Two parallel plates of infinite extent perpendicular to the page are situated relative to each other as shown in the figure. The upper plate is at 300°C and the lower plate is at 100°C. Determine the net rate of radiation heat transfer from the upper and lower plate assuming the environment is at a temperature below 100°C. Assume that both the lower surface of the upper plate and the upper surface of the lower plate are black.
GIVEN
• The planet Mars revolving around the sun
• Diameter of Mars (Dm) = 6600 km
• Distance from the sun (Rms) = 225 × 106 km
• Diameter of the sun (Ds) =1,384,000 km FIND
(a) The equilibrium temperature of Mars (Tm)
(b) Tm assuming that the albedo of Mars = 0.15
ASSUMPTIONS
• Both Mars and the sun act as blackbodies
• The sun has an equivalent blackbody temperature (Ts) of 5600 K
PROPERTIES AND CONSTANTS
The Stephan-Boltzmann constant (?) = 5.67 × 10–8 W/(m2 K4)
The energy from the sun that is incident on Mars can be calculated by integrating
where ?1 and ? 2 are the angles shown in Figure 11.28. For this case, since Dm << Rms and Ds << Rms, the following approximations can be used cos ? 1 and cos ? 2 = 1, r = Rms.
Also Eb1 = ? Ts4
Case (a)
If Mars behaves as a blackbody, it will absorb all the sun’s energy incident on it. For equilibrium, the energy radiated by Mars must equal the incident solar energy
Solving for the temperature of Mars
Case (b)
For an albedo of 0.15, Mars absorbs only 85% of the incident solar radiation, therefore
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