Page 236 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 225

Because in the initial calculation, it is assume that ρ in ¼ρ out : therefore,
the pressure drops due to acceleration:

1 1
Δp a,h ¼ G 2 ¼ 0 Pa (5.112)
1 ðÞ,h ρ ρ
h,out h,in
The total pressure drop is then obtained as
Δp h ¼ Δp in,h + Δp f,h + Δp a,h + Δp out,h ¼ 206 + 10;270 + 0 85
¼ 10;391 Pa (5.113)
With the same method, we can obtain the entrance and exit pressure
drops of air flow as Δp in,c ¼59Pa, Δp out,c ¼ 26Pa, Δp f,c ¼3117Pa, and
Δp a,c ¼0Pa, and the total pressure drop in the cold fluid flow is
Δp c ¼3149Pa. The outlet pressures are

P h,out ¼ p h,in △p h ¼ 100;000 10;391 ¼ 89;609 Pa
P c,out ¼ p c,in △p c ¼ 100;000 3149 ¼ 96;851 Pa

(4) Calculation of thermal performance of the heat exchanger
In the design of plate-fin heat exchangers, fin efficiency is an important
parameter. The fin efficiency is expressed by Eq. (2.58):

ð
tanh ml f =2Þ
η ¼
f
ml f =2
For offset-strip fins, the fin length l f ¼h fs ¼h f δ f , and m is calculated
with Eq. (3.251). So we have
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2α 1+ δ f =l s Þ
ð
ml f =2 ¼ h fs (5.114)
2 λ f δ f
r ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
1 2 299:7 1+ 0:000146=0:0063Þ
ð
m h l f,h =2 ¼ 0:009384 ¼ 0:7851
2 150 0:000146
ð
tanh 0:7851Þ
η ¼ ¼ 0:8351
f,h
0:7851
The overall fin efficiency η 0 is expressed by Eq. (2.50), η 0 ¼1 (1 η f )
A f /A, in which the ratio of the secondary surface area to the total heat
transfer surface area for the rectangular offset-strip fins is given by Eq. (3.254):

A f ,h h fs,h l s,h + δ f ,h
¼
A h h fs,h + s fs,h l s,h + h fs,h + s ofs,h δ f ,h δ f ,h
ð
0:009384 0:0063 + 0:000146Þ
¼
ð 0:009384 + 0:001724Þ 0:0063 + 0:009384 + 0:0009348 0:000146Þ 0:000146
ð
¼ 0:8464
η 0 ¼ 1 1 0:8351ð Þ 0:8464 ¼ 0:8604