235
Fundamental Radiation
PROBLEMS
11.1. A diffuse surface having the following spectral distributions
(ε λ = 0.3 for 0 ≤ λ ≤ 4 μm, ε λ = 0.7 for 4 μm ≤ λ) is maintained
at 500 K when situated in a large furnace enclosure whose walls
are maintained at 1500 K. Neglecting convection effects,
a. Determine the surface’s total hemispherical emissivity (ε) and
absorptivity (α).
b. What is the net heat flux to the surface for the prescribed
conditions?
Given: σ = 5.67 × 10 −8 (W/m 2 K 4 )
11.2. An opaque, gray surface at 27 ◦ C is exposed to an irradiation of
1000 W/m 2 , and 800 W/m 2 is reflected. Air at 17 ◦ C flows over the
surface, and the heat transfer convection coefficient is 15 W/m 2 K.
Determine the net heat flux from the surface.
11.3. A diffuse surface having the flowing spectral characteristics (ε λ =
0.4 for 0 ≤ λ ≤ 3 μm, ε λ = 0.8 for 3 μm ≤ λ) is maintained at
500 K when situated in a large furnace enclosure whose walls are
maintained at 1500 K:
a. Sketch the spectral distribution of the surface emissive power
E λ and the emissive power E λ,b that the surface would have
if it were a blackbody.
b. Neglecting convection effects, what is the net heat flux to the
surface for the prescribed conditions?
c. Plot the net heat flux as a function of the surface temperature
for 500 ≤ T ≤ 1000 K. On the same coordinates, plot the heat
flux for a diffuse, gray surface with total emissivities of 0.4 and
0.8.
d. For the prescribed spectral distribution of ε λ , how do the
total emissivity and absorptivity of the surface vary with
temperature in the range 500 ≤ T ≤ 1000 K?
11.4. The spectral, hemispherical emissivity distributions for two diffuse panels to be used in a spacecraft are as shown.
For panel A: ε λ = 0.5 for 0 ≤ λ ≤ 3 μm, ε λ = 0.2 for 3 μm ≤ λ.
For panel B: ε λ = 0.1 for 0 ≤ λ ≤ 3 μm, ε λ = 0.01 for 3 μm ≤ λ.
Assuming that the backsides of the panels are insulated and that
the panels are oriented normal to the solar flux at 1300 W/m 2 ,
determine which panel has high steady-state temperature.
11.5. From a heat transfer and engineering approach, explain how
a glass greenhouse, which is used in the winter to grow vegetables, works. Include sketches of both the system showing
energy flows and balances, and of radiation property data (radioactive properties versus wavelengths) for greenhouse components (glass and the contents inside the greenhouse). When applicable, show the appropriate equations and properties to explain
the greenhouse phenomenon. When finished with the above for
a glass greenhouse, extend your explanation to global warming, introducing new radioactive properties and characteristics if
needed.
Fundamental Radiation
PROBLEMS
11.1. A diffuse surface having the following spectral distributions
(ε λ = 0.3 for 0 ≤ λ ≤ 4 μm, ε λ = 0.7 for 4 μm ≤ λ) is maintained
at 500 K when situated in a large furnace enclosure whose walls
are maintained at 1500 K. Neglecting convection effects,
a. Determine the surface’s total hemispherical emissivity (ε) and
absorptivity (α).
b. What is the net heat flux to the surface for the prescribed
conditions?
Given: σ = 5.67 × 10 −8 (W/m 2 K 4 )
11.2. An opaque, gray surface at 27 ◦ C is exposed to an irradiation of
1000 W/m 2 , and 800 W/m 2 is reflected. Air at 17 ◦ C flows over the
surface, and the heat transfer convection coefficient is 15 W/m 2 K.
Determine the net heat flux from the surface.
11.3. A diffuse surface having the flowing spectral characteristics (ε λ =
0.4 for 0 ≤ λ ≤ 3 μm, ε λ = 0.8 for 3 μm ≤ λ) is maintained at
500 K when situated in a large furnace enclosure whose walls are
maintained at 1500 K:
a. Sketch the spectral distribution of the surface emissive power
E λ and the emissive power E λ,b that the surface would have
if it were a blackbody.
b. Neglecting convection effects, what is the net heat flux to the
surface for the prescribed conditions?
c. Plot the net heat flux as a function of the surface temperature
for 500 ≤ T ≤ 1000 K. On the same coordinates, plot the heat
flux for a diffuse, gray surface with total emissivities of 0.4 and
0.8.
d. For the prescribed spectral distribution of ε λ , how do the
total emissivity and absorptivity of the surface vary with
temperature in the range 500 ≤ T ≤ 1000 K?
11.4. The spectral, hemispherical emissivity distributions for two diffuse panels to be used in a spacecraft are as shown.
For panel A: ε λ = 0.5 for 0 ≤ λ ≤ 3 μm, ε λ = 0.2 for 3 μm ≤ λ.
For panel B: ε λ = 0.1 for 0 ≤ λ ≤ 3 μm, ε λ = 0.01 for 3 μm ≤ λ.
Assuming that the backsides of the panels are insulated and that
the panels are oriented normal to the solar flux at 1300 W/m 2 ,
determine which panel has high steady-state temperature.
11.5. From a heat transfer and engineering approach, explain how
a glass greenhouse, which is used in the winter to grow vegetables, works. Include sketches of both the system showing
energy flows and balances, and of radiation property data (radioactive properties versus wavelengths) for greenhouse components (glass and the contents inside the greenhouse). When applicable, show the appropriate equations and properties to explain
the greenhouse phenomenon. When finished with the above for
a glass greenhouse, extend your explanation to global warming, introducing new radioactive properties and characteristics if
needed.