Variational iteration and Homotopy perturbation methods for fin efficiency of convective straight fins with temperature-dependent thermal conductivity

Abstract

Variational iteration method (VIM) and homotopy perturbation method (HPM) have been used to evaluate the efficiency of straight fins with temperature-dependent thermal conductivity and to determine the temperature distribution within the fin. These methods are useful and practical for solving the nonlinear heat diffusion equation, which is associated with variable thermal conductivity condition. VIM and HPM provide an approximate analytical solution in the form of an infinite power series. The fin efficiency of the straight fins with temperature-dependent thermal conductivity has been obtained as a function of thermo-geometric fin parameter and the thermal conductivity parameter describing the variation of the thermal conductivity. It has been observed that the thermal conductivity parameter has a strong influence over the fin efficiency. The data from the present solutions has been correlated for a wide range of thermo-geometric fin parameter and the thermal conductivity parameter. The resulting correlation equations can assist thermal design engineers for designing of straight fins with temperature-dependent