Page 198 - Design and Operation of Heat Exchangers and their Networks

186 Design and operation of heat exchangers and their networks

where
1 X
Co v ¼ _ n j, int M j c p,v, j (4.242)
e
α v
j
Using the boundary condition (4.240) and the expression of the heat transfer
coefficient, α v ¼λ v /δ v , we obtain

Co v
_ q ¼ α mix,v t v t int Þ ¼ α v t v t int Þ (4.243)
ð
ð
s,v
1 e Co v
With the similar procedure, the heat flux in the liquid region is
expressed as
Co f
_ q ð Þ ¼ ð Þ (4.244)
s, f ¼ α mix, f, δ f t int t δ f α f , δ f t int t δ f
1 e Co f
where
1 X
Co v ¼ _ n j, int M j c p,v, j (4.245)
e
α v
j
The sensible heat flux through the liquid film is equal to that through the
plate and can further be expressed as
_ q ¼ k int t int t c Þ (4.246)
ð
s, f
where
1
1 δ w 1 1
k int ¼ + + + (4.247)
α c λ w α f α mix, f, δ f
The interface temperature t int can be obtained by substituting
Eqs. (4.237), (4.243), (4.246) into the energy equation:

_ q ¼ _q + _q (4.248)
s, f l s,v
which yields
k int t c + α mix,v t v + _q l
t int ¼ (4.249)
k int + α mix,v
(4.250)
s, f
t δ f ¼ t int _q =α mix, f , δ f
(4.251)
s, f
t wh ¼ t δ f _q =α f
(4.252)
t wc ¼ t wh _q δ w =λ w
s, f