Page 469 - Bird R.B. Transport phenomena

§14.7 Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces 449

EXAMPLE 14.7-1 A boiling liquid flowing in a vertical tube is being heated by condensation of steam on the
outside of the tube. The steam-heated tube section is 10 ft high and 2 in. in outside diameter.
Condensation of Steam jf sa t rated steam is used, what steam temperature is required to supply 92,000 Btu/hr of
U
on a Vertical Surface heat to the tube at a tube-surface temperature of 200°F? Assume film condensation.
SOLUTION The fluid properties depend on the unknown temperature T . We make a guess of T d = T =
o
d
200°F. Then the physical properties at the film temperature (also 200°F) are
AH vap = 978Btu/lb w
к = 0.393 Btu/hr • ft • F
p = 60.1 lb /ft 3
w
A = 0.738 Ibjit • hr
Assuming that the steam gives up only latent heat (the assumption T d = T = 200°F implies
Q
this), an energy balance around the tube gives
Q = wAH vap = тгОГАН уар (14.7-8)
in which Q is the heat flow into the tube wall. The film Reynolds number is

Г Q 92,000 = 244 (14.7-9)
тг(2/12)(0.738)(978)
Reading Fig. 14.7-2 at this value of the ordinate, we find that the flow is laminar. Equation
14.7-2 is applicable, but it is more convenient to use the line based on this equation in Fig.
14.7-2, which gives
k Y (T - T )L
2/
/3
0
P
d
= 1700 (14.7-10)
from which
-*vap
T d - 7^ = 1700
0
2/
kp Y L
/3
5/3
(0.738) (978)
= 1700
2/3
8 1/3
(0.393)(60.1) (4.17 X 10 ) (10)
= 22°F (14.7-11)
Therefore, the first approximation to the steam temperature is T = 222°F. This result is close
d
enough; evaluation of the physical properties in accordance with this result gives T = 220 as
d
a second approximation. It is apparent from Fig. 14.7-2 that this result represents an upper
limit. On account of rippling, the temperature drop through the condensate film may be as lit-
tle as half that predicted here.
QUESTIONS FOR DISCUSSION
1. Define the heat transfer coefficient, the Nusselt number, the Stanton number, and the Chilton-
Colburn j . How can each of these be "decorated" to indicate the type of temperature-differ-
H
ence driving force that is being used?
2. What are the characteristic dimensionless groups that arise in the correlations for Nusselt
numbers for forced convection? For free convection? For mixed convection?
3o To what extent can Nusselt numbers be calculated a priori from analytical solutions?
4. Explain how one develops an experimental correlation for Nusselt numbers as a function of
the relevant dimensionless groups.
5. To what extent can empirical correlations be developed in which the Nusselt number is given
as the product of the relevant dimensionless groups, each raised to a characteristic power?