Page 519 - Bird R.B. Transport phenomena

§16.4 Direct Radiation Between Black Bodies in Vacuo at Different Temperatures 499

Dimension ratio -

Fig. 16,4-3. View factors for direct radiation between adjacent rectangles in perpendicular planes
[H. C. Hottel, Chapter 3 in W. H. McAdams, Heat Transmission, McGraw-Hill, New York (1954), p. 68].

where Aj and A 2 are usually chosen to be the total areas of bodies 1 and 2. The dimen-
sionless quantities F and F , called view factors (or angle factors or configuration factors),
u 2]
are given by
COS 0] COS 0 2
dA dA (16.4-10)
x 2
COS 0, COS 0 2
12 dAdA 2 (16.4-11)
l
and the two view factors are related by А ¥ и = A F 2V The view factor F represents the
л
2
12
fraction of radiation leaving body 1 that its directly intercepted by body 2.
The actual calculation of view factors is a difficult problem, except for some very
simple situations. In Fig. 16.4-3 and Fig. 16.4-4 some view factors for direct radiation are
23 4
shown. ' When such charts are available, the calculations of energy interchanges by Eq.
16.4-9 are easy.
In the above development, we have assumed that Lambert's law and the
Stefan-Boltzmann law ma)f be used to describe the nonequilibrium transport process, in
spite of the fact that they are strictly valid only for radiative equilibrium. The errors thus
introduced do not seem to have been studied thoroughly, but apparently the resulting
formulas give a good quantitative description.

2 H. С Hottel and A. F. Sarofim, Radiative Transfer, McGraw-Hill, New York (1967).
3 H.C. Hottel, Chapter 4 in W. H. McAdams, Heat Transmission, McGraw-Hill, New York (1954).
4 R. Siegel and J. R. Howell, Thermal Radiation Heat Transfer, 3rd edition, Hemisphere Publishing Co.,
New York (1992).