Conjugate mathematical model of ignition of magnesium samples

A distributed mathematical model of ignition of a magnesium particle with allowance for the heterogeneous chemical reaction and the region of the thermal influence of the particle on the gas is developed. A solution of the problem in a steady formulation is found, which allows expanding the classification of the thermal history of the particle-gas system. A numerical model for solving the considered class of boundary-value problems of magnesium-particle ignition is proposed, and the mathematical model is verified in terms of the ignition delay as a function of the Nusselt number. A limiting size of the gas layer near the particle, which determines the ignition mode, is identified. Stability of some heating regimes to finite and infinitesimal disturbances is demonstrated. It is shown that the ignition process can be controlled by a high-frequency thermal action on unstable states of the particle-gas system.