ESCI SJR: 0.249 SNIP: 0.434 CiteScore™: 0.7

ISSN Druckformat: 1940-2503
ISSN Online: 1940-2554

# Computational Thermal Sciences: An International Journal

DOI: 10.1615/ComputThermalScien.2012003250
pages 183-191

## DIFFERENTIAL TRANSFORMATION METHOD FOR SOLVING THE NONLINEAR HEAT TRANSFER EQUATION WITH A VARIABLE SPECIFIC HEAT COEFFICIENT

Mohsen Torabi
Department of Mechanical and Biomedical Engineering, City University of Hong Kong, Hong Kong
Hessameddin Yaghoobi
Faculty of Mechanical Engineering, Semnan University, Semnan; Young Researchers and Elite Club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

### ABSTRAKT

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.

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