Page 112 - Design and Operation of Heat Exchangers and their Networks

100 Design and operation of heat exchangers and their networks

The special functions F n , h, μ 1 , and μ 2 are calculated with the MatLab
code “Examples for two-pass crossflow heat exchangers (MatLab code)”
in the appendix:

1 0:6063
F 1 a A , b A Þ ¼ 0:6063, ν a A , b A Þ ¼ F 1 a A , b A Þ ¼ ¼ 0:7579,
ð
ð
ð
b A 0:8
1 0:8407
ð
ð
ð
F 1 a B , b B Þ ¼ 0:8407, ν a B , b B Þ ¼ F 1 a B , b B Þ ¼ ¼ 0:7006,
b B 1:2
∞
X n
ðފ F n b A , a A Þ ¼ 0:2141,
hb A , a A , ϕKb B ¼ ½ ϕKb B ð
ðފ
½
n¼1
∞
X n
ðފ F n b A , a A Þ ¼ 0:1532,
ðފ
½
hb A , a A , ϕKb B ¼ ½ ϕKb B ð
n¼1
∞
X n
ðÞ=ϕŠ F n b B , a B Þ ¼ 0:1258
ðÞ=ϕŠ ¼
½
hb B , a B , Kb A ½ Kb A ð
n¼1
The numerical integration known as Simpson’s rule can be applied to the
calculation of Eqs. (3.159), (3.160), which yield
ð
1 a A
0
0
0
μ a A , b A , b B , ϕð Þ ¼ F 0 b B , ϕ a A x ފF 0 b A , a A x Þdx ¼ 0:20892
ð
½
ð
1
a A 0 ð
1 a A
0
0
0
μ a A , b A , b B , ϕð Þ ¼ F 0 b B , ϕx ÞF 0 b A , a A x Þdx ¼ 0:20485
ð
ð
2
a A 0
Example BA1,5 2 2
B A
1 1
ð
ð
ν ∗ a A , b A Þν ∗ a B , b B Þ
ε 1 ¼ 1
1 ν ∗ a A , b A Þν ∗ a B , b B Þ
ð
ð
ðÞKb B
1 b B Kb A ðÞ
ðÞ
ðÞ
Kb A + ϕKb B
0:7593 0:7051
¼ 1 ¼ 0:3752
1 0:7593 0:7051
1 1:2 0:6883 0:5823
0:6883 + 1:5 0:5823
(3.180)