Page 66 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 53

where the subscript “w” indicates the separating wall, L h and L c are the heat
exchanger length along the flow directions of hot and cold fluids, and A c,w,h
and A c,w,c are the heat conduction cross-sectional areas of the separating
walls for heat conduction along their flow directions. For counterflow
and parallel flow, L h /(λ w A c,w,h )¼L c /(λ w A c,w,c ). For crossflow, they should
be determined individually.
For the outer walls denoted with “wo,” we have similar expression:

_ L h _ L c
Pe wo,h ¼ C h ,Pe wo,c ¼ C c (2.117)
λ wo,h A c,wo,h λ wo,c A c,wo,c
If the hot fluid (or cold fluid) has no outer wall effect, then the corre-
sponding heat conduction cross-sectional area A c,wo,h (or A c,wo,c ) is zero,
and we have Pe wo,h (or Pe wo,c )¼∞.
The number of transfer units N formed with heat transfer coefficient is
defined as
α h A h α c A c
N h ¼ _ ,N c ¼ _ (2.118)
C h C c
for heat exchange between the hot and cold fluids. For heat exchange
between the fluids and outer walls, N is denoted as N wo and defined as
α wo,h A wo,h α wo,c A wo,c
N wo,h ¼ _ , N wo,c ¼ _ (2.119)
C h C c
where α wo,h and α wo,c are the heat transfer coefficients of the hot and cold
fluids at the fluid side surfaces of the outer walls A wo,h and A wo,c .

2.1.6.1 Week conduction effect
First, the limiting case of week conduction effect for high value of Pe w ,
denoted with index “∞”
1 1 2a 1 1 1
¼ + + + +
Pe ∞ ψ 2 ψ ψ ψ 2 _ _ _ _
h h c c Pe wo,h 1+ C h =C c Pe wo,c 1+ C c =C h
(2.120)
where

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
α c A c
ψ ¼ _ _ 1+ ,
h Pe w,h 1+ C h =C c
α h A h

q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
_ _ α h A h
ψ ¼ Pe w,c 1+ C c =C h 1+ (2.121)
c
α c A c
and a¼1 for counterflow, a¼ 1 for parallel flow, and a¼0 for mixed-
mixed crossflow.