Analysis of radiative heat-loss effects in thermal explosion of a gas using the integral manifold method

Abstract

Semenov's classical model of thermal explosion in a combustible gas mixture is modified to include radiative (rather than conductive) heat-loss effects and gas-density changes. A geometrical asymptotic technique (the method of integral manifolds - MIM) is exploited to perform a qualitative analysis of the governing equations. The strength of this method lies in the compact, clear geometrical/analytical rendition and classification of all possible dynamical scenarios, in terms of the physico-chemical parameters of the system. It is found that there are two main dynamical regimes of the system: cooling regimes and fast explosive regimes. Peculiarities of these dynamical regimes are investigated and their dependence on physical system parameters is analyzed. A criterion for the occurrence of thermal explosion is disclosed. An estimate for the maximum mixture temperature is also derived analytically. It is found that, under certain operating conditions, the dynamics are such that the initial explosive stage of the process essentially behaves adiabatically before succumbing to the dominance of the radiative heat loss that brings the system down to the ambient temperature.