An Analytical Study on a Model Describing Heat Conduction in Rectangular Radial Fin with Temperature-Dependent Thermal Conductivity

The coupling of the homotopy perturbation method (HPM) and the variational iteration method (VIM) is a strong technique for solving higher dimensional initial boundary value problems. In this article, after a brief explanation of the mentioned method, the coupled techniques are applied to one-dimensional heat transfer in a rectangular radial fin with a temperature-dependent thermal conductivity to show the effectiveness and accuracy of the method in comparison with other methods. The graphical results show the best agreement of the three methods; however, the amount of calculations of each iteration for the combination of HPM and VIM was reduced markedly for multiple iterations. It was found that the variation of the dimensionless temperature strongly depends on the dimensionless small parameter ${\varepsilon_1}$ . Moreover, as the dimensionless length increases, the thermal conductivity of the fin decreases along the fin.