Derive the differential equation for the temperature field ϑ = ϑ(r, t), that appears in a cylinder in transient, geometric one-dimensional heat conduction in the radial direction. Start with the...

Derive the differential equation for the temperature field ϑ = ϑ(r, t), that appears in a cylinder in transient, geometric one-dimensional heat conduction in the radial direction. Start with the energy balance for a hollow cylinder of internal radius r and thickness Δr and execute this to the limit Δr → 0. The material properties λ and c depend on ϑ; internal heat sources are not present.