CRITICAL PARAMETERS OF THERMAL-EXPLOSION

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. © 1979.