The spectral absorptivity α λ and spectral reflectivity ρ λ for a spectrally selective, diffuse material are as shown. (a) Sketch the spectral transmissivity τ λ (b) If solar irradiation with G s = 750 W / m 2 and the spectral distribution of a blackbody at 5800 K is incident on this material, determine the fractions of the irradiation that are transmitted, reflected, and absorbed by the material. (c) If the temperature of this material is 350 K, deter- mine the emissivity ε . (d) Determine the net heat flux by radiation to the material.
The spectral absorptivity α λ and spectral reflectivity ρ λ for a spectrally selective, diffuse material are as shown. (a) Sketch the spectral transmissivity τ λ (b) If solar irradiation with G s = 750 W / m 2 and the spectral distribution of a blackbody at 5800 K is incident on this material, determine the fractions of the irradiation that are transmitted, reflected, and absorbed by the material. (c) If the temperature of this material is 350 K, deter- mine the emissivity ε . (d) Determine the net heat flux by radiation to the material.
Solution Summary: The above equation shows the approximate value of spectral transmissivity of the diffused material.
The spectral absorptivity
α
λ
and spectral reflectivity
ρ
λ
for a spectrally selective, diffuse material are as shown.
(a) Sketch the spectral transmissivity
τ
λ
(b) If solar irradiation with
G
s
=
750
W
/
m
2
and the spectral distribution of a blackbody at 5800 K is incident on this material, determine the fractions of the irradiation that are transmitted, reflected, and absorbed by the material.
(c) If the temperature of this material is 350 K, deter- mine the emissivity
ε
.
(d) Determine the net heat flux by radiation to the material.
An opaque surface with the prescribed spectral, hemispherical reflectivity distribution is subject
to the spectral irradiation shown. Find:
1.0
600
0.5
0
05
10
15
λ (μm)
G₂(W/m²•μm)
300
0
0
5
10
15 20
20
λ (μm)
(1) Find the spectral absorptivity distribution (αλ).
(2) Determine the total irradiation G on the surface
(3) Determine the radiant flux that is absorbed by the surface.
(4) The total absorptivity a.
An opaque surface with the prescribed spectral, hemispherical reflectivity distribution is subjected to the spectral irradiation shown.
Assume that p₁ = 0.5 and G₁ = 650 W/m²-μm.
G₁
1.0
P₁
0 5
10
15
λ(um)
(a) Determine the total irradiation on the surface, in W/m².
G =
W/m²
(b) Determine the radiant flux that is absorbed by the surface, in W/m².
Gabs = i
W/m²
(c) What is the total, hemispherical absorptivity of this surface?
α = i
G₂(W/m².μm)
5
10
15
20
λ (um)
An opaque surface with the prescribed spectral, hemispherical reflectivity distribution is subjected to the spectral irradiation shown.
Assume that p₁ = 0.5 and G₁ = 700 W/m².um.
1.0
P₁
5
10 15
λ (um)
(a) Determine the total irradiation on the surface, in W/m².
G = i
W/m²
G₂ (W/m².um)
(b) Determine the radiant flux that is absorbed by the surface, in W/m².
W/m²
Gabs
i
(c) What is the total, hemispherical absorptivity of this surface?
α = i
G₁
10
5
10 15 20
λ (um)
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