A metal plate is placed in the sunlight. The incident radiant energy G is 780 W/m2. The air and the surroundings are at 10°C. The heat transfer coefficient by natural convection from the upper surface of the plate is 17 W/(m2 K). The plate has an average emissivity of 0.9 at solar wavelengths and 0.1 at long wavelengths. Neglecting conduction losses on the lower surface, determine the equilibrium temperature of the plate.
GIVEN
- A metal plate is sunlight
- Incident radiant energy
- Temperature of air and surroundings
- Natural convection heat transfer coefficient
- Plate emissivity (?) = 0.9 at solar wavelengths, 0.1 at long wavelengths
FIND
-The equilibrium temperature of the plate (Tp)
ASSUMPTIONS
- Steady state
- Conduction losses on the lower surface of the plate are negligible
- The surroundings behave as a blackbody enclosure
SKETCH
PROPERTIES AND CONSTANTS
the Stephan-Boltzmann constant
The plate will absorb the solar radiation with the absorptivity
Law. However, it will radiate to its surroundings at longer infrared wavelengths with
The heat gain from solar radiation must equal the heat flux loss by radiation and convection at steady state
By trial and error
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