Consider the south wall of a house that is L $50\mathrm{.}2$ m thick. The outer surface

of the wall is exposed to solar radiation and has an absorptivity of a $50\mathrm{.}5$ for

solar energy. The interior of the house is maintained at T$`1520\backslash$deg C$,$ while the

ambient air temperature outside remains at T$`255\backslash$deg C$.$ The sky$,$ the ground,

and the surfaces of the surrounding structures at this location can be modeled

as a surface at an effective temperature of Tsky $5255$ K for radiation exchange

on the outer surface. The radiation exchange between the inner surface of

the wall and the surfaces of the walls, floor, and ceiling it faces is negligible.

The convection heat transfer coefficients on the inner and the outer surfaces

of the wall are h$156$ W$/$m$2$K and h$2525$ W$/$m$2$K$,$ respectively. The thermal

conductivity of the wall material is k $50\mathrm{.}7$ W$/$m$$K$,$ and the emissivity of the

outer surface is e$250\mathrm{.}9.$ Assuming the heat transfer through the wall to be

steady and one$-$dimensional, express the boundary conditions on the inner and

the outer surfaces of the wall, and solve the question with values