A Comparison between the Modified Homotopy Perturbation Method and Adomian Decomposition Method for Solving Nonlinear Heat Transfer Equations

In this study, we applied a new algorithm based on Homotopy Perturbation Method (HPM) to evaluate the temperature distribution of a straight rectangular fin with temperature dependent surface heat flux for all possible types of heat transfer. The local heat transfer coefficient is considered to vary with a power-law function of temperature. The time interval is divided into several subintervals and the HPM solutions are applied successively over these reduced time intervals. Comparisons between the 13-term Adomian decomposition solution and 6-term modified HPM solution are made. Comparison of the results obtained by modified HPM with that obtained by the Adomian Decomposition Method (ADM) reveals that the obtained modified HPM solution is quite accurate when only the six terms are used in the series expansion.