Page 234 - Design and Operation of Heat Exchangers and their Networks

Optimal design of heat exchangers 223

Since Re* (2) <Re (2) <Re* (2) +1000 for both hot and cold fluids, we
use the linear interpolation with Eqs. (3.275)–(3.280) to determine f and
j in the transition region:
∗
Re 2ðÞ,h Re
2 ðÞ,h 1560 1320
γ ¼ ¼ ¼ 0:2407
h
1000 1000
8:12
f 2 ðÞ,h, Re 2ðÞ,h ¼Re ∗ ¼
2 ðÞ,h ∗ 0:74 0:41 0:02
Re l s,h =d ð s fs,h =h fs,h Þ
2 ðÞ,h h2ðÞ,h
8:12
¼ 0:41 0:02 ¼ 0:02874
1320 0:74 0:0063=0:002614Þ 0:001724=0:009384Þ
ð
ð
1:12
f ∗
2 ðÞ,h, Re 2ðÞ,h ¼Re + 1000 ¼
2 ðÞ,h ∗ 0:36 0:65 0:17
Re + 1000 l s,h =d δ f ,h =d
2 ðÞ,h h2ðÞ,h h2ðÞ,h
1:12
¼ 0:36 0:65 0:17 ¼ 0:06344
ð
ð 1320 + 1000Þ 0:0063=0:002614Þ 0:000146=0:002614Þ
ð
f 2 ðÞ,h ¼ 1 γ h Þf 2 ðÞ,h, Re 2ðÞ,h ¼Re ∗ + γ h f 2 ðÞ,h, Re 2ðÞ,h ¼Re ∗ + 1000
ð
2 ðÞ,h 2 ðÞ,h
¼ 1 0:2407Þ 0:02874 + 0:2407 0:06344 ¼ 0:03709
ð
0:53
j ∗
h, Re 2ðÞ,h ¼Re ¼
2 ðÞ,h 0:5 0:15 0:14
Re ∗ l s,h =d s fs,h =h fs,h
2 ðÞ,h h2ðÞ,h
0:53
¼ 0:15 0:14 ¼ 0:1621
1320 0:5 0:0063=0:002614Þ 0:001724=0:009384Þ
ð
ð
0:21
j ∗
h, Re 2ðÞ,h ¼Re + 1000 ¼
2 ðÞ,h ∗ 0:4 0:24 0:02
Re + 1000 l s,h =d δ f ,h =d
2 ðÞ,h h2ðÞ,h h2ðÞ,h
0:21
¼ 0:4 0:24 0:02 ¼ 0:008118
ð
ð 1320 + 1000Þ 0:0063=0:002614Þ 0:000146=0:002614Þ
ð
j h ¼ 1 γ h Þj h, Re 2ðÞ,h ¼Re ∗ + γ h j h, Re 2ðÞ,h ¼Re ∗ + 1000
ð
2 ðÞ,h 2 ðÞ,h
¼ 1 0:2407Þ 0:01621 + 0:2407 0:008118 ¼ 0:01426
ð
With the similar method, we can obtain the f and j factors for the cold
fluid as f (2),c ¼0.04214 and j c ¼0.01281.
From the definition of the Colburn j factor, Eq. (3.255), we obtain the
heat transfer coefficients of hot and cold fluids as
1068 15:95
c p,h G 2ðÞ,h 2
α h ¼ j h 2=3 ¼ 0:01426 2=3 ¼ 299:7W=m K
Pr 0:7301
h
c p,c G 2ðÞ,c 1006 11:71 2
α c ¼ j c 2=3 ¼ 0:01281 2=3 ¼ 189:5W=m K
Pr c 0:7102
The total pressure drop is given by