ―g‖ is reached, due primarily to the property changes with the local temperature of Bi2Te3 materials such as

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the electrical resistivity (ohm-cm), Seebeck coefficient (V/K) and thermal conductivity (W/cm K).

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Figure 14. Temperature-entropy flux (T-s) diagram showing the anti-clockwise loop of a pulsed thermoelectric cooler for the non-pulse duration for three operation points [46].

For the given configuration and current density, the maximum entropy flux is about 300 W/m2.K. At the hot junction which is assumed to remain constant at Thj, the sign of the entropy flux changes from positive to negative due to negative temperature gradient along the n-leg, resulting in the isotherm ―g‖ to ―h‖ line on the T-s diagram. Following the path in an anti-clockwise direction, the local entropy flux increases from point ―h‖ to point ―a‖, completing the cycle (denoted by A´) on the T-s diagram. Two other process cycles could also be observed for the non-contact duration, namely cycles ―B‖ and ―C‖: Both Cycles are subjected to Jnp and they show the presence of residual Joulean and Thomson heat within the p-n legs of the thermoelectrics. The balance between the cooling rate generated by the Jnp and the amount of residual Joule and Thomson heat from the previous pulsed injection yield a local thermal wave front in each of the legs (at distances closer to the hot junction) where the maximum local temperature is higher than that of the Thj. During closed contact operation, as shown in Figure 15, point A indicates the commencement of contact interval where the imposed current pulse (Jp) generates a substantial cooling, depressing the cold junction and the cold template temperature from ―f‖ to ―a‖ (see the smaller insert). As opposed to the non-contact duration, the cold junction on the T-s plot has an isotherm path, and the area enclosed below the isotherm a-a‘ indicates the amount of cooling produced at point A of the contact operation. Similar isotherms c-c‘ and d-d‘ correspond to the points B and C during the transients. Although the enclosed area for point C is slightly larger than that of point B, but the cold junction temperature of point C is found to be higher, caused by the diffusion of Joule heat from the legs of the thermoelectrics. No cooling power is developed during non-contact period but the cooling power is generated during pulse period. Figure 16 shows the time evolution of entropy flow and temperature at the cold junction and calculates the minimum time to reach the maximum

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temperature difference between the super-cooling and the steady state or Tp,max . The

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characteristics time, entropy flux and cold end temperature as shown in Figure 16 may be used to characterize the pulse cooler as functions of length of pulse tp, pulse factor M, and pulse current density, Jp. This graph is helpful to design a cooler where the user would easily calculate the amount of increasing cooling, cooling behaviors, the needed pulse current and the time between pulses.

Figure 15. Temperature-entropy flux (T-s) diagram showing the energy flow details of a pulsed period of thermoelectric cooler. Cycles A to C refer to the beginning of cooling, the lowest temperature reached and the maximum cooling power by the cooler. The details of the processes within the cold junction of thermoelectrics are shown by the small insert, denoted correspondingly by ―a‖ to ―c‖. The enclosed area below Tc isotherms in the T-s diagram indicates the cooling power.

Figure 16. The effects of pulse periods on entropy flux and the cold junction temperature subjected to a step current pulse of magnitude M = 4. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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The effects of pulse factors on entropy flux at cold end and the maximum temperature drop or Tp,max are shown in Figure 17 and the optimization is obtained at pulse factor 4 [46].

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Figure 17. Maximum pulse cooling difference in temperatures and entropy fluxes as a function of pulse factor, exhibits the optimization.

5.2.3. Summary of Section 5.2 We have successfully plotted the T-s diagrams for the transient features of a pulsed thermoelectric cooler. The thermodynamic formulation (based on the Gibbs law) provides the necessary expression for the entropy flux that is expressed in terms of the basic variables describing the device, namely, the current density, Seebeck coefficient, the local temperature and temperature gradient. Using the T-s diagram, the process paths of the pulsed and nonpulsed operations of thermoelectric cooler are accurately mapped and it has immense pedagogical value for cycle evaluation, depicting the useful energy flows and ―bottlenecks‖ of cycle operation.

5.3. Microscopic Analysis: Super-Lattice Type Devices The development of semi-conductor materials for cooling and heating applications has made steady progress with the thermoelectric (TE) coolers being made of the BismuthTelluride (Bi2Te3), Antimony-Telluride (Sb2Te3), and Silicon-Germanium (SiGe) materials [47]. Two factors, however, limit the wide spread application of such coolers, namely (i) the low efficiency or coefficient of performance (COP) at higher temperature differential across the cold and hot junctions, and (ii) the cost of the semi-conductor devices per unit cooling capacity. The cooling efficiency of TE elements, comprising the p-n layers of semiconductors, is characterized by the dimensionless ZT parameter: T is the absolute operational temperature and the thermoelectric figure of merit Z is given by α2/ρλ where α is the Seebeck coefficient, ρ is the density and λ is the thermal conductivity. The best thermoelectric materials available, hitherto, have a ZT ≈ 0.9, but for commercial viability as cooling devices

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at ambient conditions, the ZT value should exceed a value 3. Recently, there were reports of semi-conductor materials with multi-quantum well materials [48], PbSeTe-based quantum dot superlattice structures [49] and thin-film Bi2Te3/Sb2Te3-based superlattice thermoelectric element for both refrigeration and power generation applications [50, 51]. Thin-film thermoelectric coolers using silicon materials such as Si/Si0.8Ge0.2, have been fabricated by alternating barrier and conducting layers which generate the quantum wells and increase the electron mobility. The procedures of making thermoelectric modules with p and n-type (Si/ Si0.8Ge0.2) superlattices have been reported [52]. The size of thermoelectric device characterizes the transport of electrons, holes and phonons. In a very thin film with a thickness less than mean free path, electrons go through the film ballistically and experience little or no collision [53]. Scattering or collision dominants the transport process of electrons, holes and phonons in thick films or bulk materials. In case of bulk thermoelectric material such as Bi2Te3, SiGe, SbTe, the limiting speed of thermoelectric element responses from milliseconds to a few second, so the energy dissipation due to collisions of electrons, holes and phonons is not significant and heat transport is purely diffusive [54]. The reduction of device sizes to the sub-micrometer range not only increases the device switching speed from nano-second to pico-second but also increases the local rate of heat generation due to electron-phonon interactions or hole-phonon interactions [54, 55]. The motivation of this section is to model the thin-film thermo-electric cooling devices [50] as shown in Figure 18 using the BTE where both macro and micro phonological dissipations are rigorously captured at the micro-scaled dimensions. The present model treats the non-equilibrium transport of electrons-phonons (in case of n-type such as Bi2Te3/Bi2Te2.83Se0.17 thin film thermoelectric element) and holes-phonons (for p-type such as Bi2Te3/Sb2Te3 thin film thermoelectric element), and their non-equilibrium coupling or the collision contributions at different electric fields using the practical temperature-entropy (T-s) diagrams. This T-s diagram quantifies the net useful cooling effects at the cold junction and the COP. The proposed model of the thin film thermoelectric cooler that accounts for the collision contributions is validated with a recently published experimental data [50].

Figure 18. Schematic diagram of a thin film thermoelectric couple. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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5.3.1. Thermodynamic Modeling for Thin-Film Thermoelectrics The interactions of electrical and thermal phenomena are important to simulate the superlattice thermoelectric element. The most important thermal effect is the thermal runaway, in which the electrical dissipation of energy causes an increase in temperature which in turn causes a greater dissipation of energy. Without repeating the basic derivation (as derived in section 2), a complete model of electron, hole and phonon conservation equations for a thin film thermoelectric element is summarized in Table 8. As seen in Table 8, the Boltzmann Transport Equation is employed together with the phenomenological relationship [14]. The energy balance equations for electrons, holes and phonon are computed using Gibbs law. Based on these formulation, the entropy flux and entropy generation for electrons, holes and phonons in the well and barrier of the superlattice thermoelement are developed and they are summarized in Table 9. 5.3.2. Discussion The simulation results presented herein are for the transient heat transport in the direction of hot and cold junctions of Bi2Te3/Sb2Te3 thin-film thermoelectric element. Table 8. The balance equations. Particles

Equations mass

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Electrons

Holes

energy

ne n  ve ne   e t t

(72) colli

ue u  .Qe  JF e  e t t

(73) colli

entropy

se  .J se   irr ,e   colli,eh   colli,e g (74) t

mass

nh n  ve nh   h t t

Energy

entropy

(75) colli

u h u  .Qh  JF h  h t t

(76) colli

sh  .J sh   irr ,h   colli,he   colli,h g t (77)

energy Phonons entropy

Combined (Electron + Hole + Phonon)

u g t s g t

 .Qg 

u h t

(78) colli

 .J s ,g   irr ,g   colli,g e   colli,g h (79)

energy

u u (80)  .Q  JF  t t colli

entropy

ds  .J s   (81) dt

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Venkatasubra-manian et al. [50] reported the properties and dimensions of a prototype superlattice, and the values are tabulated in Table 10. In the presence of high electric fields within the thin film structure, lesser equilibrium between electrons-phonons or holes-phonons is expected. Thus, the collision effect from electrons and phonons is increased. Following the classical T-s diagram methodology, which demarcates accurately how energy input to a device is consumed in overcoming the dissipative and finite-rate heat transfer losses, the Figures 19 (a) and 19 (b) show the temperature and entropy fluxes of electrons, holes and phonons for a set of cold and hot temperatures of 270K and 300K, respectively. As can be seen, the electrons flow in n-type element (cold to hot junctions or negative Seebeck coefficient) which is opposite to the current flow, whilst the holes flow through the p-type element (cold to hot junctions or positive Seebeck coefficient) in the same direction of current flow. As the electrons of n-type thin film and holes of p-type thin film are known to have lesser dissipative losses, the based area of cold reservoir is larger, i.e.

TL  AD [in Figure 19 (a)], reflecting a larger potential for cooling.

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However, the accompanying phonons, which have larger internal and dissipative losses, reduce the cooling capacity, i.e., TL  OE  at the p-arm and TL  OH  at the n-arm, as shown in Figure 19 (a).

Figure 19. The temperature-entropy diagram of a thin film thermoelectric couple (both the p and n-type thermoelectric element are shown here) at optimum cooling capacity or maximum COP.

Taking the phonon losses into account, the combined diagram gives the flow of current density, J, from p to n arms, as given by the close loop ―a-b-c-d-a‖ which establishes the T-s diagram (denoted by the full lines) and this is shown in Figure 19 (b). Thus, the cooling capacity is given by the area, TL x (ad), and the heating power is given by TH x (bc), and power input is the area bounded by their differences, i.e., TH × (bc) – TL × (ad). The net coefficient of performance (COP) is the ratio of useful effect to energy input which is simply given by TL × (ad)/ [TH × (bc) – TL × (ad)]. Figure 20 constitutes the temperature-entropy flux plots for different electric fields of the thin film thermoelectric cooler, where the close loop o-a-b-a defines zero cooling capacity and zero COP at very low electric field (0.05 A). The close loop c-d-e-f-c represents the maximum COP or the optimum cooling capacity at high electric field (6 A). The close loop gh-i-j-g indicates the T-s diagram for the maximum cooling capacity.

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Table 9. The energy, entropy flux and entropy generation equations of the well and the barrier [4]. well Particles

cw Electron

Tw,e

Hole

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cw

cw Combined

 .w,e Tw,e 

t J2 T  w ,e  c w w ,e  w ,e t

cw

Phonon

Entropy flux W/m2 K

Energy balance

Tw,h

Tw, g



 .w, g Tw, g   cw

Tw t

w,h Tw,h  h J w,h  Tw,h Tw,h

 1  J2   wh Twh .   wh   Twh  Twh  wh c T  w wh Twh t colli

colli

Tw, g t

Tw J2  .wTw   w t  w  cw

w,e Tw,e  e J w,e  Tw,e Tw,e

 1  J2  weTwe .   we  Twe  Twe we c T  w we Twe t colli

colli

 .w,h Tw,h 

t J2 T  w,h  c w w,h  w ,h t

t



 colli



Entropy generation W/m3K

 1  wg Twg . T  wg c w Twg  Twg t colli

w, g Tw, g Tw, g

wTw Tw



colli

J w Tw

   

 1  J2   w Tw .   w  Tw  Tw w c T  w w Tw t colli

barrier Energy balance

Electron

cb

Tb,e t

 .b,e Tb,e   cb

Entropy flux

Tb,e t

 colli

 b,e Tb,e Tb,e

Entropy generation

 1    beTbe .  Tbe  c Tbe  b Tbe t colli

on?docID=3021002.

Table 9. (Continued). barrier Particles

Hole

Phonon

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Combined

Entropy flux W/m2 K

Energy balance

cb

cb

Tb ,h t

Tb , g t

 . b,h Tb,h   cb

 .b , g Tb , g   cb

T T cb b  .b Tb   cb b t t

Tb,h t



Tb,h

colli

Tb, g t

b,h Tb,h



b, g Tb, g Tb, g

colli

 colli

Entropy generation W/m3K

 1    bhTbh .  Tbh  c Tbh  b Tbh t colli

 1  bg Tbg . T  bg c Tbg  b Tbg t colli 1  b Tb .  Tb c T  b b Tb t colli

b Tb Tb

   

  

Table 10. The thermo-physical properties of thin film thermoelectric element. Sample

Electrical resistivity Ωm

Seebeck coefficient μV/oC

Phonon Thermal conductivity W/m K

Electron Thermal conductivity W/m K

Bi2Te3/Sb2Te3 (P-arm) [50]

1.2×10-5

238

0.22

0.37

Bi2Te3/Bi2Te2.83Se0.17 (n-arm) [50]

1.23×10-5

-238

0.58

0.37

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Figure 20. Temperature-entropy flux (T-Js) diagrams for the thin film thermoelectric cooler at three operating points.

The effect of collisions arising from electrons and phonons (n-arm) and holes and phonons (p-arm) is compared with the same cycle without the collision terms for different currents and these simulation results are tabulated in Table 11. For a given dimensions of thin film thermoelectric element [50] and a current range of 1 - 10 A [50], the contribution of collision dissipation is found to be less than 7.4% of the total energy input. It is noted that the COP increases with the current density increases in the thin-films, reaching an optima at 2 A when the energy lost to collision effect is 11.8%. However, at higher input current densities, the cooling capacity of the thin-films decreases to near zero due to three key effects, namely (i) the Joulean heat loss, (ii) the Fourier loss and (iii) the collision loss. The contribution from collisions becomes increasing important at these high current densities, reaching as high as 32% of the input power. As depicted on a T-s diagram, the comparative results are shown in Figure 21. Cycle AB-C-D-A is without collision terms and the cycle is superimposed onto the cycle A′-B′-C′-D′A′ that includes collision effect. At the optimal conditions, the net heat dissipation at the hot junction with and without collisions are computed to be 208 mW and 200 mW, respectively, whilst the corresponding cooling capacities are 112 mW and 120 mW, respectively. The effect of collision reduces the COP of the thin film thermoelectrics by 20%. This increase is attributed to two effects, namely, (i) the reduction of cooling power as indicated by the shaded area, TL × (AA′+DD′), and secondly, (ii) the energy input is increased by shaded area, TH × (CC′+BB′).

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Table 11. Performance analysis of the thin film thermoelectric cooler (excluding collisions effect and including collisions effect) [56]. Without collision effects

With collision effects

40 60 72

Js, hj W/cm2K 0.55 1.62 2.30

Js, cj W/cm2K 0.281 0.96 1.47

0.85 1.14 1.35

Js, hj W/cm2K 0.57 1.70 2.41

Js, cj W/cm2K 0.28 0.95 1.42

80

2.75

1.80

1.40

2.89

100

3.91

2.56

1.43

120

5.16

3.40

160

7.85

240

13.4

I kA/cm2

COP

Input energy loss due to collisions (%)

0.78 1.0 1.13

7% 12% 16%

1.72

1.15

18%

4.13

2.43

1.12

22%

1.45

5.44

3.08

1.04

27%

5.10

1.40

8.20

4.19

0.85

35%

7.60

1.04

14.41

5.56

0.53

45%

COP

For the case of optimum operation 2 A, the area under the T-s diagram are (Figure 6) QH, ncolli

200 mW

QH, colli

QL, ncolli

120 mW

QL,colli

Pinput, ncolli = QH - QL

80 mW

Pinput, colli

= QH -QL

208 mW 112 mW 96 mW

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Loss due to collisions Qcolli = 16 mW

Figure 21. The temperature-entropy diagrams of p and n-type thin film thermoelectric elements. The close loop A′-B′-C′-D′ shows the T-s diagram when the collision terms are taken into account and the close loop A-B-C-D indicates the T-s diagram when collisions are not included. Energy dissipation due to collisions is shown here. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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All results presented herein are the predictions of the performances of next generation solid state micro-coolers. As it is beneficial to compare the predictions with experiments, the measured ΔT across the hot and cold junctions of a p-type thin film superlattice [50] is depicted against the imposed current density, as shown in Figure 22. For this comparison, the thermophysical properties of the thin film thermoelectric element are extracted from Table 9. As seen from comparison, the proposed BTE model with the collision effect shows good agreement with the experimental data whilst the conventional thermoelectric model [1, 21] over predicts the absolute cooling power and could not capture the true behaviors of thinfilms.

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5.3.3. Summary of Section 5.3 This section presents the uniquely combined conservations laws where the classical irreversible (Joule heat and conduction) and electrons/holes-phonons collision losses are captured. A finite difference code for solving the BTE for finite time collisions of the particles within the thin-film super-lattice thermo-electric cooler has been demonstrated. For a broad range of current densities, the dissipative contributions from both the electron-phonons and holes-phonon collisions within the thin-film, have been derived theoretically with BTE approach and the actual data from literature were incorporated here for analysis.

Figure 22. Absolute cooling (TH-TL) as a function of current density in a p-type thin film superlattice. Hence (▲) defines the experimental data for p-type superlattice device [6], (▬) represents the simulation of present modelling for p-type superlattice, where the energy transports between holes and phonons are taken into account and (—) depicts the simulation of p-type thin film superlattice without energy transfer between phonons and holes.

Given a finite dimension of the thermo-element, the COP exhibits an optimal behaviour at medium current density level where the collision dissipation is about 10% of the power input, and increasing the current densities beyond the optimum point would accelerate the increase in the dissipative losses from collision and mitigates the COP values to naught. The

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practical and pedagogical values of a novel Temperature-entropy flux diagram for thin film thermoelectrics have also been demonstrated. To predict the performance of the thin film thermoelectric device, it is important to understand the thermal behavior, which occurs in nanosecond range. This is also useful to design a micro-structure and understand the mechanisms of phonon transport.

CONCLUSIONS

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In this chapter, a universal thermodynamic framework for both the macro and micro scale modeling of both adsorption and thermoelectric coolers has been derived and their applications have been demonstrated. It is based on the Boltzmann Transport Equation (BTE) approach, incorporating the classical Gibbs law and the energy conservation equation where their amalgamation yields the form of the temperature-entropy flux (T-s) formulation. This Ts formulation demonstrates the energy flows of adsorption and thermoelectric cooling systems and their transformation into useful and dissipative effects. The modeling is also applied to the energy flows and performance investigation of the solid state cooling devices such as the thermoelectric coolers, the pulsed-mode thermoelectric coolers and the thin-film superlattice thermoelectric device. It demonstrates the regimes of entropy generation that are associated to irreversible transport processes arising from the spatial thermal gradients, as well as the contributions from the collisions of electrons, phonons and holes in a microscaled type solid state cooler. The pedagogical value of the general temperature-entropy flux diagram is also demonstrated. The area under the process paths of a thermoelectric element indicates how energy input has been consumed by the presence of both the reversible (Peltier, Seebeck and Thomson) and the irreversible (Joule and Fourier) effects.

APPENDIX : GAUSS THEOREM APPROACH V is the volume of an element (solids, liquids, viscoelastic materials and rigid bodies) which is bounded by a closed surface . The differential element of the volume and surface area is written as dV and d = n d respectively, where n is the unit normal to  and is defined as pointing out of V. with this notation the Gauss‘ Theorem is written as,

  . X dV  X . n   d   X.d

V



(A1)



where X is any sufficiently smooth vector field and is defined on the volume V and the boundary surface  as shown below. Balance equations represent the fundamental physical laws and these include the conservation of mass, momentum, energy and some form of the second law of thermodynamics, entropy. At any instant, the mass is taken to occupy the volume V and has a bounding surface given by . The general form of the conservation laws is given by,

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The time rate of change of a quantity = actions of the surroundings on the surface of V + the actions of the surroundings on the volume itself. The word ―actions‖ means the change of quantity. Logically, the general form of the general form of the right hand side of the conservation principle always include all possible ways to influence the time rate of change of the quantity of interest. The Thomson effect in equation (55)

Figure B1. A thermoelectric element showing the transportation of heat and current.

The electrical and thermal currents are coupled in a thermoelectric device. The Peltier coefficient of the junction is a property depends on both the materials and is the ratio of power evolved at the junction to the current flowing through it. When current is applied to a thermoelectric element, thermal energy is generated or absorbed at the junction due to Peltier effect. The Seebeck coefficient depends on temperature and this is different at different places along the TE material. So the thermoelectric element is thought of as a series of many small Peltier junctions and each of which is generating or absorbing heat. This is called Thomson power evolved per unit volume J T  . In a Thomson effect, heat is absorbed or evolved when current is flow in a thermoelectric element with a temperature gradient. The heat is proportional to both the electric current and the temperature gradient. The proportionality constant is known as Thomson coefficient.

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If the heat current density of a thermoelectric element is only a result of temperature gradient and the electric current density occurs due to electric potential gradient. Then, J q  .T and J    . Using equation (3.1) the energy balance equation of a thermoelectric element is obtained.

cp

T J2  .T   t 

(B1)

The first term of right hand side of equation (B1) is Fourier conduction term and the second term indicates the Joule heat. But in a thermoelectric cooling device, the junctions are maintained at different temperatures and an electromotive force will appear in the circuit. This flow of heat has a tendency to carry the electricity along the thermoelectric arm. When two or more irreversible processes take place in a thermodynamic system, they may interfere with each other. A completely consistent theory of thermoelectricity has been developed using the Onsager symmetry relationship (Onsager, 1931). When a current is applied to a thermoelectric device, the heat current of TE arm is developed as a result of electric current and temperature gradient (cross flow) and the electric current is generated due to electric potential and the temperature gradient. Using the thermodynamic-phenomenological treatment, the heat current density is

Jq  

Qo J  T , F

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and the electric current density in amp per m2 becomes

J      

J





  Qo FT

T

Qo .T FT

Equation (55) now becomes

 cp

 cp

Q  T  J Q   .  T  o J   J   o .T   t F  FT     2 JQ J J  .T   Qo   o .T F   FT J 2 JT  Qo   .T       F  T 

T J 2 JT  Qo   .T      t  F  T 

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(B2)

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Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al.

hence the third term JT  Qo  occurs due to current flow for temperature gradient (cross F

T 

flow) and heat flow for the electric potential gradient (reciprocal effect). This term indicates the least dissipation of energy [14] JT  Qo  JT    s  , F T  F

where s  Qo  is the entropy (in J/mol.K) along the thermoelectric 

T 

arm. Hence

JT  Qo  JT    s  F T  F JT s  .T F T  T s   J .T  F T  The Thomson heat is defined as

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 T s  QT  J  .T ,  F T  QT  J   T

where Thomson coefficient    T s . F T The temperature gradient is bound to cause a certain degradation of energy by conduction of heat. The electric potential gradient must cause an additional degradation of energy, making the total rate of increase of entropy along the thermoelectric arm. So the electric current due to temperature gradient (cross flow) and the heat current due to electric potential gradient (reciprocal effect) indicate the Thomson effect, which will be discussed in the following section. Without Thomson effect, the physics of thermoelectricity is not completed. Derivation of equation (55) The energy balance of the thermoelectric arm is

 cp

T J2  .T    JT t 

(B3)

Expression of the third term Using Kelvin relations      , and  T T

 

  T 

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Study on Adsorption and Thermoelectric Cooling Systems…     JT  J   .T  T T 

   T 

205 (B4)

 .T (de Groot and Mazur, 1962) T

From equation (B4) we have JT  J J

 T



T

.T  J

 .T T



.T  J   

T





.T  J  J  T T  JT  JT   JT  T J

 JT  JT  JT   JT

 .T  JT  T T

 .T  JT  T T

Equation (B3) is now written as

 cp

T J2   .T    JT .T  JT  T t  T

(B5)

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Equation (B5) is same as equation (55).

ACKNOWLEDGMENTS The authors wish to thank King Abdullah University of Science and Technology (KAUST) for the generous financial support through the project (R265-000-286-597).

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Rowe, D. M. (ed). CRC handbook of thermoelectrics. Boca Raton FL: CRC Press. 1995. Ng, K. C., Sai, M. A., Chakraborty, A., Saha, B. B., Koyama, S., The electro-adsorption chiller: Performance rating of a novel miniaturized cooling cycle for electronics cooling, Journal of Heat Transfer, Vol. 128, No. (9), pp. 889-896, 2006. Saha, B. B., Chakraborty, A., Koyama, S., Ng, K. C., and Sai, M. A., Performance modelling of an electro-adsorption chiller, Philosophical Magazine, Vol. 86, No. 23, pp. 3613-3632, 2006.

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Bidyut Baran Saha, Anutosh Chakraborty, Kim Choon Ng et al. Chakraborty, A., Thermoelectric cooling devices: thermodynamic modelling and their applications in adsorption cooling cycles, Ph. D. Thesis, National University of Singapore, November 2005. Chen, G., Ballistic-Diffusive Heat-Conduction Equations, Physical Review Letters, Vol. 86, No. 11, pp. 2297-2300, 2001. Chen, G., Ballistic-diffusive equations for transient heat conduction from nano to macroscales, Journal of Heat Transfer, Vol. 124, pp. 320-328, 2002. Tomizawa, K., Numerical Simulation of Submicron Semiconductor Devices. pp. 171209, Boston: Artech House. 1993. Parrott, J.E., The interpretation of the stationary and transient behaviour of refrigerating thermocouples, Solid state Electronics, Vol. 1, pp. 135-143, 1960. Lee, J.S., Micro/Nano scale Energy Transport and conversion A State-of-Art Review. The 6th KSME-JSME Thermal and Fluids Engineering Conference, March 20-23, Jeju, Korea, 2005. de Groot, S.R. and Mazur, P., Non-equilibrium Thermodynamics. pp. 11-42, Amsterdam: North-Holland Pub Co. 1962. Novikov, I. I., The Efficiency of Nuclear Power Stations, Journal of Nuclear EnergyII (U.S.S.R.), Vol 7, pp. 125-128, 1958. Mey, G.D. and Vos, A.D., On the optimum efficiency of endoreversible thermodynamic processes, Journal of Physics D: Applied Physics, Vol. 27, No. 4, pp. 736-739, 1994. Moron, J.S., On second-law analysis and the failed promise of finite-time thermodynamics. Energy, Vol. 23, No. 5, pp. 517-519, 1998. Onsager, B.L., Reciprocal relations in irreversible Processes. I. Physical Review, Vol. 37, pp. 405-426, 1931. Denton, J.S., Thermal cycles in classical thermodynamics and non-equilibrium thermodynamics in contrast with finite time thermodynamics, Energy Conversion and Management, Vol. 43, pp. 1583-1617, 2002. Reif, F., Fundamentals of Statistical and Thermal Physics. New York: McGraw-Hill. 1965. de Groot, S.R., On the thermodynamics of irreversible heat and mass transfer, International Journal of Heat and Mass Transfer, Vol. 4, pp. 63-70, 1961. Bird, R.B., Transport Phenomena. New York: Wiley. 1960. Richard, C.T. and Fine, P.C., On the irreversible production of entropy. Reviews of Modern Physics, Vol. 20, No. 1, pp. 51-77, 1948. Meunier, F., Solid sorption: An alternative to CFCs, Heat recovery systems and CHP Vol. 13, pp. 289-295. 1993.

[21] Aristov, Y. I., Restuccia, G., Cacciola, G., and Parmon, V.N., A family of new working materials for solid sorption air conditioning systems, Applied Thermal Engineering, Vol. 22, No. 2, pp. 191-204, 2002. [22] Aristov, Y.I., New composite adsorbents for conversion and storage of low temperature heat: Activity in the Boreskov Institute of Catalysis, J. Heat Transfer Society of Japan, Vol. 45, No. 192, pp. 12-19, 2006. [23] Aristov, Y.I., New family of materials for adsorption cooling: material scientist approach, Journal Engineering Thermophysics, Vol. 16, No. 2, pp. 63-72, 2007.

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[24] Saha, B.B., Chakraborty, A., Koyama, S., Ng, K.C., Sai, M.A., Performance modelling of an electro-adsorption chiller, Philosophical Magazine, Vol. 86, No. 23. pp. 36133632, 2006. [25] Chua, H.T., Ng, K.C., Malek, A., Kashiwagi, T., Akisawa, A. and Saha, B.B., Multibed regenerative adsorption chiller - improving the utilization of waste heat and reducing the chilled water outlet temperature fluctuation, International Journal of Refrigeration, Vol. 24, No. 2, pp. 124-136, 2001. [26] Chua, H.T., Ng, K.C., Wang, W., Yap, C., and Wang, X.L., Transient modeling of a two-bed silica gel-water adsorption chiller, International Journal of Heat and Mass Transfer, Vol. 47, No. 4, pp. 659-669, 2004. [27] Glueckauf, E., Formulae for diffusion into spheres and their application to chromatography, Trans. Faraday Soc., Vol. 51, pp. 1540-1551, 1955. [28] Aristov, Y.I., Tokarev, M.M., Freni, A., and Restuccia, G., Comparative study of water adsorption on SWS-1L and microporous silica: equilibrium and kinetics, Proc. Sorption Heat Pumps Conference, Denver, USA (2006) (CD-ROM). [29] Aristov, Y. I., Glaznev, I. S., Freni, A. and Restuccia, G., Kinetics of water sorption on SWS-1L (Calcium chloride confined to mesoporous silica gel): Influence of grain size and temperature, Chemical Engineering Science, Vol. 61, pp. 1453-1458, 2006. [30] Chua, H.T., Ng, K.C., Chakraborty, A., Oo, M.N., and Othman, M.A., Adsorption Characteristics of Silica Gel + Water System, Journal of Chemical and Engineering Data, Vol. 47, pp. 1177-1181. 2002. [31] Aristov, Y.I., Tokarev, M.M., Cacciola, G., and Restuccia, G., Selective water sorbents for multiple applications: 1. CaCl2 confined in mesopores of the silica gel: sorption properties, React. Kinet. Cat. Lett. Vol. 59, No. 2, pp. 325-334, 1996. [32] Tokarev, M.M., Okunev, B.N., Safonov, M.S., Kheifets, L.I., and Aristov, Y.I., Approximation equations for describing the sorption equilibrium between water vapor and a SWS-1Lcomposite sorbent, Russian Journal of Physical Chemistry, Vol. 79, No. 9, pp. 1490-1493, 2005. [33] Tóth, J., State equations of the solid-gas interface layers, Acta Chem. Acad. Sci. Hung. Vol. 69, pp. 311-338, 1971. [34] Chakraborty, A., Saha, B.B., Koyama, S., and Ng, K.C., The specific heat capacity of a single component adsorbent-adsorbate system, Applied Physics Letters, Vol. 90, art no. 171902, 2007. [35] Chakraborty, A., Saha, B.B., Koyama, S., and Ng, K.C., On the thermodynamic modeling of isosteric heat of adsorption and comparison with experiments, Applied Physics Letters, Vol. 89, art no. 171901, 2006. [36] Ruthven, D. M., Principles of Adsorption and Adsorption Processes, London: J. Wiley and Sons, (1984). [37] Saha, B.B., Chakraborty, A., Koyama, S., and Aristov, Y. I., A new generation cooling device employing CaCl2-in-silica gel-water system, International Journal of Heat and Mass Transfer, Vol. 52, No. 1-2, pp. 516-524, 2009. [38] Burshteyn, A.I., Semiconductor Thermoelectric Device. pp. 1-20, London: Temple Press. 1964. [39] Hasse, R., Thermodynamics of Irreversible Processes, New York: Dover Publications Inc. 1990.

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[40] Chakraborty, A., Saha, B.B., Koyama, S., and Ng, K.C., Thermodynamic modelling of a solid state thermoelectric cooling device: Temperature-entropy analysis, International Journal of Heat and Mass Transfer, Vol. 49, No. 19-20, pp. 3547-3554, 2006. [41] Nolas, G. S., Sharp, J., and Goldsmid, H.J., Thermoelectrics Basic Principles and New Materials Developments, pp. 1-15, New York: Springer. 2001. [42] Snyder, G.J., Fleurial, J.P., Caillat, T., Yang, R., and Chen, G., Super-cooling of Peltier cooler using a current pulse, Journal of Applied Physics, Vol. 92, No. 3, pp. 1564-1569, 2002. [43] Miner, A., Majumdar, A., and Ghosal, U., Thermoelectromechanical refrigeration based on transient thermoelectric effects, Applied Physics letters, Vol. 75, No. 8, pp.11761178. 1999. [44] Landecker, K., and Findlay, A.W., Study of the fast transient behaviour of Peltier junctions, Solid state electronics, Vol. 3, pp. 239-260, 1961. [45] Field, R.L., and Blum, H.A., Fast transient behavior of thermoelectric coolers with high current pulse and finite cold junction, Energy Conversion. Vol. 19, No. 3, pp. 159-165, 1979. [46] Chakraborty, A., and Ng, K.C., Thermodynamic formulation of temperature-entropy diagram for the transient operation of a pulsed thermoelectric cooler, International Journal of Heat and Mass Transfer, Vol. 49, No. 11-12, pp. 1845-1850, 2006. [47] Goldsmid, H.J., and Douglas R.W., The use of semiconductors in thermoelectric refrigeration, British J. Appl. Phys, Vol. 5, pp. 386-390, 1954. [48] Disalvo, F.J., Thermoelectric cooling and power generation, Science, 1999, Vol. 285, pp. 703-706, 1999. [49] Harman, T.C., Taylor, P.J., Walsh, M.P., and LaForge, B.E., Quantum dot superlattice thermoelectric materials and devices, Science, Vol. 297, pp. 2229-2232, 2002. [50] Venkatasubramanian, R., Silvola, E., Colpitts, T., and Q‘Quinn, B., Thin film thermoelectric devices with high room temperature figures of merit, Nature, Vol. 413, pp. 597-602, 2001. [51] Venkatasubramanian, R., Thin film thermoelectric device and fabrication method of same, US Patent no. 6300150, 2001. [52] Elsner, N.B., and Ghamaty, S., Superlattice quantum well material, US Patent no. 5550387, 1996. [53] Swe, S.M., Physics of semiconductor device, 1981, Second edition, Wiley, New York. [54] Joshi, A.A., and Majumdar, A., Transient ballistic and diffusive phonon heat transport in thin films, J. Appl. Phys., Vol. 74, pp. 31-39, 1993. [55] Zeng, T., and Chen, G., Nonequilibrium electron and phonon transport and energy conversion in heterostructures, Microelectronics Journal, Vol. 34, pp. 201-206, 2003. [56] Chakraborty, A., Saha, B.B., Koyama, S., and Ng, K.C., Thin-film thermoelectric cooler: Thermodynamic modelling and its temperature-entropy flux formulation, Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, Vol. 221, No. 1, pp. 33-46, 2007.

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In: Cooling Systems: Energy, Engineering and Applications ISBN 978-1-61209-379-6 Editor: Aaron I. Shanley © 2011 Nova Science Publishers, Inc.

Chapter 8

NEW PROGRESS IN LIQUID DESICCANT COOLING SYSTEMS: ADSORPTION DEHUMIDIFIER # AND MEMBRANE REGENERATOR Xiu-Wei Li* and Xiao-Song Zhang School of energy and environment, Southeast University, Nanjing 210096, China

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ABSTRACT A liquid desiccant cooling system (LDCS) is a new type of air-conditioning system with good energy-saving potential. Its performance is dominated by dehumidification and regeneration processes. At present, few works have been done to propose a general principle for better dehumidifier design and most works about regeneration are only concentrated on the thermal regeneration method. For both aspects, new progress has been made and presented in this paper. On one hand, a new design method has been derived from the experiments: an adsorption dehumidifier, developed by integrating a solid desiccant with liquid dehumidifier, could greatly improve the dehumidification effects. On the other hand, a new regeneration style has been conceived: a membrane regenerator, which consists of many alternatively placed cation- and anion-exchange membranes, would regenerate the liquid desiccant in an electrodialysis way; while a solar photovoltaic generator provides electric power for fueling this process. This new regeneration method is immune from the adverse impact from outside high humidity, and it also has a pretty good performance, as well as the benefit that purified water can be obtained along with the regeneration process. These two developments can make LDCS more practical and competitive in the future market.

# A version of this chapter also appears in Air Conditioning Systems: Performance, Environment and Energy Factors, edited by Tobias Hästesko and Otto Kiljunen, published by Nova Science Publishers, Inc. It was submitted for appropriate modifications in an effort to encourage wider dissemination of research. * [email protected], 0086-025-83792722. Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

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Xiu-Wei Li and Xiao-Song Zhang

NOMENCLATURE A △ Conmol d F I m N Num PED pED r U z

area (m2) mole number change of the solute per kg solution (mol/kg) diameter (m) Faraday constant (s A/mol) current (A) mass flow rate (kg/s) cell number (no units) number of silica gel bulbs (no units) electric power consumption (kW) electric power consumption for the solution of unit mass (kW) radius (m) voltage (V) electrochemical valence (no units)

Greek Letters ζ

current utilization (no units)

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Subscripts a d deh ED PV TH w

air desiccant solution dehumidifier electrodialysis photovoltaic thermal energy water

INTRODUCTION Seeking comfortable living conditions in life is a popular trend today, which has led to the wide use of air-conditioners. However, that situation has a side effect, which upsets people by calling for a large amount of electric power to drive these ―cooling machines‖. Many new types of air-conditioner have been developed to shoulder off the heavy dependence on electric power while still guaranteeing good comfort. Among these new faces, the liquid desiccant cooling system (LDCS), which typically consists of a liquiddehumidification unit and an evaporation-cooling unit, has attracted ever increasing attention from both researchers and consumers. The reason for this is mostly from the fact that this system could be driven by heat sources with a relatively low temperature of around 70ºC.

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That means the work could be done by many renewable energies, such as solar power, geothermal power and waste heat [1-3]. The dehumidification process is the core part of this system. If the dehumidification effect is not good enough, the cooling capacity may be insufficient for the treated air to reach their expected states. The dehumidifier configuration has a great impact on this dehumidification effect, and many works have been done: Khan [4] made a theoretical analysis on an internally-cooled dehumidifier; Al-Farayedhi et al. [5] studied the geometric parameters of a gauze-type structured packing (dehumidifier); Abdul-Wahab et al. [6] took the influence of packing densities into consideration. Ani et al. [7] studied the influence of packing height on absorber performance, which was built from fibre-glass in pieces. Nevertheless, except for contacting area enlargement, it is far-fetched to say many substantial developments have been made. Recently in our experiments, an interesting attempt to improve the dehumidification effects has been made by embedding silica gel into the airdesiccant contacting surface of a liquid dehumidifier. The result shows the improved dehumidifier could achieve a more than 50% improvement in dehumidification effect than the original one, and this improvement was much greater than that could be reasonably predicted by just counting the area increase. The energy consumption of LDCS mainly lies in the regeneration of desiccant solution. The conventional regeneration method is in a thermal energy (TH) style [8-13]: with the addition of thermal energy, the desiccant solution raises its temperature so that the water molecules can evaporate from the solution body to the surrounding atmosphere. Through this method, the solution concentration will increase (regenerated). Nevertheless, this regeneration pattern has some defects: For one thing, it heavily depends on the condition of the surrounding atmosphere and can be unreliable. It is well-known that the force of mass transfer is the positive vapour pressure difference between the desiccant solution and the surrounding atmosphere. When it is hot and humid, the vapour pressure difference will fall quickly or even become negative, which leads to the instability of regeneration. For another thing, the desiccant solution is ―hot‖ after regeneration, but this high temperature is not good for the following dehumidification process. Excessive cooling measures have to be taken to remove this harmful heat, which inevitably causes a waste of energy. Besides, some droplets of desiccant solution may sneak into and pollute the air of the environment because this regeneration method always operates in open cycle. To overcome these problems, a new regeneration method has been conceived: the regenerator is designed as an electrodialysis (ED) stack composed by many ion-exchange membranes, and a solar photovoltaic (PV) generator provides energy for regeneration. The ED method is a technique based on the transport of ions through selective membranes under the influence of an electrical field [14-16]. The conceived membrane regenerator is essentially an ED stack, in which cation- and anion-exchange membranes (CM and AM) are placed alternatively between the cathode and the anode. When a potential difference is applied between electrodes, the cations move toward the cathode, and anions move toward the anode. The cations go through the cation membrane, which have fixed groups with negative charges, and are retained by the anion-exchange membrane. On the other hand, the anions circulate through the anion-exchange membranes, which have fixed groups with positive charges, and are retained by the cation-exchange membranes. This movement produces a rise in the ions concentration in some compartments (concentrate compartments) and decrease in the adjacent ones (dilute compartments). The solar

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photovoltaic (PV) system is one of the most widespread and studied systems for electricity generation [17-18]. PV cells directly convert sunlight into electricity. The advantages of the use of this type of energy are that it is non-polluting—once the solar panels have been produced—it is also silent, abundant, decentralized, free and long lasting. The low maintenance cost of these systems is also another positive factor. Inheriting the merits of the two major parts, this combined PV-ED regeneration system would have some advantages compared to the conventional TH method.

ADSORPTION DEHUMIDIFIER

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The original dehumidifier, Dehumidifier No1, is a structured corrugated packing of inorganic material as shown in figure 1: the specific area of the packing is 396 (m2/m3). Figure 1 (a) and figure 1 (b) display the shapes viewed from the upside and the sidepiece of the packing. The definition of the packing dimension is shown in figure 1 (c). Its dimensions are height H=0.5m, width W=0.2m, and length L=0.5m. Dehumidifier No2 is an improved version of Dehumidifier No1. The transforming process is depicted in figure 2: silica gel selfindicators, the adsorbent, are filled in the wind tunnels of the packing material (original Dehumidifier No1) as shown in figure 2 (c). Described in figure 2 (a), the diameter of that silica gel self-indicator is of 3.2mm on average; the change of colour from blue to red symbolizes ample water molecules have been adsorbed and the silica gel self-indicator is saturated. Figure 2 (b) presents the surface of Dehumidifier No1 before being transformed. In the transforming process, silica gel are embedded and scattered on the surface in a random manner with uncertain distance from each other [shown in figure 2 (d)]. On average, around 50 silica gel bulbs are added in one single wind tunnel and totally 3/4 tunnels of the packing materials are treated in this way.

Figure 1. The shape and structure of the packing in the dehumidifier.

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To compare the dehumidification effects between the two dehumidifiers, experiments [2] were conducted: the air temperature was maintained 27±0.5ºC; the initial air humidity was set as 14.5±0.3 g/ (kg air) and 15.5±0.3 g/ (kg air), respectively. Pure CaCl2 solution with the mass concentration of 27% was taken as the liquid desiccant. The temperature of the desiccant solution was regulated as 19±0.5ºC.

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Figure 2. Improvement from Dehumidifier No2 to Dehumidifier No3.

The experimental results are exhibited in figure 3 and figure 4, where the X axis represents the time and the Y axis represents the humidity reduction rate △d. The results show that the moisture removal rate had been respectively enhanced by 66% and 70% by using Dehumidifier No2 under two initial humidity conditions. Since the liquid desiccant was same, this enhancement could only be attributed to the difference between the dehumidifiers. In the experiment, the pores of the silica gel self-indicators had been filled with desiccant solution and could not trap water molecules. Therefore, the reason for the improvement of dehumidification effects seems to be the contacting area enlargement by adding the adsorbent. The contribution of area enlargement could be evaluated by simple mathematical calculations: assume the silica gel self-indicators as bulbs, the total area enlargement △A could be calculated: A=4 r 2 Num   d 2 Num

(1)

Num was approximate 50 for one single tunnel, and the enlarged area in one single tunnel was equal to 13.4% of the tunnel‘s original surface area. Because only 3/4 tunnels were stuffed, the total increased area was no more than 11% of the original total contacting area. It means the dehumidification effect improvement would not exceed 11%. However, that

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Xiu-Wei Li and Xiao-Song Zhang

prediction result was much lower than the true improvement. Thus, there must be some other influential factors uplifting the dehumidification effect beyond the area enlargement.

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Figure 3. Dehumidification experiment with the initial humidity of 14.5 g /(kg air).

Figure 4. Dehumidification experiment with the initial humidity of 15.5 g /(kg air).

Literally, adsorption and absorption seems to be two different processes, but actually they came from the same word known as ―Sorption‖ [19, 20]. In the meaning of ―Sorption‖, the absorption process could be considered as the combination of two stages: in the first stage, the adsorption process happens, during which the molecules of the adsorbate (absorbate) are attracted by and approach the surface of the adsorbent; in the second stage, the diffusion

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process happens, during which some molecules penetrate the interface and proceed into the absorbent. With the ―Sorption‖ conception, an assumption of adsorption potential superposition is taken to give a possible explanation for the experimental results. It is known that solid desiccant (like silica gel) could trap water molecules in its pores after it attracting these molecules with its adsorption potential. Definitely, the pores of the silica gel selfindicators were filled with desiccant solution in the experiments as the flowing film of liquid desiccant coated them. So the solid desiccant could not trap any more water molecules. Nevertheless, its adsorption potential still works for its intrinsic features, and this attracting power was hand in hand with the adsorption potential from the liquid desiccant. That came to be an overlapping of attracting power, which helped in forcing more water molecules close to the film of the desiccant. In terms of the ―Sorption‖ definition, the first stage of absorption had been strengthened in this way. Naturally, more approaching molecules would provide more chances for successful penetration and diffusion process, so the absorption ability had been reasonably enhanced.

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MEMBRANE REGENERATOR The PV-ED regeneration process with the membrane regenerator is described in figure 5. The strong desiccant solution, whose mass flow rate is md,deh, absorbs mw kg moisture from the to be treated air in the dehumidifier. The solution concentration decreases, and this weak solution is sent from the dehumidifier to the membrane regenerator. The regenerator (ED stack) consists of a multitude of cells placed in parallel between two electrodes [14]. In alternating cells the solution is concentrated and desalinated, respectively. The hydraulic circuits in two adjacent cells are referred to as dilute and concentrate flow streams and the adjacent cells are referred to as a cell pair (figure 6). At the beginning, all the dilute cells are feeding with the desiccant solution stream from Solution Storage Tank 1 (Valve 2 is open while Valve 4 is closed; Valve 1 and 3 are closed so that the water path is cut off); all the concentrate cells are feeding with the weak desiccant solution stream from the dehumidifier. The total mass flow rates of both these two streams are equal to (md,deh+ mw). It should be noticed that the total amount of desiccant solution that has been regenerated is (md,deh+ mw) in the ED method, but the needed amount of desiccant solution for dehumidification is md,deh. Therefore, for every regeneration process, excessive strong solution has been produced with the mass flow rate mw. This excessive part will accumulate in the Solution Storage Tank 2 (Valve 7 is open while Valve 5 is closed). The diluted solution will be recycled from the regenerator to the Solution Storage Tank 1 (Valve 6 is open while Valve 8 is closed) and back to the dilute cells for regeneration until its concentration falls to zero, which implies it has finally become purified water. Then, Solution Storage Tank 2, which is full of strong desiccant solution takes the place of Tank 1 by feeding desiccant solution into the dilute cells of the regenerator; the purified water in Tank 1 will be removed out (Valve 1 is open while Valve 3 stays closed) to Water Storage Pool for later other use, and Tank 1 comes to play the role that Tank 2 played before (by manipulating the valves). Like this, Tank 1 and 2 keep on alternating their roles and both the strong desiccant solution and the purified water are acquired. Neglect the energy loss, the ideal electric power PED is given by [14]:

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216

Xiu-Wei Li and Xiao-Song Zhang PED  UI 

zF  md , deh  mw  Conmol 

N

U

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Figure 5. PV-ED-LDCS system.

Figure 6. Configuration of an ED cell pair . Cooling Systems: Energy, Engineering and Applications : Energy, Engineering and Applications, Nova Science Publishers, Incorporated, 2011.

(2)

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The energy consumption for regenerating the desiccant solution of one single kilogram is: pED 

zFConmol  U N

(3)

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Under the same typical working conditions [9-18], the energy consumption for regenerating the desiccant solution of one kilogram is calculated for both the PV-ED system and the TH system. The results are presented in figure 7, which shows that the PV-ED system is immune against the change of relative humidity and has much lower energy consumption than that of the TH system. The TH system has to consume more energy for regeneration when the relative humidity rises. Nevertheless, it should be noticed the present PV generator has very poor solar energy conversion efficiency within the range of 5% ~20%. That will discount the performance of the whole PV-ED system, but even then, the performance of this new regeneration system will still be competitive with the conventional TH system in hot and humid days.

Figure 7. Energy consumption with different relative humidity of the air.

CONCLUSION A new improvement in dehumidifier design for LDCS has been achieved by combining a normal packing material with solid adsorbent. The experimental result shows this improvement did help with the enhancement of the liquid dehumidification ability. The assumption of the ―sorption‖ principle is proposed to explain the dehumidification effects enhancement by integrating liquid and solid desiccant. This assumption, buttressed by the experimental results, is reasonable and practical.

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Compared to the conventional TH regeneration method, the PV-ED regeneration method has several advantages: it is immune against the instability caused by the high humidity of the atmosphere; it gets rid of the adding heat that is harmful to the dehumidification process, and thus saves the energy for producing a cooling effect; it is environmentally friendly by preventing the droplets of desiccant solution from sneaking into the surrounding atmosphere and introducing pollution; it can also produce purified water during the regeneration process. Moreover, exposed by theoretical analysis, the new regeneration system has a better performance while putting aside the low efficiency of the PV regenerator. The ED method has been proved to be a practical and useful technology for desalination; the energyconversion efficiency for PV system has been improved every day with new emerging materials. Those will facilitate the development of a more competitive PV-ED system in the future.

REFERENCES

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[1]

Khalid Ahmed, C. S., Gandhidasan, P., and Al-Farayedhi, A. A.(1997). Simulation of a Hybrid Liquid Desiccant Based Air-conditioning System. Applied Thermal Engineering, 17(2), 125-134. [2] Li, X. W., Zhang, X. S., Wang, G., Cao, and R. Q. (2008). Research on ratio selection of a mixed liquid desiccant: Mixed LiCl-CaCl2 solution. Solar Energy, 82 (12), 11611171. [3] Gommed, K., and Grossman, G. (2004). A liquid desiccant system for solar cooling and dehumidification. Journal of Solar Energy Engineering, 126, 879-885. [4] Khan, A. Y. (1998). Cooling and dehumidification performance analysis of internallycooled liquid desiccant absorbers. Applied Thermal Engineering, 18(5), 265-281. [5] Al-Farayedhi, A. A., Gandhidasan, P., and Al-Mutairi, M.A. (2002). Evaluation of heat and mass transfer coefficients in a gauze-type structured packing air dehumidifier operating with liquid desiccant. International Journal of Refrigeration, 25, 330-339. [6] Abdul-Wahab, S.A., Abu-Arabi, M.K., and Zurigat, Y.H. (2004). Effect of structured packing density on performance of air dehumidifier. Energy Conversion and Management, 45, 2539-2552. [7] Ani, F.N., Badawi, E.M., and Kannan, K.S. (2005). The effect of absorber packing height on the performance of a hybrid liquid desiccant system. Renewable Energy, 30, 2247-2256. [8] Nelson, F., and Goswami, D.Y. (2002). Study of an aqueous lithium chloride desiccant system: air dehumidification and desiccant Regeneration. Solar Energy, 72(4), 351-361. [9] Gandhidasan, P. (2005). Quick performance prediction of liquid desiccant regeneration in a packed bed. Solar Energy, 79, 47-55. [10] Ren, C. Q., Jiang, Y., Tang, G. F., and Zhang, Y. P. (2005). A characteristic study of liquid desiccant dehumidification/regeneration process. Solar Energy, 79, 483-494. [11] Elsarrag, E. (2006). Performance study on a structured packed liquid desiccant regenerator. Solar Energy, 80, 1624-1631. [12] Elsarrag, E. (2008). Evaporation rate of a novel tilted solar liquid desiccant regeneration system. Solar Energy, 82, 663-668.

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[13] Liu, X. H., Jiang, Y., and Yi, X. Q. (2009). Effect of regeneration mode on the performance of liquid desiccant packed bed regenerator. Renewable Energy, 34, 209216. [14] Lee, H. J., Sarfert, F., Strathmann, H., and Moon, S. H. (2002). Designing of an electrodialysis desalination plant. Desalination, 142, 267-286. [15] Tsiakis, P., and Papageorgiou, L. G. (2005). Optimal design of an electrodialysis brackish water desalination plant. Desalination, 173, 173-186. [16] Ortiz, J. M., Expósito. E., Gallud. F., García-García, V., Montiel, V., and Aldaz. A. (2006). Photovoltaic electrodialysis system for brackish water desalination: Modeling of global process. Journal of Membrane Science, 274, 138-149. [17] Zondag, H. A., de Vries, D. W., van Helden, W. G. J., van Zolingen, R. J. C., and van Steenhoven, A. A. (2003). The yield of different combined PV-thermal collector designs. Solar Energy, 74, 253-269. [18] Charalambous, P. G., Maidment, G. G., Kalogirou, S. A., and Yiakoumetti, K. (2007). Photovoltaic thermal (PV/T) collectors: A review. Applied Thermal Engineering, 27, 275-286. [19] Clark, A. (1970). The Theory of Adsorption and Catalysis. Academic Press. [20] Aristov, Y.I., Tokarev, M. M., and Freni, A. (2006). Kinetics of water adsorption on silica Fuji Davison RD. Microporous and Mesoporous Materials, 96, 65-71.

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INDEX

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A absorption, 180, 218 accelerator, viii, 91, 99 activated carbon, 152, 169 activation, 148, 171 activation energy, 148, 171 adaptation, 110, 124 ADC, 168, 179, 180 adiabatic, 187, 188 adsorption, ix, x, 147, 149, 150, 152, 154, 162, 164, 168, 169, 170, 171, 172, 174, 175, 176, 177, 178, 179, 180, 204, 208, 209, 210, 213, 218, 223 adsorption isotherms, 168 air quality, viii, 3, 14, 19, 21, 22, 25, 26, 27, 28, 31, 32, 34, 69, 89 air temperature, 2, 3, 9, 11, 12, 13, 14, 15, 18, 20, 21, 23, 26, 28, 29, 217 alcohols, 168 algorithm, ix, 101, 106, 110, 112, 113, 117, 120, 121, 124, 127, 129, 130, 132, 133 ambient air, 45, 73 Amsterdam, 209 ankles, 25, 29 anode, 215 application, 154, 159, 162, 189, 195, 210 atmosphere, 46, 215, 222 automation, viii, 69, 117

B barrier, 150, 196, 197, 199, 200 basal metabolic rate, 83 base, 103, 115 behavior, 153, 169, 181, 191, 204, 211 benefits, 22, 25, 31, 32, 33, 86, 139 Bezier curves, ix, 101, 106, 113, 114, 120, 127, 132 bismuth, viii, 91, 92, 93, 99 boiling, 170 Boltzmann constant, 3, 10 Boltzmann distribution, x, 147

Boltzmann Transport Equations (BTE), ix, 147 Boston, 209 bottlenecks, x, 147, 195 boundary conditions, 171, 173, 174, 191 boundary surface, 8, 204 bounds, ix, 137, 145 brass, 56 breathing, 18, 19, 21 breeding, viii, 91, 92, 96, 99 bulbs, 214, 216, 217 bulk materials, 196

C calibration, 108, 132 carbon, 152, 169 Carnot, 186, 187 carrier, 148, 156, 157, 158, 159, 162, 167, 185 case study, 140, 142, 144 cathode, 215 cation, x, 213, 215 cell, 214, 219, 220 ceramic, 7, 51, 181 CFCs, 209 charcoal, 169 chemical, 150, 152, 161, 165 China, 35, 213 chloride, 210, 222 CHP, 209 chromatography, 210 circulation, 138 clarity, 120 classical, 152, 153, 181, 189, 198, 203, 204, 209 classification, 4, 6, 7 clean air, 18 clean rooms, viii, 69 climate, 3, 26, 33, 35 clothing, 70, 74, 75, 83 coefficient of performance (COP), 148, 175, 176, 179, 180, 187, 195, 196, 198, 201, 202, 203

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222

Index

collisions, 149, 152, 153, 154, 155, 162, 164, 196, 201, 202, 203, 204 combined effect, 161 combustion, 102, 103, 104, 107, 122 commercial, viii, 3, 22, 69, 86, 99, 169, 180, 190, 195 commercial office buildings, viii, 69 communication, 132 comparative analysis, 119 complexity, 104, 133, 142 compliance, 104 components, 170 compression, 46, 48, 162, 168 computation, 134, 186 computational capacity, 134 computational performance, 38, 63 concentration, 215, 217, 219 conceptual model, 48 condensation, vii, 1, 4, 12, 13, 21, 27, 29, 32, 72, 140, 169, 170, 174 conditioning, viii, x, 3, 4, 21, 31, 33, 35, 69, 70, 86, 209, 213, 222 conductance, 12, 183 conduction, 8, 9, 72, 181, 185, 187, 188, 189, 203, 206, 207, 209 conductivity, 3, 8, 39, 148, 150, 173, 183, 186, 190, 193, 195, 200 conductor, 159, 166, 180, 181, 195 conductors, 152, 164, 181 conference, 19 configuration, 23, 25, 104, 105, 106, 108, 111, 117, 119, 120, 122, 123, 124, 125, 127, 128, 129, 130, 132, 133, 134, 179, 193, 215 confinement, 41, 51, 53 conflict, 106, 108 congress, 65 conjugate analyses of heat transfer (CHT), ix conservation, 33, 105, 117, 145, 152, 154, 156, 157, 158, 164, 167, 168, 191, 197, 204, 205 consumers, 214 consumption, ix, 26, 27, 86, 87, 107, 119, 120, 124, 129, 131, 137, 139, 141, 143, 145, 214, 215, 221 contaminant, 2, 15, 16, 18, 19, 21, 25, 26, 28 contamination, 3 continuity, ix, 147, 157, 163 contour, ix, 48, 101, 114 control, 152, 157, 159, 164, 171, 173, 174, 191 convection, viii, 2, 9, 12, 19, 20, 29, 30, 31, 35, 51, 52, 53, 69, 70, 71, 72, 74, 75, 81, 82, 102, 103, 104, 161 convective, 148, 155, 159, 160 convention, 9, 35 convergence, 112, 120, 121, 133

conversion, 209, 211, 221, 222 cooling capacity, vii, ix, 1, 4, 12, 13, 19, 22, 23, 25, 27, 28, 29, 30, 31, 32, 50, 137, 171, 175, 176, 179, 180, 195, 198, 201, 215 cooling holes, viii, 101, 105, 106, 111, 112, 113 cooling panel (CP), viii, 69 cooling process, x, 116, 147 copper, 62 correlations, 30, 35, 41, 54, 56, 81, 82, 115, 116,140 cost, viii, 4, 69, 86, 102, 104, 195, 216 Coulomb, 148 coupling, x, 148, 181, 196 covering, 28, 51 CPU, 127 CRC, 208 CVD, 152 cycles, 153, 180, 193, 209

D decay, 48 decoupling, viii, 69, 86 defects, 215 definition, 157, 158, 183, 216, 219 deflation, 63 degradation, 207 density, 148, 150, 152, 156, 157, 158, 159, 167, 182, 183, 190, 191, 193, 195, 198, 201, 203, 206, 222 deposition, 152 derivatives, 155 desalination, 222, 223 designers, 4 desorption, 150, 164, 169, 171, 172, 173, 174, 179 deviation, 82 dew, 5, 12, 27, 31 diamonds, 46 diffusion, 72, 148, 160, 165, 166, 193, 210, 218 diffusion process, 219 diffusivity, 171 discomfort, 16, 17, 28, 29 discrete ordinates method (DOM), viii, 70 discretization, 78, 131 displacement, 2, 3, 4, 18, 19, 20, 21, 22, 25, 28, 29, 30, 32, 34, 35, 41, 43 distribution, ix, x, 14, 15, 20, 25, 26, 38, 40, 48, 49, 50, 63, 76, 105, 111, 115, 116, 123, 124, 125, 128, 129, 130, 131, 132, 133, 137, 142, 145, 147, 148, 155, 180 distribution function, x, 147, 148, 155, 180 divergence, 77 diversity, 51, 112 draft, 2, 16, 17, 19, 24, 25, 28, 29 draught, 25

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Index drying, 37, 86 durability, 103, 104, 105, 107, 109, 120 duration, 189, 191, 192, 193 dyes, 56

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E effusion, vii, 37, 38, 56, 59, 60, 61, 62, 63 Egypt, 147 electric charge, 149, 159, 161 electric current, 166, 181, 183, 186, 205, 206, 207 electric field, 148, 156, 159, 161, 181, 196, 198 electric potential, 150, 181, 206, 207 electric power, x, 213, 214, 219 electrical conductivity, 150, 190 electrical power, 188 electrical resistance, 6 electricity, 6, 206, 216 electrodes, 215, 219 electrodialysis, x, 213, 214, 215, 223 electromagnetic waves, 9 electromotive force, 206 electron, 150, 166, 167, 180, 196, 197, 203, 211 electron gas, 181 electron-phonon, 196, 203 electrons, ix, 147, 149, 150, 151, 152, 154, 157, 162, 164, 167, 181, 183, 196, 197, 198, 201, 203, 204 emission, 77, 102 energy consumption, viii, 3, 7, 25, 26, 27, 35, 69, 215, 221 energy density, 161 energy efficiency, viii, 69, 86 energy input, 152, 198, 201, 204 energy savings, vii, 1, 3 energy transfer, 4, 8, 161, 203 engineering, vii, 14, 37, 42, 133, 162, 167 England, 18 enlargement, 215, 217, 218 entropy, ix, 147, 148, 149, 150, 152, 154, 164, 165, 166, 167, 168, 181, 182, 183, 184, 185, 186, 187, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 201, 202, 204, 207, 209, 211 environment, viii, 3, 7, 8, 9, 10, 14, 15, 22, 26, 34, 153, 170, 174, 188, 189, 213, 215 equilibrium, ix, 21, 25, 147, 148, 152, 153, 155, 162, 165, 167, 171, 180, 189, 196, 198, 209, 210 equipment, vii, viii, 31, 32, 37, 38, 63, 69, 86 evaporation, 169, 171, 214 exchange rate, 22 experimental condition, 32, 59 extraction, 14 extracts, 23

223

F fabrication, 211 family, 169, 209 feeding, 219 FEM, ix, 101, 117 film, 152, 195, 196, 197, 198, 203, 204, 211, 219 films, 152, 153, 154, 164, 196, 201, 203, 211 financial, 208 financial support, 208 Finite Element Method (FEM), ix, 101 fission, viii, 91, 92, 93, 96, 99 fitness, 110, 112, 113 flame, 38 flaws, vii, 1 flexibility, 145 flow, ix, 147, 148, 149, 153, 155, 157, 159, 160, 161, 162, 165, 166, 172, 173, 174, 180, 181, 182, 186, 189, 193, 194, 198, 205, 206, 207, 214, 219 flow field, 39, 48, 51 flow rate, 172, 214, 219 fluctuations, 12, 26, 43, 153 fluid, vii, 7, 8, 9, 15, 16, 37, 38, 39, 43, 46, 53, 59, 63, 82, 130, 150, 152, 153, 157, 159, 162, 164, 172, 173, 174, 177, 189 fluid mechanics, 164 fluorescence, 56 flux diagram, 187, 204 force, 16, 148, 154, 155, 159, 161, 166, 171, 206, 215 formation, 48 formula, 17, 110, 113, 115, 116, 117, 120, 121 Fourier, 181, 190, 201, 204, 206 fragments, ix, 101 France, 1, 99 free energy, 166 freezing, 38 friction, 116, 166

G gas, 149, 150, 163, 167, 171, 181, 210 gas turbine cooling, vii, 37, 38, 63 gel, 148, 149, 150, 151, 152, 169, 171, 172, 175, 176, 177, 178, 179, 180, 210, 214, 215, 216, 217, 219 generation, x, 147, 152, 154, 162, 164, 166, 167, 169, 179, 181, 185, 191, 195, 196, 197, 199, 200, 204, 210, 211, 216 genotype, 111, 112, 113 geometry, vii, 37, 38, 41, 55, 56, 62, 63, 70, 75, 81, 102, 105, 108, 117, 127, 142

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Index

geothermal, 215 Germany, 18 Gibbs, x, 148, 154, 165, 195, 197, 204 glass, 215 grain size, 210 grains, 171, 210 gravitational field, 161 gravitational force, 159 Greece, 18 greenhouse gas emissions, vii, 1, 7 grids, 84, 130, 131, 132 guidelines, 27, 29

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H harmony, 106 health, viii, 14, 69 health-care facilities, viii, 69 heat, x, 147, 148, 149, 151, 152, 153, 154, 160, 161, 162, 164, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 179, 180, 181, 182, 183, 185, 186, 187, 188, 189, 191, 192, 193, 196, 197, 198, 201, 203, 205, 206, 207, 209, 210, 211, 214, 215, 222 heat capacity, 148, 162, 173, 210 heat loss, 3, 7, 13, 72, 73, 75, 188, 201 heat removal, 50, 51, 141, 145 heat shield, 47 heat transfer, vii, viii, ix, 2, 3, 5, 6, 7, 8, 9, 10, 11, 12, 13, 19, 20, 26, 28, 29, 30, 31, 34, 37, 38, 39, 40, 41, 42, 43, 44, 48, 49, 51, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 69, 70, 72, 74, 75, 77, 79, 81, 82, 85, 86, 101, 102, 103, 115, 116, 140, 142, 146, 148, 153, 166, 172, 173, 185, 187, 193, 198 heating, 149, 152, 169, 172, 174, 175, 176, 177, 179, 188, 189, 192, 195, 198 heavy metals, 91 height, 40, 54, 81, 86, 94, 105, 117, 119, 132, 215, 216, 222 heterostructures, 211 high heat transfer, vii, 37, 55, 62 high temperature, 215 high-density electrical equipment cooling, vii, 37, 38, 63 Holland, 209 hot spots, 62 hot water, 180 house, 88, 209 human, 2, 11, 34 human body, 2, 11 humidity, x, 12, 13, 15, 27, 73, 213, 217, 218, 221, 222 hybrid, 4, 21, 22, 25, 27, 28, 29, 32, 35, 43, 59, 222

I illumination, 70 image, 56 impingements on effusion surface, vii, 37, 63 improvements, 22, 31, 38, 63 independence, 83, 84 indication, 186 indicators, 216, 217, 219 individual character, 128 individuals, 110, 111, 112, 113, 120, 121, 127, 131 indoor air quality (IAQ), viii, 14, 69 induction, 3, 19, 20 industries, 168 industry, 88, 102 inequality, 107 inertia, 29 infrared, 189 injection, 193 inorganic, 169, 216 insertion, vii, 37, 41, 42 instability, 215, 222 insulation, 74, 83 interactions, 153, 159, 162, 167, 196, 197 interface, 79, 119, 189, 210, 219 interface layers, 210 interference, 22 interval, 175, 193 intrinsic, 219 investment, 102 ion-exchange, 215 ions, 215 Iran, 69 Ireland, 66 irradiation, 76, 77 isothermal, 153, 188 isotherms, 168, 171, 172, 173, 187, 193, 194 isotope, viii, 91, 92, 96, 99 issues, vii, viii, 5, 13, 22, 53, 101, 102, 103, 132 Italy, 1, 18 iteration, 75

J Japan, 18, 65, 209 jet vibration, vii, 37, 38, 63

K kinetic energy, 160, 162 kinetics, 168, 171, 210

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Index King, 208 Korea, 37, 64, 209

L laminar, 40, 81, 82, 122, 124, 127 lattice, 162, 198, 203 law, x, 148, 152, 188, 195, 197, 204, 209 laws, ix, 147, 152, 153, 154, 164, 184, 203, 204 lead, viii, ix, 24, 91, 92, 93, 95, 96, 98, 99, 102, 110, 113, 124, 125, 141, 145, 147, 177 legend, 84 legs, 186, 187, 192, 193 liberation, 170 light, 91, 168 linear, 153, 171 linear model, 12 liquid desiccant coolingxe "cooling" system (LDCS), vii, x, 213, 214 liquid phase, 150, 151, 173, 174 liquids, 8, 204 lithium, 222 living conditions, 214 London, 210 losses, 154, 186, 187, 188, 189, 198, 203 low temperatures, 16, 86, 131 Luo, 41, 64

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M machines, 214 magnetic, 159 magnitude, 76, 93, 95, 148, 181, 194 maintenance, 216 majority, 56 management, 32 manipulation, 159 manufacturing, viii, 69, 99 manufacturing plants, viii, 69 mapping, 132 market, x, 213 mass, 2, 7, 21, 37, 38, 41, 54, 58, 59, 60, 61, 62, 63, 66, 103, 108, 115, 117, 120, 140, 148, 149, 150, 152, 154, 156, 157, 158, 159, 160, 164, 165, 168, 169, 170, 171, 174, 175, 182, 197, 204, 209, 214, 215, 217, 219, 222 mass transfer, 152, 169, 175, 209, 215, 222 materials, 6, 8, 38, 93, 102, 152, 155, 180, 182, 185, 189, 193, 195, 196, 204, 205, 209, 211, 216, 222 mathematics, 159 matrix, 159, 169 matrix functions, 159

225

matter, 4, 19, 51, 167 meanings, 156 measurements, 9, 13, 41, 51, 53, 63, 83 measures, 215 mechanical energy, 160 mechanical ventilation, 13, 22 medical, 14 Mediterranean, 18 Mediterranean countries, 18 melting, 92, 104 melting temperature, 92, 104 membranes, x, 213, 215 metals, 8, 181 methanol, 169 methodology, 105, 119, 127, 129, 130, 140, 142, 145, 182, 190, 198 Miami, 99 microclimate, 14 micrometer, 196 military, 3 miniature, 152 miniaturization, 152 mixing, 2, 4, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 30, 32, 35, 40, 45, 46, 48, 52, 86, 104, 175 mobility, 196 modelling, 104, 106, 111, 114, 115, 132, 154, 174, 181, 203, 208, 209, 210, 211 models, viii, 63, 70, 71, 152 modifications, 147, 213 modules, 148, 149, 151, 196 moisture, 72, 217, 219 mole, 172, 214 molecular dynamics, 152 molecules, 154, 164, 215, 216, 217, 218 momentum, 15, 41, 148, 149, 152, 154, 156, 157, 158, 159, 164, 168, 204 monolayer, 171 Monte Carlo method, 76 Moon, 66, 223 Moscow, 100 motion, 155, 160, 165, 166 motivation, 196 movement, 215 multiplication, 94 multiplier, 120 mutation, 111, 112, 113

N naphthalene, 38, 57, 62, 63 National University of Singapore, 147, 209 natural, 168 neural network, 103

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226

Index

neutron capture, viii, 91, 93, 95, 96 neutron radiation capture, viii, 91, 92, 93, 96, 97, 98 neutron spectra, viii, 91, 92, 93, 96, 97 neutrons, viii, 91, 92, 93, 94, 95, 96, 97, 98 New York, 209, 210, 211 next generation, 92, 99, 203 nodes, 84, 85, 114, 115 noise, 169 non-uniform, 180 non-uniformity, 181 normal, 189, 190, 191, 204, 221 nozzle geometry, vii, 37, 38, 41, 63 nozzle insertion, vii, 37 n-type, 181, 196, 198, 202 nuclides, 92, 96, 99

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O obstacles, 102 obstruction, 77, 85 omission, 104 one dimension, 173 operating costs, ix, 31, 137, 139 operations, 56, 112, 113, 115, 121, 195 operator, 148, 152, 154, 155, 157 opportunities, vii, 1, 4, 32, 102 optimization, viii, ix, 39, 56, 101, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 114, 115, 117, 119, 120, 121, 124, 125, 126, 127, 129, 130, 131, 132, 133, 134, 194, 195 optimization method, 106 optimization of the cooling system, viii, 101, 103, 106, 115, 119, 120, 130, 132 ozone, 168

P parallel, 4, 18, 31, 32, 33, 47, 51, 86, 104, 121, 127, 133, 134, 138, 142, 143, 181, 189, 219 parallel processing, 104, 121, 127 parallelism, 117 parameter, 175, 195 Pareto, ix, 101, 105, 106, 108, 109, 110, 121, 122, 124, 126, 127, 128, 131, 132, 133, 135 Pareto approach, ix, 101, 105, 106, 109, 121, 127, 133 P-arm, 188, 200 particles, 152, 154, 156, 157, 159, 161, 162, 174, 203 pedagogical, 186, 195, 204 permeability, 14 phonological, 196

phonon, 150, 152, 153, 196, 197, 198, 199, 200, 203, 204, 211 phonons, ix, 147, 150, 151, 152, 154, 157, 162, 196, 197, 198, 201, 203, 204 photovoltaic, x, 213, 214, 215, 216 physical characteristics, 91, 93, 99 physical features, viii, 91 physical fields, 104, 106, 107 physical laws, 204 physical phenomena, 12 physical properties, 140, 181, 186, 191, 200 physics, 39, 88, 207 plants, viii, 69 plutonium, 92, 93, 94, 96, 99 Poland, 101 polar, 77 polarization, 76 pollutants, 14, 102 pollution, 222 polonium, 92 polynomial, 172 poor, 221 population, 111, 112, 113, 120, 121, 127, 130 pores, 168, 169, 217, 219 porosity, 174 porous, 169 porous materials, 103 positive interactions, 32 potential energy, 150, 160, 161 power, x, 149, 179, 188, 193, 194, 195, 198, 201, 203, 205, 211, 213, 214, 219 power generation, 195, 211 prediction, 218, 222 pressure, 149, 150, 158, 159, 163, 165, 167, 169, 170, 171, 174, 176, 182, 183, 215 pressure gradient, 183 prevention, 62 principles, 18, 19, 142, 145 probability, 112, 113 production, 154, 166, 209 project, 32, 92, 99, 100, 208 propagation, 76, 78, 84 property, 168, 193, 205 proportionality, 205 protection, 106 protective coating, 102 prototype, 198 p-type, 181, 196, 198, 203 pulse, 148, 151, 181, 189, 190, 191, 192, 193, 194, 195, 211 pumping, 169, 170 pumps, 3, 31, 138, 141, 143, 145 pure water, 53

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Index

Q quantum dot, 195 quantum well, 195, 211

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R radial distance, 50 radial distribution, 40 radiant cooling, vii, 1, 3, 4, 5, 12, 21, 22, 31, 32, 33, 35 radiant heating, vii, 1, 6, 7, 33 radiation, viii, 4, 5, 7, 9, 10, 12, 13, 20, 26, 29, 34, 69, 70, 71, 72, 75, 76, 77, 79, 83, 84, 85, 86, 91, 92, 93, 95, 96, 97, 98 radiative and convective transfer, viii, 69, 83 radio, 92 radius, 47, 105, 112, 113, 120, 149, 171, 214 random, 216 range, 154, 155, 159, 179, 196, 201, 203, 204, 221 reading, 5 real gas, 162, 163 recalling, 8 reciprocity, 153 recombination, 162, 166 recovery, 39, 41, 49, 209 recycling, ix, 137 redistribution, 139 reduce energy consumption, viii, 69 redundancy, 86 refrigerant, 151, 168, 170, 172, 174 refrigeration, 170, 181, 195, 211 regenerate, x, 213 regeneration, x, 213, 215, 216, 219, 221, 222, 223 regeneration process, x, 213, 219, 222 rejection, 120 relaxation, 153 relaxation time, 153 renewable energy, 3 reproduction, 112 requirements, viii, 19, 31, 50, 69, 70, 81, 83, 102, 145 reservoir, 153, 181, 192, 198 reservoirs, 153, 187, 189 resistance, 104, 166 resistive, 189 resistivity, 193, 200 resolution, 49, 51 respiration, 72, 73 response, 58, 106, 142, 145, 146, 189 restaurants, 19 restrictions, 112, 113, 120

227

risk, 4, 12, 13, 16, 19, 24, 25, 27, 28, 29, 32 risks, vii, 1, 19, 22 rocket launcher cooling, vii, 37, 63 rods, 43 room temperature, 15, 211 root-mean-square, 85 Russian, 210

S safety, 13 salt, 169 saturation, 73, 74, 151 savings, vii, 1, 3 scalar, 159 scale system, 164, 168 schema, 70 scope, 119 secondary injection, vii, 37, 38, 63 semiconductor, ix, 147, 152, 157, 166, 167, 181, 184, 189, 211 sensation, 25, 72 sensitivity, 132 sensors, 51, 175 shape, viii, 43, 101, 104, 105, 106, 109, 111, 113, 114, 127, 131, 132, 133, 134, 216 shear, 40, 43, 44, 45, 46 shock, 46, 47, 48, 49 shock waves, 46, 48, 49 short-range, 159 shoulder, 214 showing, 60, 153, 192, 194, 205 sign, 180, 193 silica, 148, 149, 150, 151, 152, 169, 171, 172, 175, 176, 177, 178, 179, 180, 210, 214, 215, 216, 217, 219, 223 silicon, 196 simulation, 35, 81, 140, 141, 142, 143, 164, 175, 179, 197, 201, 203 simulations, 40, 57, 70, 103, 121, 129, 191 Singapore, 147, 209 skin, 72, 73, 74 smoothness, 115 software, 117, 130 solar, x, 213, 215, 221, 222 solar cooling systems, vii solar energy, 221 solar panels, 216 solid state, 154, 203, 204, 211 solution, 4, 11, 22, 25, 27, 50, 80, 83, 84, 86, 102, 103, 105, 106, 108, 109, 110, 111, 112, 113, 115, 117, 119, 123, 124, 125, 128, 129, 131, 132, 133, 214, 215, 217, 219, 221, 222

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228

Index

sorbents, 169, 210 sorption, 151, 169, 172, 175, 209, 210, 221 Spain, 18 spatial, 160, 176, 193, 204 spatial location, 10 specific heat, 2, 21, 39, 148, 162, 173, 210 specific surface, 10, 12 speed, 196 spheres, 210 Spring, 39, 63, 66 stabilization, 124 stages, 218 state, 8, 12, 46, 71, 72, 104, 110, 121, 145, 146, 153, 154, 157, 169, 176, 178, 180, 192, 193, 203, 204, 209, 211 steady state, 157, 176, 178, 180, 192, 193 steel, 38 stratification, 18, 19, 20, 21, 25, 26, 28 streams, 219 strength, 150, 154, 166, 185 stress, ix, 7, 101, 106, 107, 108, 110, 117, 120, 121, 122, 123, 124, 125, 127, 128, 129, 130, 159 structure, 6, 40, 44, 46, 48, 58, 102, 103, 104, 105, 111, 112, 113, 121, 139, 142, 198, 204, 216 style, x, 213, 215 subcritical fast reactors, viii, 91 subjectivity, 14 substrate, 181, 189, 190, 191, 193 suction flow, vii, 37, 38, 45, 63 sunlight, 216 superlattice, 150, 151, 152, 154, 168, 195, 197, 203, 204, 211 superlattices, 196 superposition, 180, 219 surface area, ix, 9, 56, 72, 83, 137, 139, 141, 145, 204, 217 surface diffusion, 148 surface layer, 7, 23 surface properties, 75 surplus, 96, 99 survival, 112 survival rate, 112 switching, 174, 175, 176, 179, 180, 196 symmetry, 206

T target, 43, 49, 51, 55, 56, 59, 60, 110 technetium, 91 techniques, vii, 18, 37, 38, 43, 51, 56, 63, 102, 104, 141, 152 technology, vii, x, 1, 4, 28, 33, 112, 148, 152, 222 temperature gradient, 181, 193, 195, 205, 206, 207

tension, 150 testing, ix, 47, 101, 119, 179 textiles, 38 thermal analysis, 51 thermal comfort cooling, viii, 69 thermal conditioning, viii, 69 thermal conduction, 188 thermal energy, 7, 47, 159, 161, 205, 214, 215 thermal equilibrium, 153 thermal expansion, 3 thermal load, viii, 2, 7, 16, 22, 23, 47, 69, 71, 83, 84, 105, 130 thermal zone, viii, 69, 76 thermodynamic, x, 147, 150, 153, 154, 164, 165, 168, 181, 182, 183, 187, 189, 195, 204, 206, 209, 210 thermodynamic parameters, 117 thermodynamic properties, 123, 129, 133 thermoelectric cooling systems, vii, x, 148, 204 thin film, 152, 153, 154, 164, 167, 168, 196, 197, 198, 200, 201, 202, 203, 204, 211 Thomson, 150, 180, 181, 182, 184, 188, 189, 192, 193, 204, 205, 207 throws, 23 time frame, 176 tin, 116 tissue, 38 tonic, 106 total energy, 26, 48, 148, 160, 201 toxicity, 92 tracking, 193 transfer, 148, 153, 164, 167, 172, 173, 185, 187, 193, 198, 203 transformation, 180, 204 transparent medium, 76, 77 transpiration, 59, 103 transport, vii, viii, ix, 18, 51, 69, 70, 75, 76, 86, 147, 149, 152, 153, 154, 155, 156, 158, 166, 167, 168, 182, 183, 184, 196, 197, 204, 211, 215 transport phenomena, 168 transport processes, 154, 166, 204 transportation, 164, 205 treatment, viii, 70, 75, 79, 153, 183, 206 turbulence, 2, 17, 25, 30, 39, 41, 42, 44, 48, 52, 54, 63, 102 Turkey, 63

U universal gas constant, 149, 171 uranium, 91, 92, 93, 94, 99 USA, 33, 65, 66, 99, 135, 186, 210

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Index

229

V

W

vacuum, 9 valence, 214 validation, 35, 83, 85 values, 167, 171, 172, 175, 187, 198, 203 valve, 170 van der Waals forces, 168 vapor, 54, 73, 152, 170, 172, 210 variables, 38, 72, 105, 106, 108, 111, 112, 114, 115, 120, 121, 127, 129, 130, 140, 154, 158, 187, 195 variations, 38, 140, 179 vector, 47, 58, 108, 111, 112, 115, 149, 151, 155, 156, 158, 159, 160, 166, 204 velocity, 2, 3, 9, 11, 12, 15, 16, 17, 19, 22, 23, 25, 30, 31, 38, 39, 40, 41, 43, 45, 46, 47, 52, 53, 54, 55, 57, 58, 74, 81, 82, 149, 151, 154, 155, 156, 157, 158, 159, 182 ventilation, vii, viii, 1, 2, 3, 4, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 28, 29, 30, 31, 32, 34, 35, 69, 73, 74, 86, 87 ventilation airflow rates, vii, 1 ventilation strategy, vii, 1, 15, 31, 32 ventilation system, vii, 1, 13, 14, 15, 21, 22, 23, 25, 30, 31, 34, 35 vibration, vii, 37, 38, 63, 169 viscoelastic materials, 204 viscosity, 150, 166 visualization, 41, 43, 45, 46, 47, 58

wall temperature, 35, 39, 48 Washington, 66, 88 waste, 168, 210, 215 waste heat, 168, 210, 215 water, viii, ix, x, 3, 6, 7, 27, 31, 51, 53, 58, 69, 71, 72, 73, 74, 86, 137, 138, 139, 140, 141, 142, 143, 145, 146, 148, 151, 168, 170, 171, 174, 175, 176, 177, 178, 179, 180, 210, 213, 214, 215, 216, 217, 219, 222, 223 water sorption, 210 water vapor, 73, 74, 171, 210 wavelengths, 10, 152 wells, 196 wind, 216 wind tunnels, 216 working conditions, 221

Y yield, 51, 157, 191, 193, 223

Z

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zeolites, 152

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