Page 135 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 123

2 2
K e 1 σ (3.258)
The Fanning frictional factor f in Eq. (3.256) is defined by

Δpρ d h
m
f ¼ (3.259)
2
2G L
The correlations for f is provided as follows for different fin types.

3.5.4.1 Rectangular plain fins
The flow and heat transfer inside a rectangular plain-fin surface can be trea-
ted as fluid flow and heat transfer through a rectangular channel (see
Chapter 2), with the difference in the thermal boundary condition at the
extended surface. If no suitable correlations are available, the correlations
for constant wall temperature can be adopted.
Diani et al. (2012) proposed their correlations based on CFD simulations
for air flow under constant heat flux at the plate in the Reynolds number
range of 2700 Re 10,100 as
0:034 0:169

f ¼ 0:029Re 0:09 δ f s f (3.260)
h fs h fs
0:208 0:208

j ¼ 0:233Re 0:48 δ f s f (3.261)
h fs h fs
The correlations based on the CFD simulation was given by Chennu
(2018) as

f ¼ 12:892Re 1:229 ð h fs =s fs Þ 0:452 ð δ f =s fs Þ 0:198 ð 100 Re 1000Þ (3.262)
f ¼ 3:133Re 1:285 ð h fs =s fs Þ 0:247 ð δ f =s fs Þ 0:181 ð 1000 < Re 7500Þ (3.263)

j ¼ 0:454Re 0:977 ð h fs =s fs Þ 0:435 ð δ f =s fs Þ 0:227 ð 100 Re 1000Þ (3.264)
j ¼ 0:166Re 1:011 ð h fs =s fs Þ 0:228 ð δ f =s fs Þ 0:366 ð 1000 < Re 7500Þ (3.265)

3.5.4.2 Offset strip fins
In the literature, different researchers have used different expressions for the
hydraulic diameter. For clarity, we use the index (i) to distinguish its used in
their correlations by

G iðÞ d h iðÞ
Re iðÞ ¼ (3.266)
μ