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

Abstract

This paper investigates both the transient and the steady state of a one-stepnth-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.