Page 95 - Design and Operation of Heat Exchangers and their Networks

Steady-state characteristics of heat exchangers 83

3.2.2.3 Heat exchangers with one fluid having phase change
In an evaporator or a condenser, one fluid undergoes a phase change during
which the fluid temperature maintains at its evaporation (or condensation)
temperature. In such a case, the thermal capacity of the phase-changing fluid
becomes infinitive large, that is, R¼0. The ε-NTU relation in Eqs. (3.58),
(3.71) reduces to

ε ¼ 1 e NTU (3.72)

3.2.2.4 1-2 shell-and-tube heat exchangers
Nagle (1933) investigated the 1-2, 1-4, 1-6, and 2-4 shell-and-tube heat
exchangers and derived a series of curves giving the correction factor for
the logarithmic mean temperature difference. Here, “n-m” means n shell
passes and m tube passes. The multipass shell-and-tube heat exchangers with
one shell pass and two tube passes (1-2 type) are shown in Fig. 3.4.
Underwood (1934) obtained an explicit analytical solution for 1-2
shell-and-tube heat exchangers:

0
St t s 00
s
Δt m ¼ (3.73)
00
t + t t t + St t 00
0
0
00
0
s
s
t
t
s
s
ln
0
0
00
0
t + t t t St t 00
00
s s t t s s
where
q ffiffiffiffiffiffiffiffiffiffiffiffiffi
2 _ _
S ¼ (3.74)
1+ R , R s ¼ C s =C t
s
For sizing problems, Eq. (3.73) can be rewritten as
kA 1 2 ε s 1+ R s SÞ
ð
NTU s ¼ _ ¼ ln (3.75)
C s S 2 ε s 1+ R s + Sð Þ

Fig. 3.4 1-2 shell-and-tube heat exchanger. (A) Case I: The first tube pass is counterflow
to the shell pass. (B) Case II: The first tube pass is parallel flow to the shell pass.