Consider the same problem as homework $9,$ except that now the temperature of the outside wall is unknown. The inside surface is at $27C.$ The wall thickness is $25$ cm and conductivity is $4\frac{W}{m}\frac{?}{K}.$ The outside surface of the wall exchanges heat by radiation with the surrounding surfaces at $40C,$ and by convection with air 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 $200\frac{W}{m^2}.$ Both the emissivity and the solar absorptivity of the outer surface are $0\mathrm{.}8.$

a$)$ Find the temperature of the outside wall.

b$)$ Find the rate of heat transfer across the wall.