Page 467 - Bird R.B. Transport phenomena

§14.7 Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces 447

condense if cooled slowly at the prevailing pressure. This temperature is very nearly that
of the liquid at the liquid-gas interface. Therefore h m may be regarded as a heat transfer
coefficient for the liquid film.
Expressions for h m have been derived 3 for laminar nonrippling condensate flow by ap-
proximate solution of the equations of energy and motion for a falling liquid film (see
Problem 14C.1). For film condensation on a horizontal tube of diameter D, length L, and
3
constant surface temperature T the result of Nusselt may be written as
0/
- "
( 1 4 7 2 )
Here w/L is the mass rate of condensation per unit length of tube, and it is understood
that all the physical properties of the condensate are to be calculated at the film tempera-
ture, T = \{T d + T ).
f
o
For moderate temperature differences, Eq. 14.7-2 may be rewritten with the aid of an
energy balance on the condensate to give
^ 2 \i/4
( 1 4 7 3 )
-
Equations 14.7-2 and 3 have been confirmed experimentally within ±10% for single hori-
zontal tubes. They also seem to give satisfactory results for bundles of horizontal tubes, 4
in spite of the complications introduced by condensate dripping from tube to tube.
For film condensation on vertical tubes or vertical walls of height L, the theoretical re-
sults corresponding to Eqs. 14.7-2 and 3 are
4 /*W\ (i47 4)
1Ш -
and

respectively. The quantity Г in Eq. 14.7-4 is the total rate of condensate flow from the bot-
tom of the condensing surface per unit width of that surface. For a vertical tube, Г = W/TTD,
where w is the total mass rate of condensation on the tube. For short vertical tubes (L < 0.5 ft),
the experimental values of h m confirm the theory well, but the measured values for long ver-
tical tubes (L > 8 ft) may exceed the theory for a given T d — T by as much as 70%. This dis-
o
crepancy is attributed to ripples that attain greatest amplitude on long vertical tubes. 5
We now turn to the empirical expressions for turbulent condensate flow. Turbulent
flow begins, on vertical tubes or walls, at a Reynolds number Re = Г//х of about 350. For
higher Reynolds numbers, the following empirical formula has been proposed: 6

К = 0.003^-^Л — I (14.7-6)

This equation is equivalent, for small T — T , to the formula
d o
h m = 0.02l| -=-f- I (14.7-7)

3 W. Nusselt, Z. Ver. deutsch. Ing., 60, 541-546, 596-575 (1916).
4 B. E. Short and H. E. Brown, Proc. General Disc. Heat Transfer, London (1951), pp. 27-31. See also
D. Butterworth, in Handbook of Heat Exchanger Design (G. F. Hewitt, ed.), Oxford University Press,
London (1977), pp. 426-462.
5
W. H. McAdams, Heat Transmission, 3rd edition, McGraw-Hill, New York (1954) p. 333.
6 U. Grigull, Forsch. Ingenieurwesen, 13, 49-57 (1942); Z. Ver. dtsch. Ing., 86,444-445 (1942).