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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 423421, 12 pages
Research Article

Approximate Analytic Solutions of Transient Nonlinear Heat Conduction with Temperature-Dependent Thermal Diffusivity

1Department of Mathematics, Statistics and Physics, Qatar University, Doha 2713, Qatar
2Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, P.O. Box 5087, Dhahran 31261, Saudi Arabia
3Department of Mathematics, Hafr Al-Batin Community College, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia

Received 7 April 2014; Accepted 17 June 2014; Published 13 July 2014

Academic Editor: Mariano Torrisi

Copyright © 2014 M. T. Mustafa et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A new approach for generating approximate analytic solutions of transient nonlinear heat conduction problems is presented. It is based on an effective combination of Lie symmetry method, homotopy perturbation method, finite element method, and simulation based error reduction techniques. Implementation of the proposed approach is demonstrated by applying it to determine approximate analytic solutions of real life problems consisting of transient nonlinear heat conduction in semi-infinite bars made of stainless steel AISI 304 and mild steel. The results from the approximate analytical solutions and the numerical solution are compared indicating good agreement.