Consider a roof of a house of thickness L = 20 cm, thermal conductivity k = 1 W/m K, and emittance of the external surface epsilon= 0.95, which is exposed to a clear night sky while the outside air temperature is T 0 = -5 degree C and the corresponding heat transfer coefficient is 5 W/m2 K. If the inner and outer surface temperatures of the roof are 20 degree C and -9 degree C, estimate the effective sky temperature T sky. If because of a wind the outside convective heat transfer coefficient is increased from 5 to 30 W/m2 K, what would be the new outside surface temperature of the roof when its inner surface temperature remains 20 degree C? What is the corresponding change in heat flux through the roof when the heat transfer coefficient changes from 5 to 30 W/m2 K?