Page 116 - Design and Operation of Heat Exchangers and their Networks

104 Design and operation of heat exchangers and their networks

Example BA 5,5 —cont’d

We can solve Eqs. (3.190), (3.191) and obtain α n and β n :
2 3 2 3 2 3
1 0:55556
α 0
6 7
6 7 1 1 6 0:41651 7
α 1
6 7 ¼ A 6 7 ¼ 6 7
β
1
4 0 5 4 5 4 0:92288 5
β 1 1 0:06057
F n (b A , a A ) can be evaluated with Eq. (3.167) or (3.172):
F 1 b A , a A Þ ¼ 0:20630
ð
F 2 b A , a A Þ ¼ 0:039560
ð
Finally, we obtain
" #
N
1 1 X
ε 1 ¼ 1 α n F n +1 b A , a A Þ
ð
R 1 a A
n¼0

1 1
¼ 1 ð 0:55556 0:20630 0:41651 0:03956Þ ¼ 0:3773
2 0:4

Example BA 5,6 2 2
B A
1 1

For the flow arrangement type BA 5,6 , the ε-NTU relationship is expressed
with Eq. (3.189), however, in which α n and β n are determined by
N
X
inv
ðÞβ ¼ 1 m ¼ 0, 1, 2, …, NÞ
A ð b A , b B , a A Þα n + B mn b B n ð (3.194)
mn
n¼0
N
X
id
ðÞα n + A ð
ð
B mn a A a B , a A , b B Þβ ¼ 1 m ¼ 0, 1, 2, …, NÞ (3.195)
mn n
n¼0
ð q 0 m
ð m +1Þ! q
id 0 0
ð
A ð p, q, rÞ ¼ G n pq =q, rÞ dq
mn m +1
q 0 m!
" k #
m
ð m +1Þ! X m r n + k +1 p m k X k
¼ F n + j +1 p, rð Þ
p m +1 k ð n + k +1Þ! ð m kÞ! j
k¼0 j¼0
(3.196)
inv
The functions A mn (p,q,r) and B mn (x) are determined by Eqs. (3.192),
(3.193), respectively.