The flat roof of a building has an area of 36 m2 . It may be treated as a gray surface with an emissivity of 0.6. The roof absorbs solar radiation at steady rate of 390 Wmí2 . The roof looses heat by...

The flat roof of a building has an area of 36 m2 . It may be treated as a gray surface with an emissivity of 0.6. The roof absorbs solar radiation at steady rate of 390 Wmí2 . The roof looses heat by convection due to wind. The convective heat transfer hw (Wmí2 Kí1 ) at a wind speed V (msí1 ) is given by

The roof exchanges thermal radiation with the sky which may be treated as a black hemispherical surface at the ambient temperature of 22°C. The wind speed is 5 msí1 . The roof is well insulated on the inside so that the heat flow into the building is negligible. Calculate (i) the temperature of the roof, (ii) the rate of heat loss by convection and (iii) the rate of heat loss by radiation.