Page 168 - Design and Operation of Heat Exchangers and their Networks

156 Design and operation of heat exchangers and their networks

According to the relation between the critical heat flux and pressure
(Eq. (27) of Gorenflo, 2013), if the value of the critical heat flux q cr1 at
p r1 is available, we can evaluate it for other pressure with

0:4
q cr2 p ð 1 p r2 Þ
r2
¼ 0:4 (4.27)
q cr1 p ð 1 p r1 Þ
r1
4.1.1.4 Minimum heat flux (Leidenfrost point)
The minimum heat flux of film boiling occurs at
" # 1=4
ð
σg ρ ρ Þ
v
l
q min ¼ C 2 Δh V ρ (4.28)
v 2
ð ρ + ρ Þ
l v
The stability analysis of Zuber and Tribus (1958) resulted in π 1 1=4 C 2
24 3
π (0.099 C 2 0.131). Applying the Taylor instability analysis and com-
24
paring the predicted results with the experimental data, Berenson (1960,
1961) determined the value of C 2 ¼0.09.
If the heat flux drops below this minimum, the film will collapse, liquid
will attach the wall, and nucleate boiling will be reestablished.
4.1.1.5 Film boiling
Once the critical heat flux is exceeded, the heating surface is blanketed by a
continuous vapor film. In such a case, the additional effect of radiation heat
transfer through this vapor film due to very high wall temperature should
be considered. Bromley (1948) obtained the following equation for the
calculation of heat transfer coefficient with simultaneous conduction and
radiation:
1=3
α ¼ α cond α cond =αð Þ + α rad (4.29)
where α cond is the coefficient for heat transport purely by conduction across
a laminar film of vapor

3 1=4

g ρ ρ ÞΔh V l
ð
λ v l v
α cond ¼ C (4.30)
l λ v ν v T w T s Þ
ð
For horizontal tube, the characteristic length l¼d, and for vertical
heating surface l¼H. The liquid properties are determined with the
mean temperature T m ¼(T w +T s )/2, whereas the vapor properties are eval-
uated at the system pressure and saturation temperature. The correction con-
stant C¼0.62 for a horizontal tube and C¼0.8 for a vertical heating surface.