A thin metal plate is insulated on the back and exposed to solar radiation at th

Question

A thin metal plate is insulated on the back and exposed to solar radiation at the front surface. the exposed surface of the plate has an absorbtivity of 0.6 for solar radiation. if solar radiation is incedent on the plate at a rate of 700 W/m^2 and the surrounding air temperature is 25 °c determine the surface temperature of the plate when the heat loss by convection and radiation equals the solar energy absorbed by the plate. assume the combined convection and radiation heat transfer coefficent to be 50 w/m^2•°C.

Explanation / Answer

Let the steady state temperature of the plate be T K

Atmospheric air temperature Ta= 25 oC= 300 K

Heat lost by plate to atmosphere = h(T-Ta) = 50(T-300) W/m2

Heat absorbed by plate = Incident radiation x absorptivity

=700x0.6 W/m2

=420 W/m2

Heat lost by convection and radiation = radiation heat absorbed

Hence

50(T-300) = 420

T= 308.4 K

Or

t= 33.4 o C

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