Friction and localised heat initiation of ignition: the asymmetrical slab and cylindrical annulus

Abstract

Certain chemical compounds undergoing a heat-producing reaction and not normally classified as deflagrating or detonating explosives can nevertheless decompose with violence. The presence of surface heating generated, for example, by friction arising from the handling and transportation of these materials decreases the relative stability of these materials and therefore can pose an industrial problem. When reactant consumption is ignored and thermal conduction controls heat-flow, explicit solutions can be obtained for the dependence of temperature on position in the steady state, provided the physical shapes of these materials are simple. In this thesis the first chapter briefly introduces the theory of thermal ignition and also the formulation of the two models considered, the first being the asymmetrical slab, ( the slab heated on one side ), and the second being the cylindrical annulus heated on its inner surface. Following this introduction, the second chapter looks at the background of the bifurcation theory which plays an important role in determining the explicit solutions and the critical conditions under which an explosion might occur. Here a simple classical example is used to illustrate the inner workings of the theory. Having established the necessary background material, the rest of this thesis primarily deals with the two models already mentioned. Two approaches are taken when considering the solutions for the asymmetrical slab. The first is a direct approach where a solution can be found in terms of a transcendental equation, while the second involves using a regular series to approximate the values of the critical parameters for small effects of surface heating. In the case of the cylindrical annulus a direct approach is taken which again results in a solution involving a transcendental equation. For both models, tables for the values of the critical parameters have been produced and these help to verify some of the results obtained analytically.