Assessment of homotopy–perturbation and perturbation methods in heat radiation equations

One of the newest analytical methods to solve the nonlinear heat transfer equations is using both homotopy and perturbation methods in equations. Here, homotopy–perturbation method is applied to solve heat transfer problems with high nonlinearity order. The origin of using this method is the difficulties and limitations of perturbation or homotopy. It has been attempted to show the capabilities and wide-range applications of the homotopy–perturbation method in comparison with the previous ones in solving heat transfer problems. In this research, homotopy–perturbation method is used to solve an unsteady nonlinear convective-radiative equation and a nonlinear convective-radiative conduction equation containing two small parameters of ε₁ and ε₂.