Consider a cylindrical shell of length L, inner radius r₁, and outer radius r₂ whose thermal conductivity varies in a specified temperature range as k(T) = k₀(1 + βT²) where k₀ and β are two specified constants. The inner surface of the shell is maintained at a constant temperature of T₁ while the outer surface is maintained at T₂. Assuming steady one-dimensional heat transfer, obtain a relation for the heat transfer rate through the shell.