Page 244 - Design and Operation of Heat Exchangers and their Networks

234 Design and operation of heat exchangers and their networks

where ε j is the dimensionless temperature change of the hot fluid
∗
j ð
t 0 t 00 1 e NTU 1 R jÞ
E,h, j E,h, j
ε j ¼ ¼ ∗ (6.4)
t 0 t 0 NTU 1 R jÞ
j ð
E,h, j E,c, j 1 R j e
R j is the ratio of thermal capacity rates
_ _
R j ¼ C E,h, j =C E,c, j (6.5)
∗
and NTU j is the number of transfer units as a counterflow heat exchanger
∗ _
NTU ¼ FkAð Þ =C E,h, j (6.6)
j
E, j
Following special cases should be considered in the calculation of the
coefficient matrix V j :

∗ 0 1
NTU ! ∞andR j 1 : V ¼ (6.7)
j
R j 1 R j

∗ 1 1=R j 1=R j
NTU ! ∞and R j > 1 : V ¼ (6.8)
j 1 0
2 ∗ 3
1 NTU j
∗
6 ∗ 7
j
j
6 1 + NTU 1 + NTU 7
R j ¼ 1 : V ¼ 6 ∗ 7 (6.9)
NTU 1
4 j 5
∗
1 + NTU 1 + NTU ∗ j
j
NTU ∗ NTU ∗
e j 1 e j
R j ¼ 0 : V j ¼ (6.10)
0 1

1 0
R j ! ∞ : V ¼ NTU ∗ NTU ∗ (6.11)
1 e c, j e c, j
where
∗ _
NTU ð (6.12)
c, j ¼ FkAÞ =C E,c, j
E, j
For a counterflow heat exchanger, the correction factor of mean temper-
ature F¼1. The equations of F for some typical types of heat exchangers can
be found in Chapter 3.
Extending Eq. (6.2) to the whole network yields the relation between
the inlet and outlet temperature vectors as follows:
00
T ¼ VT 0 (6.13)
E E