Page 232 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 221

(2) Calculation of geometric parameters
We use the optimal geometric parameters of Mishra et al. (2009) as the initial
values as length of the heat exchanger in the hot fluid flow direction
L h ¼0.994m, length of the heat exchanger in the cold fluid flow direction
L c ¼0.887m, fin height h f,h ¼h f,c ¼0.00953m, fin thickness
δ f,h ¼δ f,c ¼0.000146m, fin strip length l s,h ¼l s,c ¼0.0063m, number of fins
1
per meter FPM h ¼FPM h ¼534.9m , and number of fin layers N fl,h ¼8.
To reduce the heat loss to the surrounding, we put the cold side fin layer
at the outermost sides of the exchanger; therefore, the number of fin layers
for cold fluid N fl,c is one more than N fl,h :
N fl,c ¼ N fl,h +1 ¼ 8+ 1 ¼ 9 (5.101)
The fin-free spacing in height
h fs,h ¼ h f,h δ f,h ¼ 0:00953 0:000146 ¼ 0:009384 m
The fin pitch
s f,h ¼ 1=FPM h ¼ 1=534:9 ¼ 0:00187 m
The fin-free spacing in width
s fs,h ¼ s f,h δ f,h ¼ 0:001870 0:000146 ¼ 0:001724 m
The hydraulic diameter for the calculation of the entrance and exit
pressure loss is defined by Eq. (3.245):

2h fs,h s fs,h 2 0:009384 0:001724
d h1ðÞ,h ¼ ¼ ¼ 0:002912 m
h fs,h + s fs,h 0:009384 + 0:001724
The hydraulic diameter for the correlations of Joshi and Webb (1987) is
defined by Eq. (3.246):
2h fs,h s fs,h δ f,h Þ
ð
d h2ðÞ,h ¼
h fs,h + s fs,h + h fs,h δ f,h =l s,h
ð
2 0:009384 0:001724 0:000146Þ
¼ ¼ 0:002614m
0:009384 + 0:001724 + 0:009384 0:000146=0:0063
Similarly, we have h fs,c ¼0.009384m, s f,c ¼0.001870m,
s fs,c ¼0.001724m, d h(1),c ¼0.002912m, and d h(2),c ¼0.002614m.
The crossflow areas for hot and cold fluids are calculated with
Eqs. (5.102), (5.103), respectively:
A c,h ¼ FPM h L c N fl,h h fs,h s fs,h ¼ 534:9 0:887 8
0:009384 0:001724 ¼ 0:06139 m 2 (5.102)
A c,c ¼ FPM c L h N fl,c h fs,c s fs,c ¼ 534:9 0:994 9
0:009384 0:001724 ¼ 0:07739 m 2 (5.103)
The ratio of free flow area to frontal area can be expressed as