Page 119 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 107

∗
∗
ν a, bÞ ¼ e aK bðÞ ¼ e 0:5 0:6321 ¼ 0:7290, ν 2a, bÞ ¼ e 2aK bðÞ
ð
ð
¼ e 2 0:5 0:6321 ¼ 0:5315
The special functions F n , h, and μ are calculated with the MatLab code in
the appendix:
1 0:7263
F 1 a, bð Þ ¼ 0:7263, ν a, bÞ ¼ F 1 a, bÞ ¼ ¼ 0:7263
ð
ð
b 1
1 1:6013
F 1 a,2bð Þ ¼ 1:6013, ν a,2bÞ ¼ F 1 a,2bð Þ ¼ ¼ 0:8006
ð
2b 2 1
1 0:5238
ð
F 1 2a, bð Þ ¼ 0:5238, ν 2a, bÞ ¼ F 1 2a, bÞ ¼ ¼ 0:5238
ð
b 1
1 0:2263
ð
ð
F 1 b, að Þ ¼ 0:2263, ν b, aÞ ¼ F 1 b, aÞ ¼ ¼ 0:4525
a 0:5
1 0:1013
ð
ð
F 1 2b, að Þ ¼ 0:1013, ν 2b, aÞ ¼ F 1 2b, aÞ ¼ ¼ 0:2026
a 0:5
∞
X n
ð
hb, a, Kbðފ ¼ K bðÞF n b, aÞ ¼ 0:1666
½
n¼1
∞
X n
hb, a, Kbðފ ¼ ½ Kbðފ F n b, aÞ ¼ 0:1238
ð
½
n¼1
ð 1
1 2 1
μ a, bÞ ¼ F 1 b, að Þ a F b, axÞdx ¼ 0:2263 0:5 0:2070ð Þ
ð
ð
0
b 0 1
¼ 0:1228
ð 1
1 2 1
ð
ð
μ b, aÞ ¼ F 1 a, bð Þ b F a, bxÞdx ¼ 0:7263 1 0:5312Þ
ð
0
a 0 0:5
¼ 0:3901
Example AB 1,5 2 2
A B
1 1
∗
½
½
ε 1 ¼ 1 bK bðÞ=2Š 1 ν 2a, bފ
ð
(3.199)
¼ 1 1 0:6321=2Þ 1 0:5315Þ ¼ 0:3205
ð
ð