Page 237 - Design and Operation of Heat Exchangers and their Networks

226 Design and operation of heat exchangers and their networks

Similarly, we have m c l f,c /2¼0.6244, η f,c ¼0.8876, A f,c /A c ¼0.8464,
and η 0,c ¼0.9048.
For hot fluid side, the total heat transfer area can be expressed by

A h ¼ 2N fl,h FPM h L h L c h fs,h + s fs,h + h fs,h + s ofs,h δ f,h δ f,h =l s,h
¼ 2 8 534:9 0:994 0:887 0:009384 + 0:001724 + 0:009384
ð
½
+0:0009348 0:000146Þ 0:000146=0:0063Š¼ 85:59m 2
ð
A c ¼ 2N fl,h FPM c L h L c h fs,c + s fs,c + h fs,c + s ofs,c δ f,c Þ δ f,c =l s,c Š
½
2
¼ 85:59 m (5.116)
in which only half of the surface area of the two outermost sides for the cold
stream are taken into account.
The overall heat transfer coefficient based on the area of the hot fluid
side is determined by
1 1 δ p + δ h + δ c Þ=2 1
ð
¼ + +
k h A h α h η 0,h A h 2λ f N fl,h L h L c α c η 0,c A c
1 0:0008 + 0:000146 + 0:000146Þ=2
ð
¼ +
299:7 0:8604 85:59 2 150 8 0:994 0:887
1 4
+ ¼ 1:139 10 K=W (5.117)
189:5 0:9048 85:59
The number of transfer units NTU h and the ratio of thermal capacity
rates of hot and cold fluids R h are calculated as
1
k h A h
NTU h ¼ ¼ 4 ¼ 9:173
_ m h c p,h 0:8962 1068 1:139 10
0:8962 1068
_ m h c p,h
R h ¼ ¼ ¼ 1:147
_ m c c p,c 0:8296 1006
The dimensionless outlet temperature of hot fluid is given by
Eq. (3.121):
∞ n 1 n 1 k
X ð R h NTU h Þ X NTU
t h,out ¼ e R h NTU h e NTU h ð n kÞ h (5.118)
n! k!
n¼1 k¼0
The calculation of this infinite series results in t h,out ¼ 0:2390. The
outlet fluid temperatures can then be obtained:

ð
t h,out ¼ t c,in + t h,in t c,in Þt h,out ¼ 277 + 513 277ð Þ 0:2390 ¼ 333:4K
t c,out ¼ t c,in + R h t h,in t h,out Þ ¼ 277 + 1:147 513 333:4ð Þ ¼ 483:0K
ð
After we have obtained the outlet temperatures and pressures of the fluids,
we can update their values repeatedly until their changes become negligible.
The final outlet fluid temperatures and pressure drops are the following:
t h,out ¼329.3K, t c,out ¼481.8K, Δp h ¼10,488Pa, and Δp c ¼3472Pa. The
heat duty of the exchanger is given by