Page 118 - Design and Operation of Heat Exchangers and their Networks

106 Design and operation of heat exchangers and their networks

Example BA 6,6 —cont’d

For the data given in Example BA 5,6 , we have
" #
id
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
0:21592 0:04469 1 0:8
6 7
¼ 6 7
4 1 0:2 0:59887 0:41189 5
1 0:26667 0:56695 0:38401
and get the inverse matrix as
2 3
0:36246 0:44106 4:16148 2:97849
A 1 ¼ 6 0:1378 0:68478 15:1034 14:9889 7
6
7
4 4:12564 2:90520 0:30562 0:065989 5
5:05152 4:96229 0:10252 0:049083
which yields
2 3 2 3 2 3
α 0 1 0:37947
6 7 1 1 6 0:43249 7
6 7
α 1
6 7 ¼ A 6 7 ¼ 6 7
β
1
4 5 4 5 4 0:84883 5
0
β 1 1 0:06238
" #
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 0:37947 0:20630 + 0:43249 0:03956Þ ¼ 0:3808
2 0:4
3.3.4.4 Examples for cross parallelflow arrangements
The ε-NTU relationships for the cross parallelflow arrangement types with
at least one fluid unmixed throughout can be found in Table 5 of Baclic
(1990), in which the two passes are equally sized, that is, ϕ¼1. Totally,
11 examples of such flow arrangements are represented as follows:
Let R 1 ¼2 and NTU 1 ¼1; we have
1 b
a ¼ NTU 1 =2 ¼ 0:5, b ¼ R 1 NTU 1 =2 ¼ 1, KbðÞ ¼ 1 e
b
1 1
¼ 1 e ¼ 0:6321,
1