Heat conduction with temperature-dependent thermal conductivity (Fig. 10B.12) the curved surfaces and the end surfaces (both shaded in the figure) of the solid in the shape of a half-cylindrical shell are insulated. The surface θ = π, of area (r₂ – r₁) L, is maintained at temperature T₀, and the surface at θ = π, also of area (r₂ – r₁) L, is kept at temperature T_π. The thermal conductivity of the solid varies linearly with temperature from k₀ at T = T₀ to kπ at T = Tπ. 

(a) Find the steady-state temperature distribution. 

(b) Find the total heat flow through the surface at θ = 0.