Consider an opaque, gray surface whose directional absorptivity is 0.8 for 0 ≤ θ ≤ 60 ∘ and θ > 60 ∘ . The surface is horizontal and exposed to solar irradiation comprised of direct and diffuse components. (a) What is the surface absorptivity to direct solar radiation that is incident at an angle of 45 ∘ C from the normal? What is the absorptivity to diffuse irradiation? (b) Neglecting convection heat transfer between the surface and the surrounding air, what would be the equilibrium temperature of the surface if the direct and diffuse components of the irradiation were 600 and 100 W / m 2 , respectively? The back side of the surface is insulated.
Consider an opaque, gray surface whose directional absorptivity is 0.8 for 0 ≤ θ ≤ 60 ∘ and θ > 60 ∘ . The surface is horizontal and exposed to solar irradiation comprised of direct and diffuse components. (a) What is the surface absorptivity to direct solar radiation that is incident at an angle of 45 ∘ C from the normal? What is the absorptivity to diffuse irradiation? (b) Neglecting convection heat transfer between the surface and the surrounding air, what would be the equilibrium temperature of the surface if the direct and diffuse components of the irradiation were 600 and 100 W / m 2 , respectively? The back side of the surface is insulated.
Solution Summary: The author explains the absorptivity of an opaque, gray surface to direct solar radiation and to diffuse irradiation.
Consider an opaque, gray surface whose directional absorptivity is 0.8 for
0
≤
θ
≤
60
∘
and
θ
>
60
∘
. The surface is horizontal and exposed to solar irradiation comprised of direct and diffuse components.
(a) What is the surface absorptivity to direct solar radiation that is incident at an angle of
45
∘
C
from the normal? What is the absorptivity to diffuse irradiation?
(b) Neglecting convection heat transfer between the surface and the surrounding air, what would be the equilibrium temperature of the surface if the direct and diffuse components of the irradiation were 600 and
100
W
/
m
2
, respectively? The back side of the surface is insulated.
Spectral hemispherical reflectivity distribution of an opaque surface is shown below. Surface is subjected to the spectral irradiation as shown.
1.0
400
a 0.4
200
5
10 15 20
a (um)
5
10
15
2 (um)
Calculate the total irradiation on the surface in W/m2
Calculate the irradiation absorbed by the surface in W/m2
3250 || 3750 || 4250|| 5000 || 5750|| 6250|| 7500
1050 || 1200
1400|| 1600|| 1750| 1850 || 2000
The spectral hemispherical absorptivity and irradiation profiles for an opaque surface are shown in the figure. Find the total hemispherical absorptivity.
Two concentric spheres of diameter D = 0.9 m and D2 = 1.2 m are separated by an air space and have surface temperatures of
T = 390 Kand T2 = 300 K.
(a) If the surfaces are black, what is the net rate of radiation exchange between the spheres, in W?
912 =
i
w
(b) What is the net rate of radiation exchange between the surfaces if they are diffuse and gray with ej = 0.5 and ez = 0.05, in W?
912 =
W
(c) What is the net rate of radiation exchange if D2 is increased to 20 m, with e, = 0.05, e = 0.5, and D = 0.9 m, in W?
912 =
(d) What is the net rate of radiation exchange if the larger sphere behaves as a black body (82 = 1.0) and with e1 = 0.5, D2 = 20 m,
and D, = 0.9 m, in W?
412 =
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