The application of He's homotopy perturbation method to nonlinear equations arising in heat transfer

In this Letter, homotopy perturbation method (HPM), which does not need small parameters in the equations, is compared with the perturbation and numerical methods in the heat transfer field. The perturbation method depends on small parameter assumption, and the obtained results, in most cases, end up with a non-physical result, the numerical method leads to inaccurate results when the equation is intensively dependent on time, while He's homotopy perturbation method (HPM) overcomes completely the above shortcomings, revealing that the HPM is very convenient and effective. Comparing different methods shows that, when the effect of the nonlinear term is negligible, homotopy perturbation method and the common perturbation method have got nearly the same answers but when the nonlinear term in the heat equation is more effective, there will be a considerable difference between the results. As the homotopy perturbation method does not need a small parameter, the answer will be nearer to the exact solution and also to the numerical one.