Page 223 - Design and Operation of Heat Exchangers and their Networks

212 Design and operation of heat exchangers and their networks

Since Re tb 800, the Hagen number for staggered tube bundles is
obtained from Eq. (5.46):
Hg ¼ Hg lam ¼ 48;114
Finally, we obtain the Nusselt number from Eq. (5.42) as
2 1=3
ð
Nu id ¼ 0:404 0:92HgPr s 4s t s l =π d = s l s d Þ
o
¼ 0:404 0:92 48114 444:14
½

2 1=3
4 0:03536 0:01768=π 0:019 = 0:01768 0:025ð ފ ¼ 108:4
which yields
2
α id ¼ Nu id λ s =d o ¼ 108:4 0:13937=0:019 ¼ 795 W=m K
The correction factors are calculated with Eqs. (5.56), (5.57), (5.61),
(5.68), (5.70). Some of them depend on the shell-side Reynolds number
Re sd defined by Eq. (5.63):

_ m s d o 36:6 0:019
Re sd ¼ ¼ ¼ 721
A sc μ 0:03209 0:02981
s
Because the shell-side Reynolds number Re sd >100, the coefficient in
Eq. (5.61) is given by Eq. (5.62) as C bh ¼1.25, and the exponent in
Eq. (5.68) is n¼0.6. Thus, we have

J c ¼ 0:55 + 0:72F c ¼ 0:55 + 0:72 0:6437 ¼ 1:013

ð
J l ¼ 0:44 1 r s Þ +1 0:44 1 r s Þ½ ð Še 2:2r lm
¼ 0:44 1 0:4265Þ +1 0:44 1 0:4265ފe 2:2 0:1132 ¼ 0:8351
½
ð
ð
1=3 1=3
½
½
ð
ð
J b ¼ e C bh r b 1 2r ss Þ Š ¼ e 1:25 0:263 1 2 0:1111Þ Š ¼ 0:8784
1 n 1 n
ð
N b 1+ l bi =l bc Þ + l bo =l bc Þ
ð
J s ¼
N b 1+ l bi =l bc Þ + l bo =l bc Þ
ð
ð
1 0:6 1 0:6
14 1+ 0:3365=0:279Þ +0:3365=0:279Þ
ð
ð
¼ ¼ 0:9834
ð
ð
14 1+ 0:3365=0:279Þ +0:3365=0:279Þ
J r ¼ 1
The shell-side heat transfer coefficient can be evaluated with Eq. (5.39):
α s ¼ α id J c J l J b J s J r ¼ 795:5 1:013 0:8351 0:8784 0:9834 1
2
¼ 581:6W=m K
(5) Calculation of thermal performance of the heat exchanger
The overall heat transfer coefficient based on the shell-side heat transfer area
can be expressed as