Page 465 - Bird R.B. Transport phenomena

§14.7 Heat Transfer Coefficients for Condensation of Pure Vapors on Solid Surfaces 445

Mixed Free and Forced Convection
Finally, one must deal with the problem of simultaneous free and forced convection, and
this is again done through the use of an empirical combining rule: 6
forced\3il/3
ota l e e 3 r c e d 3 (14.6-12)
Nu; n = [Nu|; ) + (Nu!; ) ]
This rule appears to hold reasonably well for all geometries and situations, provided
only that the forced and free convection have the same primary flow direction.

EXAMPLE 14.6-1 Estimate the rate of heat loss by free convection from a unit length of a long horizontal pipe, 6
in. in outside diameter, if the outer surface temperature is 100°F and the surrounding air is at
Heat Loss by Free 1 atm and 80°F.
Convection from a
Horizontal Pipe
SOLUTION
The properties of air at 1 atm and a film temperature T = 90°F = 550°R are
;
ix = 0.0190 cp = 0.0460 lb /ft • hr
w
p = 0.0723 lb /ft 3
w
C p = 0.241 Btu/lb m • R
к = 0.0152 Btu/hr • ft • R
8 = l/T =(l/550)R- 1
i /
2
8
Other relevant values are D = 0.5 ft, AT = 20°R, and g = 4.17 X 10 ft/hr . From these data we
obtain
3
/(0.5) (0.0723) (4.17 X 10 )(20/550)V(0.241)(0.0460)\
8
2
GrPr =
V (0.0460) 2 "Д 0.0152
6
= (4.68 X 10 )(0.729) = 3.4 X 10 6 (14.6-13)
Then from Eqs. 14.6-1 to 3 and Table 14.6-1 we get
6 1/4
Nu = 0.772(- 0.671 (4.68 X 10 )
m ,9/1614/9
\[1 + (0.492/0.729)'
= 0.772^^4(46.51) = 18.6 (14.6-14)
The heat transfer coefficient is then

= 0.57 Btu/hr • ft 2 • F (14.6-15)

The rate of heat loss per unit length of the pipe is
Q h m AAT
L L
= (0.57X3.1416)(0.5)(20) = 18 Btu/hr • ft (14.6-16)

This is the heat loss by convection only. The radiation loss for the same problem is obtained in
Example 16.5-2.

E. Ruckenstein, Adv. in Chem. Eng., 13,11-112 (1987) E. Ruckenstein and R. Rajagopalan, Chem.
6
Eng. Communications, 4,15-29 (1980).