Page 117 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 105

Example BA 5,6 —cont’d
For the data given in Example BA 5,6 , we have
inv
ðÞ
A ð b A , b B , a A Þ B mn b B
mn
A ¼
id
ðÞ
B mn a A A ð a B , a A , b B Þ
mn
2 3
0:24212 0:05505 1 0:6
0:26832 0:05641 1 0:8
6 7
¼ 6 7
4 1 0:2 0:59887 0:41189 5
1 0:26667 0:56695 0:38401
Its inverse matrix can be obtained as
2 3
0:37169 0:44782 4:17985 2:96969
A 1 ¼ 6 0:12347 0:69527 15:1319 14:97529 7
7
6
4 4:06485 2:94969 0:18465 0:008077 5
4:94769 5:03829 0:10409 0:049834
which yields
2 3 2 3 2 3
α 0 1 0:39064
6 7
6 7 1 1 6 0:41514 7
α 1
6 7 ¼ A 6 7 ¼ 6 7
β
1
4 5 4 5 4 0:92243 5
0
β 1 0:06334
1
" #
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 0:39064 0:20630 + 0:41514 0:03956Þ ¼ 0:3787
2 0:4
Example BA 6,6 2 2
B A
1 1
For the flow arrangement type BA 6,6 , the ε-NTU relationship is expressed
with Eq. (3.189), however, in which α n and β n are determined by
N
X
id
ðÞβ ¼ 1 m ¼ 0, 1, 2, …, NÞ
A ð b A , b B , a A Þα n + B mn b B ð (3.197)
mn n
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 (3.198)
mn n
n¼0
id
The functions A mn (p,q,r) and B mn (x) are determined by Eqs. (3.196),
(3.193), respectively.
Continued