Page 211 - Design and Operation of Heat Exchangers and their Networks

200 Design and operation of heat exchangers and their networks

5.2.2 Heat transfer calculation correlations
The relation between the outlet fluid temperatures and heat transfer area for
parallel-flow or counterflow heat exchangers can be found in Chapter 3. For
multipass shell-and-tube heat exchangers, we can obtain the temperature
distributions and the outlet temperatures with known heat transfer area using
the general analytical solution introduced in Chapter 3. For the shell-and-
tube heat exchangers with one shell pass and two tube passes, a simple rela-
tionship between the exchanger area and outlet temperatures can be
expressed with the correction factor for the logarithmic mean temperature
difference as (Kern, 1950).

00
0
t t t 00 t t 0 t
s
s
Q ¼ FkAΔt LM,c ¼ FkA ð 2:77Þ, (5.32)
ln t t = t t 0
0
00
00
s t s t
where
p ffiffiffiffiffiffiffiffiffiffiffiffiffi 1 S
2
R +1 ln
1 RS
F ¼ p ffiffiffiffiffiffiffiffiffiffiffiffiffi (5.33)
2
2 SR +1 R +1
ð R 1Þ ln p ffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2 SR +1+ R +1
with
_ 0 00 00 0
C t t t s t t t
s
t
R ¼ _ ¼ , S ¼ (5.34)
00
0
t
C s t t 0 t t t t 0
s
The main task of the thermal design is the determination of shell-side
heat transfer coefficient. There are two well-known methods for the eval-
uation of heat transfer and pressure drop in the shell side: Kern (1950)
method and Bell-Delaware method (Shah and Sekulic, 2003).
5.2.2.1 Kern method
Kern considered the shell-and-tube heat exchanger as a crossflow through
the tube bundle and suggested the following correlation for the shell-side
heat transfer coefficient that is calculated with the Kern correlation (Kern,
1950):
α s d hs 0:55 1=3 0:14
¼ 0:36Re Pr ð μ =μ Þ (5.35)
s s s w
λ s