Numerical and approximate solutions to problems in spontaneous ignition : a thesis presented in partial fulfilment of the requirements for the degree of Master of Philosophy in Mathematics at Massey University

Abstract

This thesis considers the subject of time-independent spontaneous ignition of materials of arbitrary shape.

Chapter One reviews the major advances up to the work ofD.A.Frank-Kamenetskii. Chapter Two discusses the modern, Gray Wake, formulation of the problem. In Chapter Three, ignition in the class A shapes is approximated by a numerical finite differences method. The same method is applied to some non-class A geometries.

Solutions to the Gray Wake formulation for ignition in the infinite slab geometry are sought in Chapter Four by approximating the internal energy gradient by the maximum internal energy and by the average internal energy.

Chapter Five considers an industrial application of the spontaneous ignition of moist powder.