ing information for the integral-fin tubes is very limited. Webb (1984), Gogonin and
Dorokhov (1981) report data for R-12 condensing on two different 800-fins/m tubes,
under a range of operating pressure and heat fluxes, and a maximum vapor velocity of 8
m/s. Their data indicate that the effect of vapor velocity for finned tubes is very small
compared with the effect for smooth tubes. This observation is in contradiction with the
results obtained by Yau et al. (1986), who measured the condensation coefficient for steam
condensing on a family of finned tubes and found that the heat transfer enhancement due
to assisting vapor shear stress was essentially the same for plain and finned tubes. This
latter result has been confirmed in a recent study by Bella et al. (1993) who condensed R-11
and R-113 on a finned horizontal tube, with vapor velocity ranging from 2 to 30 m/s. The
work of Bella et al. (1993) concludes that the enhancement due to the vapor velocity
begins to appear when the vapor Reynolds number exceeds 10. They also found that the
heat transfer coefficient at a vapor velocity of 30 m/s was 50% more than the value for
stagnant vapor. Studies by Lee and Rose (1984) and Michael et al. (1989) also underscore
the beneficial effect of vapor shear in finned tubes.
Effect of tube bundle geometry
When condensation occurs over a vertical column of tubes, the condensate drains from
tube to tube, causing the film thickness to increase on the lower tubes. The net effect is to
lower the overall heat transfer coefficient compared with a single tube. The classical
Nusselt analysis takes this condensate inundation effect into account by multiplying the
single tube heat transfer coefficient by a factor Nm giving
h N = h1 N -m
(99)
when h N = the average heat transfer coefficient for a N-tube column
h1 = the average heat transfer for a single tube, given by eq 91
m = an exponent which equals 1/4 for the Nusselt analysis.
The experimental values of h N are usually higher than those predicted by eq 99. The
enhancement in h N has been attributed by Fujii (1991) to the splashing of the condensate
from one tube as it impinges on the next tube. Kern (1958) recommended m = 1/6 to
account for the enhancement effect.
Several studies have attempted to apply eq 99 to a column of finned tubes. Katz and
Geist (1948) obtained data for R-12, n-butane, and steam condensing on a 6-tube column
of finned tubes, each having a fin density of 590 fins/m and 1.6-mm-high fins. They found
that eq 99 best fit their data for m = 0.04. Marto (1986) also recommends m = 0.04 based on
his data for a column of integral-fin tubes. Pearson and Withers (1969) used two identical
60-tube condensers to condense R-22. Both condensers were equipped with integral-fin
tubes, one having tubes with 748 fins/m and other have tubes with 1024 fins/m. These
authors suggested that the average heat transfer coefficient for tube bundles can be
estimated by multiplying the Beatty-Katz h N , given by eq 9093, with a correction factor
CN/N1/4, where CN = 134 for the 748-fins/m-density tubes and CN = 1.31 for the 1024-
fins/m density tubes.
More recently, Webb and Murawski (1990) have conducted experiments on four en-
hanced tube geometries (1024 standard integral fin, Tred-26D, Turbo C, and GEWA-SC).
For each geometry, they arranged five tubes in a column and measured the heat transfer
coefficient with R-11 condensing over the column. The data were correlated by an equa-
tion of the form
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