*157*
*36*
*209KB*

*English*
*Pages [6]*
*Year 2021*

- Author / Uploaded
- Mohammad Olfati
- Mohammad Jamshidmofid

Derivation of the differential equation of entropy generation rate

t.me/exergy_destruction

q q + dy dx T y y T y

q dy T x

ρvs + y ( ρvs ) dy dx

q q T + x T dx dy x x

y

ρs ( ) t dxdy

ρusdy y, v

x

x, u

q dx T y

ρvsdx

S g = −

Q S − ms + ms + T t i e t.me/exergy_destruction

ρus + ρus dx ( ) dy x

q q q q q q S gdxdy = + dx dy + + dy dx − dy − dx T x T y T y y T y T x x T x + ρus + ( ρus ) dx dy + ρvs + ( ρvs ) dy dx − ρusdy − ρvsdx x y ( ρs ) + dxdy t

q S g = x x T

qy + y T

+ ρus + ρvs + ( ) ( ) ( ρs ) y t x

1 qx qx T 1 q y q y T ρ u s ρ v s s ρ Sg = − 2 + − 2 + us + ρs + ρu + vs + ρs + ρv + ρ + s T x T x T y T y x x x y y y t t t.me/exergy_destruction

s u v 1 qx q y 1 T T s s ρ ρ ρ S g = + + qy − 2 qx + ρ + u + v + s + u + v + ρ + T x y T x y x y t x y t x y

S g =

1 1 Ds 1 1 Ds Dρ .q − 2 q.T + ρ +s + ρ.V → S g = .q − 2 q.T + ρ T T Dt T T Dt Dt

1 ρ P Ds ρ De P Dρ Tds = de + Pd → ρds = de − dρ → ρ = − T ρT Dt T Dt ρT Dt ρ

t.me/exergy_destruction

S g =

1 1 ρ De P Dρ .q − 2 q.T + − T T T Dt ρT Dt ρ

S g =

De = −.q − P ( .V ) + μΦ Dt

1 1 1 P μ P Dρ .q − 2 q.T − .q − ( .V ) + Φ − T T T T T ρT Dt

1 μ P Dρ S g = − 2 q.T + Φ − + ρ . V ( ) T T ρT Dt

t.me/exergy_destruction

1 μ S g = − 2 q.T + Φ T T

1 μ q =− K T K μ 2 S g = − 2 q.T + Φ → S g = 2 ( T ) + Φ T T isotropic T T 2 2 2 2 2 u v K T T μ u v S g = 2 + 2 + + + + T x y T x y y x

Thank You t.me/exergy_destruction