Exact Heat-Transfer Solutions to Radial Fins of General Profile

In this paper, the heating process in fin problems of engineering interest is revisited with a target to work out analytical solutions representing the thermal diffusion in a variety of radial fin shapes. The difficulty arisen due to the strong nonlinearity when the physical properties are temperature-dependent and given by power laws is tackled, and explicit expressions for the fin base heat-transfer rate, fin tip temperature, and fin efficiency are obtained. Taking into account these three effects, the optimal radial fin shape is decided, which is of most physical interest.