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Analytical Heat Transfer
ε ∼ = α 2
""
q
= h(T s − T ∞ )
conv
11.2. A thin glass is used on the roof of a greenhouse. The glass is totally transparent for λ < 1 μm, and opaque with an absorptivity α = 1 for λ > 1 μm.
Assume that solar flux = G s , atmospheric emission flux = G atm , thin glass
temperature = T g , and interior surface emission flux=G i , where G atm and G i
are concentrated in the far IR region (λ > 10 μm), and determine the temperature of the greenhouse ambient air (i.e., inside room air temperature,
T ∞,i ).
SOLUTION
Performing an energy balance on the thin glass plate per unit surface
area, and considering two convection processes (inside and outside greenhouse), two emissions (inside and outside the glass plate), and three
absorbed irradiations (from solar, atmospheric, interior surface), we obtain
T ∞,i from
α s G s + α atm G atm + h o (T ∞,o − T g ) + h i (T ∞,i − T g ) + α i G i − 2εσT g
4 = 0
where α s = solar absorptivity for absorption of G λ,s ∼ E λ,b (λ, 5800 K)
= α 1 F 0−1 μm + α 2 [1 − F 0−1 μm
= 0 × 0.72 + 1.0[1 − 0.72]
= 0.28(Note that from Table 11.1, λT = 1 μm × 5800 K, F 0−1 μm = 0.72)
α atm = absorptivity for λ > 10 μm = 1
α i = absorptivity for λ > 10 μm = 1
ε = α λ for λ » 1 μm, emissivity of the glass for long wavelength
emission = 1
h o = convection heat transfer coefficient of the outside roof
h i = convection heat transfer coefficient of the inside room
Remarks
This chapter covers the same topics as in the undergraduate-level heat transfer. These include spectrum thermal radiation intensity and emissive power
for a blackbody as well as a real surface at elevated temperatures; surface radiation properties such as spectral emissivity and absorptivity for real-surface
radiation; how to obtain the total emissivity or absorptivity from the fraction
method; how to perform energy balance from a flat surface including radiation and convection; and solar and atmospheric radiation problems. This
chapter provides fundamental thermal radiation and surface properties that
are useful for many engineering applications such as surface radiators, space
vehicles, and solar collectors.
Analytical Heat Transfer
ε ∼ = α 2
""
q
= h(T s − T ∞ )
conv
11.2. A thin glass is used on the roof of a greenhouse. The glass is totally transparent for λ < 1 μm, and opaque with an absorptivity α = 1 for λ > 1 μm.
Assume that solar flux = G s , atmospheric emission flux = G atm , thin glass
temperature = T g , and interior surface emission flux=G i , where G atm and G i
are concentrated in the far IR region (λ > 10 μm), and determine the temperature of the greenhouse ambient air (i.e., inside room air temperature,
T ∞,i ).
SOLUTION
Performing an energy balance on the thin glass plate per unit surface
area, and considering two convection processes (inside and outside greenhouse), two emissions (inside and outside the glass plate), and three
absorbed irradiations (from solar, atmospheric, interior surface), we obtain
T ∞,i from
α s G s + α atm G atm + h o (T ∞,o − T g ) + h i (T ∞,i − T g ) + α i G i − 2εσT g
4 = 0
where α s = solar absorptivity for absorption of G λ,s ∼ E λ,b (λ, 5800 K)
= α 1 F 0−1 μm + α 2 [1 − F 0−1 μm
= 0 × 0.72 + 1.0[1 − 0.72]
= 0.28(Note that from Table 11.1, λT = 1 μm × 5800 K, F 0−1 μm = 0.72)
α atm = absorptivity for λ > 10 μm = 1
α i = absorptivity for λ > 10 μm = 1
ε = α λ for λ » 1 μm, emissivity of the glass for long wavelength
emission = 1
h o = convection heat transfer coefficient of the outside roof
h i = convection heat transfer coefficient of the inside room
Remarks
This chapter covers the same topics as in the undergraduate-level heat transfer. These include spectrum thermal radiation intensity and emissive power
for a blackbody as well as a real surface at elevated temperatures; surface radiation properties such as spectral emissivity and absorptivity for real-surface
radiation; how to obtain the total emissivity or absorptivity from the fraction
method; how to perform energy balance from a flat surface including radiation and convection; and solar and atmospheric radiation problems. This
chapter provides fundamental thermal radiation and surface properties that
are useful for many engineering applications such as surface radiators, space
vehicles, and solar collectors.