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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.

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.

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.

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

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

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.