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Abstract and Applied Analysis
Volume 2014, Article ID 684293, 9 pages
Research Article

A Series Solution for Heat Conduction Problem with Phase Change in a Finite Slab

Department of Mechanical Systems Engineering, Asahikawa National College of Technology, 2-2-1-6 Shunkodai, Asahikawa 071-8142, Japan

Received 19 March 2014; Accepted 8 August 2014; Published 4 November 2014

Academic Editor: Marco Donatelli

Copyright © 2014 Ryoichi Chiba. 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 two-dimensional differential transform method is applied to solve one-dimensional phase change problems in a slab of finite thickness, which is subjected to convective thermal loading at one surface and a constant prescribed temperature at the other. In the problems, the initial temperature of the slab does not necessarily have to be the same as the fusion temperature. A series solution is derived for the temperature profile in the melting or solidifying slab with temperature-dependent thermal conductivity and volumetric heat capacity. The latent heat effect of the phase change is incorporated into the temperature-dependent heat capacity. Numerical results demonstrate the effects of the temperature-dependent parameters on the transient temperature profile of the slab.