Page 111 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 99

∞
X k k +1Þ=2 p ffiffiffiffiffi
G n x, yÞ ¼ e x y ð y=xÞ ð I k +1 2 xy n 0ð Þ (3.173)
ð
n
k¼n
∞ k j
X y k + n +1 X ð k + n jÞ!x
x y
G n x, yð Þ ¼ e ð n 0Þ (3.174)
ð k + n +1Þ! ð k jÞ!n!j!
k¼0 j¼0
to calculate F n (x, y) and G n (x, y).
3.3.4.3 Examples for cross counterflow arrangements
The ε-NTU relationships for the cross counterflow arrangement types with
at least one fluid unmixed throughout can be found in Table 3 of Baclic
(1990). We represent the ε-NTU relationship examples for the cross
counterflow arrangements BA m,5 (m¼1, 2, …, 5) and BA m,6 (m¼1, 2, …,6)
as follows. For the flow arrangement BA m,n (m>n), we can exchange
the fluid indices “1” and “2” and find the corresponding flow arrangement
listed in the succeeding text. The same symbols of Baclic are used in the
expressions

a A ¼ NTU 1,A , a B ¼ NTU 1,B (3.175)
(3.176)
b A ¼ NTU 2,A ¼ R 1 NTU 1,A , b B ¼ NTU 2,B ¼ R 1 NTU 1,B
a ¼ NTU 1 =2, b ¼ NTU 2 =2 ¼ R 1 NTU 1 =2 (3.177)

NTU 1,B a B b B
ϕ ¼ ¼ ¼ (3.178)
NTU 1,A a A b A
(3.179)
NTU 1 ¼ NTU 1,A + NTU 1,B
Let R 1 ¼2, NTU 1,A ¼0.4, NTU 1,B ¼0.6; we have

a A ¼ 0:4, b A ¼ 0:8, a B ¼ 0:6, b B ¼ 1:2, ϕ ¼ 1:5, NTU 1 ¼ 1
1 1 0:8
Kb A ¼ 1 e b A ¼ 1 e ¼ 0:6883,
ðÞ
b A 0:8
1 1 1:2
ðÞ
Kb B ¼ 1 e b B ¼ 1 e ¼ 0:5823,
b B 1:2
∗
∗
ðÞ
ðÞ
ν a A b A Þ ¼ e a A Kb A ¼ e 0:4 0:6883 ¼ 0:7593, ν a B b B Þ ¼ e a B Kb B
ð
ð
0:6 0:5823
¼ e ¼ 0:7051: