Chapter 2, Problem 160P

Consider a cylindrical sheel of length L, inner radius r₁, and outer radius r₂ whose thermal conductivity varies in a specified temperature range as $(k(T)=k_0\text{(1+}\beta {\text{T}}^{\text{2}}\text{), where }{k}_0\text{ and }\beta$ 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, obatain a relation for the heat transfer rate through the shell.