Determining the fin efficiency of convective straight fins with temperature dependent thermal conductivity by using Homotopy Perturbation Method

Abstract

Purpose

The purpose of this paper is to determine the fin efficiency of convective straight fins with temperature dependent thermal conductivity by using Homotopy Perturbation Method.

Design/methodology/approach

Most engineering problems, especially heat transfer equations are in nonlinear form. Homotopy Perturbation Method (HPM) has been applied to solve a wide series of nonlinear differential equations. In this paper, HPM is used for obtaining the fin efficiency of convective straight fins with temperature‐dependent thermal conductivity. Comparison of the results with those of Homotopy Perturbation Method, exact solution, numerical results and Adomian's decomposition method (ADM) were been done by Cihat Arslanturk.

Findings

Results show that both Homotopy Perturbation Method and ADM applied to the nonlinear equations were capable of solving them with successive rapidly convergent approximations without any restrictive assumptions or transformations causing changes in the physical properties of the problem. Moreover, adding up the number of iterations leads to explicit solution for the problem. The results are just obtained with two iterations. This shows the accuracy and great potential of this method. Finally, it can be seen that, with increase of thermo‐geometric fin parameter (v), the fin efficiency increases too.

Originality/value

The results demonstrate good validity and great potential of the HPM for Heat Transfer equations in engineering problems.

Citation

Ganji, D.D., Rahimi, M. and Rahgoshay, M. (2012), "Determining the fin efficiency of convective straight fins with temperature dependent thermal conductivity by using Homotopy Perturbation Method", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 2, pp. 263-272. https://doi.org/10.1108/09615531211199872