
Radiation Heat Transfer 329
The spectral-directional absorptivity is dened as the fraction of the spectral
intensity at wavelength λ incident in the direction of θ and ϕ,
, that is
absorbed by the surface,
αλθφ
λθφ
λθφ
λθ
λ
λ
,
,
,
(,,)
(,,)
(,,)
.=
I
I
a
i
(13.31)
The relationships between the spectral-directional absorptivity, spectral absorp-
tivity, and total absorptivity are
αλ
αλθφ λθφθθθφ
λ
λθ λ
θ
()
(,,) (,,)cossin
,,
=
=
Idd
i
0
ππ
φ
π
λ
θ
π
φ
λθφθθθφ
/
,
/
(,,)cossin
2
0
2
0
2
∫∫
∫
=
==
Idd
i
00
2π
∫
,
(13.32)
(13.33)
Equations 13.29 through 13.31 shows that the surface absorptivity of an object is
independent from its own temperature. Howev ...