$1-107$ The inner and outer surfaces of a $25-$cm$-$thick wall in summer are at $27C$ and $44C,$ respectively. The outer surface of the wall exchanges heat by radiation with surrounding surfaces at $40C$ and by convection with ambient air also at $40C$ with a convection heat transfer coefficient of $8\frac{W}{m^2}*K.$ Solar radiation is

incident on the surface at a rate of $150\frac{W}{m^2}.$ If both the emissivity and the solar absorptivity of the outer surface are $0\mathrm{.}8,$ determine the effective thermal conductivity of the wall.

FIGURE P$1-107$