Consider the East wall of a house that has a thickness of L. The outer surface of the wall exchanges heat by both convection and radiation. The interior of the house is maintained at T_∞1, while the ambient air temperature outside remains at T_∞2. 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 T_sky 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 outer surfaces of the wall are h₁ and h₂, respectively. The thermal conductivity of the wall material is k and the emissivity of the outer surface is ε₂. Assuming the heat transfer through the wall to be steady and one-dimensional, express the mathematical formulation (the differential equation and the boundary and initial conditions) of this heat conduction problem. Do not solve.

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Tool 0 Wall L m₂ Too2 Tsky X