Application of variational iteration method to nonlinear heat transfer equations using He's polynomials

Abstract

Purpose

The purpose of this paper is to solve an unsteady nonlinear convective‐radiative equation and a nonlinear convective‐radiative‐conduction equation containing two small parameters of ε₁ and ε₂ by variational homotopy perturbation method.

Design/methodology/approach

The heat transfer equations are described. The variational homotopy perturbation method as a powerful method for solving linear and nonlinear equations is applied to find the solutions of our model equations.

Findings

The solutions of heat transfer equations are calculated in the form of convergent series with easily computable components. Two examples are solved as illustrations, using symbolic computation.

Originality/value

The results show that the suggested method is easy to implement and has high level of accuracy. The method introduces a reliable tool for solving many linear and nonlinear differential equations.

Citation

Matinfar, M. and Ghasemi, M. (2013), "Application of variational iteration method to nonlinear heat transfer equations using He's polynomials", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 23 No. 3, pp. 520-531. https://doi.org/10.1108/09615531311301281