Accession Number : AD0705761

Title :   THERMAL EXPLOSION IN THE SPHERE AND THE HOLLOW SPHERICAL SHELL HEATED AT THE INNER FACE,

Corporate Author : DEFENCE STANDARDS LABS MARIBYRNONG (AUSTRALIA)

Personal Author(s) : Gray,P. ; Lee,P. R. ; MacDonald,J. A.

Report Date : NOV 1968

Pagination or Media Count : 11

Abstract : The steady state heat conduction equation for reactants of spherical symmetry decomposing by a zero-order exothermic process has been converted by means of the fifth-power (quintic) approximation into a form which is soluble analytically. The method of solution depends upon the physical model under examination: two models have been discussed, that of self ignition of a hollow spherical shell of reactant heated at the inner face and cooling to the surroundings from the outer face and the solid sphere immersed in a constant temperature bath. Approximate Frank-Kamenetsky criticality criteria for hollow spheres of varying thickness and hot face temperatures were derived analytically by a method involving the use of incomplete elliptic integrals of the first kind. The results were compared with numerical solutions of the equation wherein the exponential approximation had been made and found to be in good agreement. It has been shown how these results fit into the pattern established by those for the asymmetrically heated slab and the infinite hollow cylindrical shell heated at the inner face. (Author)

Descriptors :   (*EXPLOSIONS, SPHERES), (*HEAT TRANSFER, SPHERES), COMBUSTION, AUSTRALIA

Subject Categories : Physical Chemistry
      Thermodynamics
      Combustion and Ignition

Distribution Statement : APPROVED FOR PUBLIC RELEASE