Page 241 - Mechanical Engineers' Handbook (Volume 4)

230 Furnaces

The factor em will be somewhat less than e for the source or a for the receiving surface,
and can be calculated:
em 1 1 1 1
A r
a A s e
where a receiver absorptivity at T r
A /A area ratio, receiver/source
r s
e source emissivity at T
s
8.2 Emissivity–Absorptivity
While emissivity and absorptivity values for solid materials vary with temperatures, values
for materials commonly used as furnace walls or loads, in the usual range of temperatures,
are:
Refractory walls 0.80–0.90
Heavily oxidized steel 0.85–0.95
Bright steel strip 0.25–0.35
Brass cake 0.55–0.60
Bright aluminum strip 0.05–0.10
Hot-rolled aluminum plate 0.10–0.20
Cast heat-resisting alloy 0.75–0.85
For materials such as sheet glass, transparent in the visible light range, radiation is
reflected at both surfaces at about 4% of incident value, with the balance absorbed or trans-
mitted. Absorptivity decreases with temperature, as shown in Fig. 11. The absorptivity of
liquid water is about 0.96.

8.3 Radiation Charts
For convenience in preliminary calculations, black-body radiation, as a function of temper-
ature in F, is given in chart form in Fig. 12. The value for the receiver surface is subtracted
from that of the source to find net interchange for blackbody conditions, and the result is
corrected for emissivity and view factors. Where heat is transmitted by a combination of
solid-state radiation and convection, a blackbody coefficient, in Btu/hr F, is shown in the
chart in Fig. 13. This can be added to the convection coefficient for the same temperature
interval, after correcting for emissivity and view factor, to provide an overall coefficient (H)
for use in the formula
Q/A H(T T )
r

8.4 View Factors for Solid-State Radiation
For a receiving surface completely enclosed by the source of radiation, or for a flat surface
under a hemispherical radiating surface, the view factor is unity. Factors for a wide range
of geometrical configurations are given in available references. For cases commonly involved
in furnace heat-transfer calculations, factors are shown by the following charts.
For two parallel planes, with edges in alignment as shown in Fig. 14a, view factors are
given in Fig. 15 in terms of ratios of x, y, and z. For two surfaces intersecting at angle of