The roof of Prob. 14.2 is painted with an aluminum paint, which has an emissivity of 0.9 and an absorptivity for solar radiation of 0.5. What is the equilibrium temperature of the painted roof?

Prob. 14.2

The black flat roof of a building has an emissivity of 0.9 and an absorptivity of 0.8 for solar radiation. The sun beats down at midday with an intensity of 300 Btu/ft²·h. 

(a) If the temperature of the air and of the surroundings is 68°F, if the wind velocity is negligible, and if no heat penetrates the roof, what is the equilibrium temperature of the roof? For the rate of heat transfer by conduction-convection use q/A = 0.38(ΔT)^1.25, where ΔT is the temperature drop between roof and air in degrees Fahrenheit.

(b) What fraction of the heat from the roof is lost by radiation?