Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2010 / Development of safe storage for reactive combustible materials to prevent possible human and environmental hazards as well as ensure and enhance industrial safety can significantly benefit from mathematical modelling of systems. In the recent past, models with varying degrees of sophistication have been developed and applied to the problem of predicting thermal criticality conditions, temperature and concentration profiles of such system. In this thesis, a model showing the temperature history of an nth order exothermic oxidation reaction in a slab of combustible material with variable pre-exponential factor, taking the consumption of the reactant into account in the presence of a convective heating and oxygen exchange at the slab surface with the ambient is presented Both transient and steady state problems are tackled The critical regime separating the regions of explosive and non-explosive paths of a one step exothermic chemical reaction is determined The governing nonlinear partial differential equations are solved numerically by method of lines (MOL), with finite difference schemes used for the discretisation of the spatial derivatives. Moreover, both fourth order Runge-Kutta numerical integration coupled with shooting methods and perturbation techniques together with a special type of Hermite-Pade series summation and improvement method were employed to tackle the steady state problem. The crucial roles played by the boundary conditions in determining the location ofthe maximum heating were demonstrated. In chapter one, the relevant applications together with previous published work on the problem were highlighted The basic mathematical theory and equations needed to tackle the problem were derived in Chapter two. In chapter three, the transient model problem was formulated, analysed and discussed. The steady state problem was formulated and solved in Chapter four. Furtherwork and concluding remarks were highlighted in Chapter five.