Page 198 - Mechanical Engineers' Handbook (Volume 4)

3 Radiation Heat Transfer 187

Table 19 Comparison of Absorptivities of Various Surfaces to Solar and Low-Temperature Thermal
Radiation a
Absorptivity
For Low-
For Temperature
Solar Radiation
Surface Radiation ( 300 K)
Aluminum, highly polished 0.15 0.04
Copper, highly polished 0.18 0.03
Tarnished 0.65 0.75
Cast iron 0.94 0.21
Stainless steel, No. 301, polished 0.37 0.60
White marble 0.46 0.95
Asphalt 0.90 0.90
Brick, red 0.75 0.93
Gravel 0.29 0.85
Flat black lacquer 0.96 0.95
White paints, various types of pigments 0.12–0.16 0.90–0.95
a
Adapted from Ref. 20 after J. P. Holman, Heat Transfer, McGraw-Hill, New York, 1981.
cos cos
F di j i j dA j
Aj R 2
Finite area A to finite area A
i j
cos cos
1
F i j i j dA dA j
i
A i Aj Aj R 2
Analytical expressions of other configuration factors have been found for a wide variety of
simple geometries and a number of these are presented in Figs. 21–24 for surfaces that emit
and reflect diffusely.

Reciprocity Relations
The configuration factors can be combined and manipulated using algebraic rules referred
to as configuration factor geometry. These expressions take several forms, one of which is
the reciprocal properties between different configuration factors, which allow one configu-
ration factor to be determined from knowledge of the others:
dA dF di dj dA dF dj di
j
i
dA dF di j AdF j di
j
i
AF AF j i
j
ii j
These relationships can be combined with other basic rules to allow the determination of the
configuration of an infinite number of complex shapes and geometries form a few select,
known geometries. These are summarized in the following sections.
The Additive Property
For a surface A subdivided into N parts (A , A ,..., A i N ) and a surface A subdivided into
i
j
i 1
i 2
M parts (A , A ,..., A ),
j 1 j 2 j M