New perturbation‐iteration solutions for nonlinear heat transfer equations

Abstract

Purpose

The purpose of this paper is to apply, for the first time, the authors' newly developed perturbation iteration method to heat transfer problems. The effectiveness of the new method in nonlinear heat transfer problems will be tested.

Design/methodology/approach

Nonlinear heat transfer problems are solved by perturbation iteration method. They are also solved by the well‐known technique variational iteration method in the literature.

Findings

It is found that perturbation iteration solutions converge faster to the numerical solutions. More accurate results can be achieved with this new method for nonlinear heat transfer problems.

Research limitations/implications

A few iterations are actually sufficient. Further iterations need symbolic packages to calculate the solutions.

Practical implications

This new technique can practically be applied to many heat and flow problems.

Originality/value

The new perturbation iteration technique is successfully implemented to nonlinear heat transfer problems. Results show good agreement with the direct numerical simulations and the method performs better than the existing variational iteration method.

Citation

Aksoy, Y., Pakdemirli, M., Abbasbandy, S. and Boyacı, H. (2012), "New perturbation‐iteration solutions for nonlinear heat transfer equations", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 22 No. 7, pp. 814-828. https://doi.org/10.1108/09615531211255725