Consider the south wall of a house that is 0.2 m thick. The outer surface
of the wall is exposed to solar radiation and has an absorptivity of 0.5 for
solar energy. The interior of the house is maintained at T1 = 20°C, while the
ambient air temperature outside remains at T2 = 5°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 = 255 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 h1 = 6 W/m^2·K and h2 = 25 W/m^2·K, respectively. The thermal
conductivity of the wall material is k = 0.7 W/m·K, and the emissivity of the
outer surface is e2 = 0.9. 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.