The application of differential transformation method to nonlinear equations arising in heat transfer

In this paper two nonlinear heat transfer problems were solved by considering variable specific heat coefficient. The calculations are carried out by using differential transformation method (DTM) which is a semi-numerical–analytical solution technique. By using DTM, the nonlinear constrained governing equations are reduced to recurrence relations and related initial conditions are transformed into a set of algebraic equations. The principle of differential transformation is briefly introduced, and then applied for the aforementioned problems. The solutions are subsequently solved by a process of inverse transformation. The current results are then compared with those derived from the variational iteration method (VIM), homotopy perturbation method (HPM), perturbation method (PM) and the exact solutions in order to verify the accuracy of the proposed method. The findings reveal that the DTM can achieve more suitable results in predicting the solution of such problems.