Comparison of HAM and HPM solutions in heat radiation equations

In this paper it is proved that the perturbation and homotopy perturbation solutions for the two problems namely (i) unsteady convective-radiative equation and (ii) non-linear convective-radiative conduction equation are only valid for weak non-linearity. It is worth mentioning that homotopy perturbation method (HPM) does not provide exact and convergent solutions in most of the situations. Moreover, HPM have no criteria for establishing the convergence of the series solution. In the present study, it is shown and commented that the results in the two examples are valid only for small values of the parameters. The homotopy analysis method (HAM) is used in obtaining more meaningful and valid solutions.