Page 109 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 97

For two-pass crossflow heat exchangers, Baclic (1990) summarized
totally 32 possible flow arrangements with both fluids mixed in interpasses
and their corresponding ε-NTU relationships. For more complicated multi-
pass crossflow heat exchangers, in which each fluid is mixed either in the
previous pass, or in the current pass, or between the previous and current
passes, all the interpass temperatures are not the functions of the spatial coor-
dinate x or y. So, we can treat the exchanger as a heat exchanger network in
which each unit is a one-pass crossflow heat exchanger with uniform inlet
temperatures of the two fluids flowing through the unit and calculate the
interpass and outlet temperatures by the use of the general solution intro-
duced in Section 6.1.

3.3.4.2 Two-pass crossflow heat exchangers with at least one fluid
unmixed throughout
For two-pass crossflow heat exchangers, Baclic (1990) summarized totally
40 flow arrangements with at least one fluid unmixed throughout. Their
ε-NTU relationships have been summarized by Baclic (1990), which are
expressed based on the following special functions:
1
y
KyðÞ ¼ ð 1 e Þ (3.154)
y
1
ð
ν x, yÞ ¼ F 1 x, yÞ (3.155)
ð
y
∗ xK yðÞ
ν x, yð Þ ¼ e (3.156)
∞
X
n
ð
hx, y, zÞ ¼ z F n x, yÞ (3.157)
ð
n¼1
ð x
1 2
0
μ x, yÞ ¼ F 1 y, xð Þ F y, x Þdx 0 (3.158)
ð
ð
0
y 0
ð x
1
0
0
½
ð
ð
μ x, y, z, ϕð Þ ¼ F 0 z, ϕ x x ފF 0 y, x x Þdx 0 (3.159)
1
x 0
ð x
1
0
0
ð
μ x, y, z, ϕð Þ ¼ F 0 z, ϕx ÞF 0 y, x x Þdx 0 (3.160)
ð
2
x 0
where the special function F n is defined by Romie (1987) as
∂F n x, yÞ
ð
¼ G n F n (3.161)
∂x