On the Surface Ignition of Self-Heating Materials

Abstract

Abstract The solutions of two classic problems in thermal ignition theory are derived beginning with conventional integral expression for the temperature due to internal heat generation. For both problems solutions appropriate for high dimensionless surface temperatures have been sought. The essence of the treatment of the two problems is an expansion of the term representing the rate of heat release in an integral expressing its contribution to the temperature rise or the surface gradient. For a constant high net flux on the surface of a semi-infinite solid a relationship between the flux and the ignition time is obtained which is of the same form as was derived by Lifian and Williams and virtually identical numerically to their and to Bradley's “average” result. A first approximation has also been obtained for the time of runaway or “blow-up” resulting from a constant high temperature imposed on the surface of a semi-infinite solid. The results lie numerically close to those recently obtained by Liñán and Williams and the forms appear to be simpler. The first term in the correction to the use of the Frank-Kamenetskii approximation for the Arrhenius law is easily obtained and agrees with that given by Liñán and Williams. An exact equation similar to their equation matching the inner reaction zone and the outer inert zone but different in detail is deduced from conventional heat conduction theory.