The roof of a house consists of a 0.8-ft-thick concrete slab (k = 1.1 Btu/h · ft · °F) tha...

The roof of a house consists of a 0.8-ft-thick concrete slab (k = 1.1 Btu/h · ft · °F) that is 25 ft wide and 35 ft long. The emissivity of the outer surface of the roof is 0.8,and the convection heat transfer coefficient on that surface is estimated to be 3.2 Btu/h · ft2 · °F. On a clear winter night, the ambient air is reported to be at 50°F, while the night sky temperature for radiation heat transfer is 310 R. If the inner surface temperature of the roof is T1= 62°F, determine the outer surface temperature of the roof and the rate of heat loss through the roof when steady operating conditions are reached.