Page 94 - Design and Operation of Heat Exchangers and their Networks

82 Design and operation of heat exchangers and their networks

Then, we have
1 e NTU h 1+ R h Þ
ð
ε h ¼ (3.62)
1+ R h
1 e NTU c 1+ R c Þ
ð
ε c ¼ (3.63)
1+ R c
where
_
NTU h ¼ kA=C h (3.64)
_
NTU c ¼ kA=C c ¼ R h NTU h (3.65)
_ _
R h ¼ C h =C c (3.66)
_ _
R c ¼ C c =C h ¼ 1=R h (3.67)
The relation between the two dimensionless temperature changes is

ε c ¼ R h ε h (3.68)
Furthermore, since “hot” and “cold” is only a relative description, there-
fore, we can refer the “hot” fluid to any one of the two fluids and the “cold”
fluid to the other.

3.2.2.2 Counterflow heat exchangers
For a counterflow heat exchanger, the ε-NTU relation is given by
Eq. (3.37) as

ð
ð
t t c 0 1 e kA= _ C cÞ 1 _ C c = _ C hÞ 1 e NTU c 1 R c Þ
00
ð
c
ε c ¼ ¼ ¼
t t 0 _ _ kA= _ C cÞ 1 _ C c = _ C hÞ 1 R c e NTU c 1 R c Þ
0
ð
ð
ð
h c 1 C c =C h e
(3.69)
Using Eq. (3.68), we can obtain
ð
1 e NTU h 1 R h Þ
ε h ¼ ε c =R h ¼ (3.70)
1 R h e NTU h 1 R h Þ
ð
Because Eqs. (3.69), (3.70) have the same form, they can be expressed by
the ε-NTU relation as
ð
1 e NTU 1 RÞ
ε ¼ (3.71)
1 Re NTU 1 RÞ
ð