Convection–radiation from a continuously moving fin of variable thermal conductivity

The homotopy analysis method (HAM) is applied to generate an analytic solution for heat transfer in a moving fin of variable thermal conductivity which is losing heat by simultaneous convection and radiation to its surroundings. The accuracy of the analytic solution is validated by comparing it with the direct numerical solution of the problem. The analytic solution is found to be accurate to at least three places of decimal for a wide range of values of the parameters that are commonly encountered in thermal processing application. Graphs displaying the results are interpreted in physical terms.