Page 38 - Design and Operation of Heat Exchangers and their Networks

Basic thermal design theory for heat exchangers 25

In thermally developing laminar flow, we can use the approximate equa-
tions of Shah and London (1978):
8
1=3
1:849 RePrd h =LÞ , L= d h RePrÞ 0:0005
ð
ð
<
1=3
Nu T ¼ 1:849 RePrd h =Lð Þ +0:6, 0:0005 < L= d h RePrÞ 0:006
ð
:
7:541 + 0:0235RePrd h =L, L= d h RePrÞ > 0:006
ð
(2.26)
8
1=3
1:233 RePrd h =xð Þ +0:4, x= d h RePrÞ 0:001
ð
<
0:488
Nu x,T ¼ 7:541 + 6:874 0:001RePrd h =xð Þ x= d h RePrÞ > 0:001
ð
:
e 245= RePrd h =xÞ ,
ð
(2.27)
8
1=3
ð
< 2:236 RePrd h =Lð Þ , L= d h RePrÞ 0:001
1=3
Nu H ¼ 2:236 RePrd h =Lð Þ +0:9, 0:001 < L= d h RePrÞ < 0:01
ð
:
8:235 + 0:0364RePrd h =L, L= d h RePrÞ 0:01
ð
(2.28)
8
1=3
ð
1:490 RePrd h =xð Þ , x= d h RePrÞ 0:0002
>
>
<
1=3
ð
1:490 RePrd h =xð Þ 0:4 0:0002 < x= d h RePrÞ 0:001
Nu x,H ¼ 0:506
ð
> 8:235 + 8:68 0:001RePrd h =xð Þ x= d h RePrÞ > 0:001
>
:
e 164= RePrd h =xÞ ,
ð
(2.29)
For the thermally and hydrodynamically developing laminar flow,
Stephan (1959) proposed the following correlation:
1:14
0:024 RePrd=LÞ
ð
Nu T ¼ 7:55 + 0:64 (2.30)
1+ 0:0358Pr 0:81 ð Red=LÞ
2.1.1.5 Fully developed laminar flow in rectangular ducts
The Nusselt number for fully developed laminar flow in rectangular chan-
nels was approximately expressed by Shah and London (1978) as
!
5
X
Nu ¼ a 0 1+ a n γ n ð γ ¼ aspect ratio, 0 γ 1, Re < 2200, Pr > 0:6Þ
n¼1
(2.31)
For constant wall temperature (T): a 0 ¼7.541, a 1 ¼ 2.61, a 2 ¼4.97,
a 3 ¼ 5.119, a 4 ¼2.702, and a 5 ¼ 0.548. For the boundary condition of
constant heat flux in the flow direction and uniform peripheral wall