$2-4(20$ Points$)$: Radiation

Solar irradiation of $1100\frac{W}{m^2}$ is incident on a large,

flat, horizontal metal roof on a day when the wind

blowing over the roof causes a convection heat trans$-$

fer coefficient of $25\frac{W}{m^2}*K.$ The outside air tem$-$

perature is $27C,$ the metal surface absorptivity for

incident solar radiation is $0\mathrm{.}60,$ the metal surface

emissivity is $0\mathrm{.}20,$ and the roof is well insulated from

below.

Estimate the roof temperature under steady$-$state

conditions.