ness would result in total flooding if the fin density were greater than 1000 fins/m.
Indeed, the experimental work of Jaber and Webb (1993) on enhanced tubes for steam
condensers shows that integral-fin tubes for steam condensation should use no more than
630 fins/m (16 fins/in.).
Theoretical models for
heat transfer coefficient
Perhaps the first theoretical model for predicting the condensation heat transfer coeffi-
cient for integral-fin tubes was proposed by Beatty and Katz (1948). They assumed the
condensate flow to be purely gravity driven and applied a Nusselt type analysis for both
the fin surface and the tube surface between the fins. The average heat transfer coefficient,
h , for the configuration of Figure 20 was expressed as
A
Ar
h η = hh
+ ηf hf f
(90)
A
A
where A = heat transfer area
= Ar + Af, Ar
= surface area of tube at base of fins
Af = fin surface area
ηf = fin efficiency
η = total surface efficiency
hh = heat transfer coefficient for horizontal tube surface
hf = heat transfer coefficient for the fin surfaces.
gρl (ρl - ρv ) kl hfg
1/ 4
3
hh = 0.728
(91)
l (Tsat - Tb ) dr
gρl (ρl - ρv ) kl hfg
1/ 4
3
hf = 0.943
(92)
l (Tsat - Tb ) Lf
Af
η = 1 - (1 - ηf )
(93)
A
(
)
where Lf is the average fin height over the diameter do equals π do - dr / 4do .
2
2
Beatty and Katz (1948) used eq 90 to predict their test data for six low surface tension
fluids condensing on finned tubes ranging in fin density from 433 to 630 fins/m. They
found that if the coefficient in eq 91 was changed from 0.728 to 0.689, eq 90 predicted their
data within 10%. Despite the fact that the Beatty and Katz's model does not account for
condensate retention and surface tension effects, the model has enjoyed success in the
refrigeration industry for many years.
The first model to include the effect of tension in draining condensate from horizontal
finned tubes was presented by Karkhu and Borovkov (1971). They postulated that con-
densate drainage from the fin surface was purely surface tension driven, while that from
the tube surface between the fins was purely gravity driven. From experiments in which
R-12 was condensed on the face of a cylinder with machined in rectangular fins, Webb et
33
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