Approximate solution for convective fins with variable thermal conductivity

The Galerkin method is used to obtain approximate analytical solutions to the nonlinear problem of the performance of a convective fin with variable temperature-dependent thermal conductivity. The analysis is applied to the efficiency of a straight rectangular convecting fin insulated at the tip under steady state conditions, with both the heat transfer coefficient and the ambient fluid temperature assumed uniform. The effectiveness of the Galerkin procedure is compared both to that of the numerical and perturbation solutions and is found to be as accurate as the former and somewhat more accurate than the latter.