Page 98 - Design and Operation of Heat Exchangers and their Networks

86 Design and operation of heat exchangers and their networks

where
p ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ð
S 3 ¼ 9 4R s 1 R s Þ (3.86)
If R s ¼1, the denominator of Eq. (3.85) becomes zero. In such a case, we
9
can add a very small deviation, for example, 10 ,to R s .
Another solution was proposed by Roetzel (1988) for the same value of
kA in the counterflow passes (the first and third passes) and different kA value
in the parallel-flow pass (the second pass). The kA ratio γ is defined by
Eq. (3.78).
R s 6¼ 1 :
s 1 s 3 s 2 s 2 s 3 s 1 s 2 s 1 s 3
ð
s 1 e + e Þ e 1Þ + s 2 e + e Þ 1 e Þ + NTU s 1 R s Þ e e Þ 1+ e Þ
ð
ð
ð
ð
ð
ð
ε s ¼ s s s s s s s s s
ð
ð
ð
ð
ð
ð
s 1 e 1 + e 3 Þ R s e 2 1ð Þ + s 2 e 2 + e 3 Þ 1 R s e 1 Þ + NTU s 1 R s Þ e 2 e 1 Þ 1+ R s e 3 Þ
(3.87)
R s ¼ 1 :
ε s γ 1 γÞ
ð
¼ NTU s
1+ ε s 1+3γ
1
1+ γ 1+ 3γÞNTU s =2 1 1 γÞNTU s =2 1
2
2 e ð 1 + e ð +1 (3.88)
1+3γ
where
r ffiffiffiffiffiffiffiffiffiffiffi
p p 2
s 1 ¼ + q (3.89)
2 4
r ffiffiffiffiffiffiffiffiffiffiffi
p p 2
s 2 ¼ q (3.90)
2 4
1
s 3 ¼ R s NTU s 1 γð Þ (3.91)
2

1
p ¼ NTU s 1 R s 1 3γð Þ (3.92)
2
1 2
ð
q ¼ γ 1 γð ÞNTU R s 1 R s Þ (3.93)
s
2
The solutions of general n-m shell-and-tube heat exchangers can be
obtained by the use of the analytical solution for multistream parallel channel
heat exchangers introduced in Section 3.6.
3.2.3 Rating problem
In rating problem, since the geometry is specified, the surface area A is
known. In order to calculate the fluid properties, we will first assume the