A novel effective approach for solving nonlinear heat transfer equations

In this paper, a novel analytic technique, namely the Laplace transform new homotopy perturbation method (LTNHPM), is applied for solving the nonlinear differential equations arising in the field of heat transfer. This approach is a new modification to the homotopy perturbation method based on the Laplace transform. Unlike the previous approach implemented by the present authors for these problems, the present method does not consider the initial approximation as a power series. The nonlinear convective–radiative cooling equation and nonlinear equation of conduction heat transfer with the variable physical properties are chosen as illustrative examples. The exact solution has been found for the first case and for the others; results with remarkable accuracy have been achieved which verify the efficiency as well as accuracy of the presented approach.