Critical parameters of thermal explosion

Abstract

An analysis of the critical conditions of thermal explosion based on bifurcation theory for nonlinear elliptic equations is presented. It has been proved that the value of the Frank-Kamenetsky parameter δ equals the principal eigenvalue of the equation of heat conduction linearized about the point of bifurcation of the solution u(δ), which correspond to self-ignition and extinction points. From this two computational procedures for determining critical conditions of self-ignition or extinction have been worked out. Both procedures are illustrated with examples of numerical calculations.