Page 108 - Design and Operation of Heat Exchangers and their Networks

96 Design and operation of heat exchangers and their networks

As is shown in Fig. 3.6A, a two-pass cross counterflow heat exchanger
can be coupled with two crossflow units in a counterflow scheme, in which
fluid 1 first enters unit A (the first pass of fluid 1) and then enters unit B (the
second pass of fluid 1), but fluid 2 first enters unit B and then flows from unit
B to unit A. If each fluid is mixed in one of its two passes or in its interpass,
∗
∗
the interpass temperatures, t 1 and t 2 , and the outlet temperature of fluid 1 of
00
the exchanger, t 1 , can be expressed with the dimensionless temperature
changes of fluid 1 in unit A and unit B, ε 1,A and ε 1,B , which are defined
by Eq. (3.60):
∗
∗
t ε 1,A t ¼ 1 ε 1,A Þt 0 1 (3.145)
ð
1
2
∗
00
t 1 ε 1,B Þt ¼ ε 1,B t 0 (3.146)
ð
1 1 2
The ε-NTU relationships for the crossflow with both fluids unmixed,
with one fluid unmixed and the other mixed, and with both fluids mixed
are given by Eqs. (3.122), (3.134) (or (3.135)), (3.144), respectively.
According to the energy balance, we also have
∗
∗
00
R 1 t R 1 t + t ¼ t 0 (3.147)
1 1 2 2
∗
∗
00
Solving Eqs. (3.145)–(3.147) for unknown t 1 , t 1 , and t 2 results in
∗
t t 0 1 ε 1,A
1 2
¼ (3.148)
t t 0 1 R 1 ε 1,A ε 1,B
0
1 2
∗
t t 0 R 1 ε 1,B ε 1,A Þ
ð
2 2
¼ (3.149)
t t 0
0
1 2 1 R 1 ε 1,A ε 1,B
t t 1 00 ε 1,A + ε 1,B 1+ R 1 Þε 1,A ε 1,B
0
ð
1
ε 1 ¼ ¼ (3.150)
t t 0
0
1 2 1 R 1 ε 1,A ε 1,B
The dimensionless temperatures in a parallel-crossflow heat exchanger
can be obtained with the similar method as follows, if each fluid is mixed
in one of its two passes or in its interpass:
∗
t t 0 2
1
¼ 1 ε 1,A (3.151)
0
t t 0
1 2
∗
t t 0
2 2
¼ R 1 ε 1,A (3.152)
0
t t 0
1 2
t t 00
0
ð
ε 1 ¼ 1 1 ¼ ε 1,A + ε 1,B 1+ R 1 Þε 1,A ε 1,B (3.153)
t t 0 2
0
1