Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 536056, 14 pages
http://dx.doi.org/10.1155/2011/536056
Research Article

On the Critical Behaviour of Exothermic Explosions in Class A Geometries

Mustapha Er-Riani1 and Khaled Chetehouna2

1Department of Mathematics, LMPMH, Faculty of Sciences and Techniques, BP 416, Tangier 90000, Morocco
2ENSI de Bourges, Institut PRISME UPRES EA 4229 EP-RES, 88 Boulevard Lahitolle, 18020 Bourges Cedex, France

Received 30 March 2011; Accepted 16 June 2011

Academic Editor: J. Jiang

Copyright © 2011 Mustapha Er-Riani and Khaled Chetehouna. 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

The aim of this work is to apply the homotopy perturbation method for solving the steady state equations of the exothermic decomposition of a combustible material obeying Arrhenius, Bimolecular, and Sensitised laws of reaction rates. These equations are formulated on some Class A geometries (an infinite cylinder, an infinite slab, and a sphere). We also investigate the effect of Frank-Kamenetskii parameter on bifurcation and thermal criticality by means of the Domb-Sykes graphical method.