Newton-variational solution of the Frank–Kamenetskii thermal explosion problem

Abstract

The Newton method was shown by Vatsya to be suitable for solving the generalised elliptic problem, and we show that this approach can be used to treat the Frank–Kamenetskii model of a thermal explosion, by using a variational solution of the sequence of linear equations that are encountered in the Newton method. Convergence to the desired solution is rapid in the case of spherical geometry. The method produces converging upper and lower bounds to the critical value of the dimensionless heat production rate, δc, and lower bounds to the dimensionless temperature excess distribution function θ and its critical form θc. Keywords: thermal explosions, Frank–Kamenetskii model.