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`Journal of Applied MathematicsVolume 2012 (2012), Article ID 174604, 20 pageshttp://dx.doi.org/10.1155/2012/174604`
Research Article

## Approximate Analytical Solution for One-Dimensional Solidification Problem of a Finite Superheating Phase Change Material Including the Effects of Wall and Thermal Contact Resistances

1Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Fluid Mechanics and Energetics Laboratory, Affiliate to CNRST, URAC 27, P.O. Box 2390, Marrakesh, Morocco
2Department of Physics, Faculty of Sciences Semlalia, Cadi Ayyad University, Automatic, Environmental and Transfer Process Laboratory, Affiliate to CNRST, URAC 28, P.O. Box 2390, Marrakesh, Morocco

Received 2 February 2012; Accepted 19 July 2012

Academic Editor: Oluwole D. Makinde

Copyright © 2012 Hamid El Qarnia 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.

#### Abstract

This work reports an analytical solution for the solidification of a superheating phase change material (PCM) contained in a rectangular enclosure with a finite height. The analytical solution has been obtained by solving nondimensional energy equations by using the perturbation method for a small perturbation parameter: the Stefan number, . This analytical solution, which takes into account the effects of the superheating of PCM, finite height of the enclosure, thickness of the wall, and wall-solid shell interfacial thermal resistances, was expressed in terms of nondimensional temperature distributions of the bottom wall of the enclosure and both PCM phases, and the dimensionless solid-liquid interface position and its dimensionless speed. The developed solution was firstly compared with that existing in the literature for the case of nonsuperheating PCM. The predicted results agreed well with those published in the literature. Next, a parametric study was carried out in order to study the impacts of the dimensionless control parameters on the dimensionless temperature distributions of the wall, the solid shell, and liquid phase of the PCM, as well as the solid-liquid interface position and its dimensionless speed.