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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 239052, 13 pages
http://dx.doi.org/10.1155/2012/239052
Research Article

Computational Modelling of Thermal Stability in a Reactive Slab with Reactant Consumption

Institute for Advance Research in Mathematical Modelling and Computations, Cape Peninsula University of Technology, P.O. Box 1906, Bellville 7535, South Africa

Received 10 February 2012; Accepted 10 March 2012

Academic Editor: Muhammad Aslam Noor

Copyright © 2012 O. D. Makinde. 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 paper investigates both the transient and the steady state of a one-step nth-order oxidation exothermic reaction in a slab of combustible material with an insulated lower surface and an isothermal upper surface, taking into consideration reactant consumption. The nonlinear partial differential equation governing the transient reaction-diffusion problem is solved numerically using a semidiscretization finite difference technique. The steady-state problem is solved using a perturbation technique together with a special type of the Hermite-Padé approximants. Graphical results are presented and discussed quantitatively with respect to various embedded parameters controlling the systems. The crucial roles played by the boundary conditions in determining the thermal ignition criticality are demonstrated.