Consider the same problem as homework $9,$ except that now the temperature of the outside wall is unknown. The inside surface is at $27$C$.$ The wall thickness is $25$ cm and conductivity is $4$ W$/$m$/$K$.$ The outside surface of the wall exchanges heat by radiation with the surrounding surfaces at $40$C$,$ and by convection with air at $40$C with a convection heat transfer coefficient of $8$ W$/$m$2$K$.$ Solar radiation is incident on the surface at a rate of $200$ 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