Application of homotopy perturbation method in nonlinear heat conduction and convection equations

One of the newest analytical methods to solve nonlinear equations is the application of both homotopy and perturbation techniques. In this Letter, homotopy perturbation method (HPM), which does not need small parameters, is compared with the perturbation method in the field of heat transfer. The justification for using this method is the difficulties and limitations of perturbation and homotopy when used individually. In this research, homotopy perturbation method is used to solve for the temperature distribution in lumped system of combined convection–radiation and also a nonlinear equation of the steady conduction in a slab with variable thermal conductivity.