Comparison of HAM and HPM methods in nonlinear heat conduction and convection equations

Recently, Rajabi et al. (Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys. Lett. A 360 (2007) 570-573.) discussed the solutions of temperature distribution in lumped system of combined convection-radiation. They solved a nonlinear equation of the steady conduction in a slab with variable thermal conductivity using both perturbation and homotopy perturbation methods. They claim that homotopy perturbation method (HPM) does not require any small parameter. However, this statement is not true always. Moreover, HPM have no criteria for establishing the convergence of the series solution. In this letter we have explicitly shown that the results of the problem considered in example 2 of (Rajabi, Ganji, Therian, Application of homotopy perturbation method in nonlinear heat conduction and convection equations, Phys. Lett. A 360 (2007) 570-573.) are valid only for 0 ≤ ε{lunate} ≤ 1. We have used the homotopy analysis method for finding the more meaningful solution.