The neighborhood cat likes to sleep on the roof of our shed in the backyard. The roofing surface is weathered galvanized sheet metal (ε = 0.65, αS = 0.8). Consider a cool spring day when the ambient air temperature is 10°C and the convection coefficient can be estimated from an empirical correlation of the form h = 1.0∆T1/3, where ∆T is the difference between the surface and ambient temperatures. Assume the sky temperature is – 40°C.

(a) Assuming the backside of the roof is well insulated calculate the roof temperature when the solar irradiation is 600 W/m2. Will the cat enjoy sleeping under these conditions?

(b) Consider the case when the backside of the roof is not insulated, but is exposed to ambient air with the same convection coefficient relation and experiences radiation exchange with the ground, also at the ambient air temperature. Calculate the roof temperature and comment on whether the roof will be a comfortable place for the cat to snooze.