Differential transformation method for solving the nonlinear heat transfer equation with a variable specific heat coefficient

In this paper, the nonlinear heat transfer equation is investigated by considering a variable specific heat coefficient. The calculations are carried out by using the differential transformation method (DTM), which is a seminumerical analytical solution technique. Using the 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 is then applied to the aforementioned equation. The solutions are subsequently solved by a process of inverse transformation. The current results are then compared with those derived from the established Fehlberg fourth-fifth order Runge-Kutta method in order to verify the accuracy of the proposed method. Accordingly, several illustrative numerical computations are given to demonstrate the effectiveness of the present method. The findings reveal that the DTM can achieve accurate results in predicting the solution of such problems.