231
Fundamental Radiation
The brick wall is not a gray surface, and hence α(T s ) = ε(T s ). But it is a diffuse
surface, and hence α(λ) = ε(λ). The irradiation from the black coal bed (at
temperature T c = 2000 K) to the brick wall is G(λ) ∝ E b . The following shows
a similar way to determine brick wall absorptivity.
� ∞
� ∞
0 α(λ)G(λ) dλ
0 ε(λ)E b dλ
α(T s ) ≡ � ∞
=
(11.18)
0 G(λ) dλ
E b
= ε 1 F 0−λ 1 + ε 2 [F 0−λ 2 − F 0−λ 1 ] + ε 3 [1 − F 0−λ 2 ]
(11.19)
= 0.1 × 0.275 + 0.5 × (0.986 − 0.273) + 0.8 × (1 − 0.986)
where the fraction value can be found from Table 11.1, or from Figure 11.9,
with T = T c = 2000 K, irradiation from the black coal bed.
Therefore, average absorptivity can be calculated as
α(T s ) = 0.395 < 0.61 for ε(T s )
11.3 Solar and Atmospheric Radiation
Solar radiation is essential to all life on earth. Through the thermal and
photovoltaic process, solar radiation is important for the design of solar collectors, air-conditioning systems for buildings and vehicles, temperature control
systems for spacecrafts, and photocells for electricity. The sun is approximate as a spherical radiation source with a diameter of 1.39 × 10 9 m and is
located around 1.50 × 10 11 m from the earth. The average solar flux (solar
constant) incident on the outer edge of the Earth’s atmosphere is about
1353 W/m
2 . Assuming a blackbody radiation, the sun’s temperature can be
estimated at about 5800 K. Figure 11.10 shows the spectral distribution of
solar radiation [2]. The radiation is concentrated in the low-wavelength region
(0.2 ≤ λ ≤ 3 μm) with the peak value of 0.50 μm.
The magnitude spectral and directional distributions of solar flux change
significantly as solar radiation passes through the Earth’s atmosphere. The
change is due to absorption and scattering of the radiation by the atmosphere particles and gases. The effect of absorption by the atmosphere gases
O 3 (ozone), H 2 O vapor, O 2 , and CO 2 is shown by the lower curve in Figure
11.10. Absorption by ozone is strong in the UV region, providing considerable
attenuation below 0.3–0.4 μm. In the visible light region (0.4–0.7 μm), absorption is contributed by O 3 and O 2 ; in the IR region (0.7–3.0 μm), absorption is
due to H 2 O vapor and CO 2 . The effect of scattering by particles and gases is
that about half goes back to atmosphere and half comes to the earth surface.
Therefore, the average solar flux incident on the Earth’s surface is reduced
to about 300–800 W/m 2 , depending on the time of the day, the season, the
latitude, and the weather conditions.
Fundamental Radiation
The brick wall is not a gray surface, and hence α(T s ) = ε(T s ). But it is a diffuse
surface, and hence α(λ) = ε(λ). The irradiation from the black coal bed (at
temperature T c = 2000 K) to the brick wall is G(λ) ∝ E b . The following shows
a similar way to determine brick wall absorptivity.
� ∞
� ∞
0 α(λ)G(λ) dλ
0 ε(λ)E b dλ
α(T s ) ≡ � ∞
=
(11.18)
0 G(λ) dλ
E b
= ε 1 F 0−λ 1 + ε 2 [F 0−λ 2 − F 0−λ 1 ] + ε 3 [1 − F 0−λ 2 ]
(11.19)
= 0.1 × 0.275 + 0.5 × (0.986 − 0.273) + 0.8 × (1 − 0.986)
where the fraction value can be found from Table 11.1, or from Figure 11.9,
with T = T c = 2000 K, irradiation from the black coal bed.
Therefore, average absorptivity can be calculated as
α(T s ) = 0.395 < 0.61 for ε(T s )
11.3 Solar and Atmospheric Radiation
Solar radiation is essential to all life on earth. Through the thermal and
photovoltaic process, solar radiation is important for the design of solar collectors, air-conditioning systems for buildings and vehicles, temperature control
systems for spacecrafts, and photocells for electricity. The sun is approximate as a spherical radiation source with a diameter of 1.39 × 10 9 m and is
located around 1.50 × 10 11 m from the earth. The average solar flux (solar
constant) incident on the outer edge of the Earth’s atmosphere is about
1353 W/m
2 . Assuming a blackbody radiation, the sun’s temperature can be
estimated at about 5800 K. Figure 11.10 shows the spectral distribution of
solar radiation [2]. The radiation is concentrated in the low-wavelength region
(0.2 ≤ λ ≤ 3 μm) with the peak value of 0.50 μm.
The magnitude spectral and directional distributions of solar flux change
significantly as solar radiation passes through the Earth’s atmosphere. The
change is due to absorption and scattering of the radiation by the atmosphere particles and gases. The effect of absorption by the atmosphere gases
O 3 (ozone), H 2 O vapor, O 2 , and CO 2 is shown by the lower curve in Figure
11.10. Absorption by ozone is strong in the UV region, providing considerable
attenuation below 0.3–0.4 μm. In the visible light region (0.4–0.7 μm), absorption is contributed by O 3 and O 2 ; in the IR region (0.7–3.0 μm), absorption is
due to H 2 O vapor and CO 2 . The effect of scattering by particles and gases is
that about half goes back to atmosphere and half comes to the earth surface.
Therefore, the average solar flux incident on the Earth’s surface is reduced
to about 300–800 W/m 2 , depending on the time of the day, the season, the
latitude, and the weather conditions.