Page 133 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 121

or using Eq. (3.241)

2h fs s fs δ f Þ
ð
d h2ðÞ ¼ ð Joshi and Webb, 1987Þ (3.246)
h fs + s fs + h fs δ f =l s
or using Eq. (3.242) and neglecting a higher-order small term

2h fs s fs
d h3ðÞ ¼ ð Manglik and Bergles, 1995Þ (3.247)
ð
h fs + s fs + h fs + s fs =2Þδ f =l s
3.5.3 Fin efficiency

As has been mentioned in the previous section, in a two-stream plate-fin
heat exchanger, the fins can be considered adiabatic at the half height of
the fins. Thus, the fin efficiency η f for a fin of constant section and with con-
stant heat transfer coefficient α over the surface is given by (from Eq. 2.58)

tanh ml f =2Þ
ð
η ¼ (3.248)
f
ml f =2
where (from Eq. 2.59)
s ffiffiffiffiffiffiffiffiffiffiffiffi
αP
m ¼ (3.249)
λ f A c, f
P is the perimeter of the fin and A c,f is its cross-sectional area. For plain and
wavy fins,
r ffiffiffiffiffiffiffiffi
2α
m ¼ (3.250)
λ f δ f
For offset strip fins,
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2α 1+ δ f =l s Þ
ð
m ¼ (3.251)
λ f δ f
The fin length l f is the actual fin length along the fin surface perpendicular to
flow direction. For example, the actual fin length of the triangular plain fin
2 2 1/2
can be expressed as l f ¼[(h f δ f ) +(s f /2) ] , and that of the rectangular
plain fins and the rectangular offset strip fins is l f ¼h fs ¼h f δ f .
The overall fin efficiency η 0 of a plate-fin heat exchanger is determined
by Eq. (2.50):

A f
η ¼ 1 1 ηð Þ (3.252)
0 f
A