Page 423 - Design and Operation of Heat Exchangers and their Networks

406 Design and operation of heat exchangers and their networks

van Rooyen et al. (2012) discussed the history of the Wilson plot evo-
lution and alternative methods to the Wilson plot as well as their advantages
and disadvantages and developed a modified Wilson plot method for
enhanced heat transfer tubes. The Gnielinski correlation (Gnielinski,
1975) is used for tube-side convective heat transfer:

ð
λ i ð f =8Þ Re i 1000ÞPr i
α i ¼ C i α gni ¼ C i (8.58)
p ffiffiffiffiffiffiffi 2=3
d i 1+12:7 f =8 Pr i 1
where
2
f ¼ 1:82lg Re i Þ 1:64½ ð Š (8.59)
For pool boiling on the enhanced outside surface of the tube, the heat
transfer coefficient is formulated with Eq. (8.54). The unknown C i in
Eq. (8.58) and C o and n in Eq. (8.54) are determined by minimizing the
difference between the measured overall heat transfer coefficients and the
corresponding predicted values:
" # 2
N
X 1 ln d o,r =d i,r Þ 1 1
ð
min + + (8.60)
n
C i,C o,n C i α gni, j A i 2πLλ t C o q A o ð kAÞ
j¼1 o, j j
Steinhoff et al. (2018) measured condensation heat transfer coefficients
for R134a on a horizontal plain tube and several structured tubes having
three-dimensional fin geometries on the outside and helical ribs on the
inside of the tubes. The test rig is shown schematically in Fig. 8.5. They used
the correlation, Eq. (8.61), for the cooling water:

0:14
λ i n m μ i
α i ¼ C i Re Pr (8.61)
i i μ
d i
w,i
and Eq. (8.54) for condensation heat transfer coefficients.
In the common modified Wilson plot method, the mean heat flux is
taken for the evaluation. Since the temperature difference between the
hot and cold fluids varies along the tube, the heat flux q o and the conden-
sation or boiling heat transfer coefficient α o also vary along the tube.
Wang et al. (2007) proposed a differential method considering the varia-
tion of heat flux. Take an enhanced boiling heat transfer tube as an example;
the energy equation for the hot water flowing through the tube is given as

dt i A o q o
¼ (8.62)
dx _ m i c p,i