Page 67 - Design and Operation of Heat Exchangers and their Networks

54 Design and operation of heat exchangers and their networks

2.1.6.2 Strong conduction effect
The limiting case for infinite large thermal conductivity, that is, Pe w ¼0, is
denoted with index “0.” For this case, the dimensionless temperature
change can be determined with
1 N wo,h 1
¼ +
ð
ð
ε h,0 N h N h + N wo,h Þ 1 e N h + N wo,hÞ
_
C h N wo,c 1
+ + (2.122)
_
ð
ð
C c N c N c + N wo,c Þ 1 e N c + N wo,cÞ
_
C h
ε c,0 ¼ _ ε h,0 (2.123)
C c
Eq. (2.122) is valid for all one-pass flow arrangements. With Eqs. (2.122),
(2.123), we can calculate the outlet temperatures of the hot and cold fluids
and evaluate the mean temperature difference Δt m appearing in the expres-
sion of the limiting Peclet number Pe 0 :
" #
_
1 1 Δt m 1 C h
¼ _ _ _ (2.124)
0
Pe 0 1+ C h =C c ε h,0 t t 0 N h C c N c
h c
For parallel-flow and counterflow arrangements, Δt m is the logarithmic
mean temperature difference. Eq. (2.124) is also exactly valid for pure
crossflow and is approximate for other one-pass flow arrangements, if
Δt m is replaced by the correct mean temperature difference for the flow
arrangement under consideration.

2.1.6.3 Asymptotic equation for general cases
For general cases 0 Pe w ∞, Roetzel and Na Ranong (2018b) proposed
an asymptotic equation as follows:

0:87 0:87 1=0:87
Pe ¼ Pe +Pe (2.125)
0 ∞
Applying this Peclet number to both fluids according to the dispersion
model gives the outlet fluid temperatures with consideration of axial wall
heat conduction.

2.2 Pressure drop analysis

In the thermal design of a heat exchanger, the total pressure drop (in some
cases also the pressure distribution) analysis should be performed