Thermal explosion of single particles in a random medium-temperature field

A model is proposed for the thermal explosion of a single particle with an exothermic chemical reaction in a turbulent temperature field of the medium. The chemical reaction rate is represented by a modified Arrhenius law, which takes into account changes in the internal structure of the particle material. Temperature fluctuations are modeled by a Gaussian random process. The study was carried out using the Lagrange and Euler approaches. In the Lagrange approach, in which a system of stochastic ordinary differential equations is solved, random temperature fluctuations of the medium and particle ensemble are calculated. Based on the results of numerical simulation of the ensemble, the dynamics of the empirical probability density function of the random particle temperature distribution is simulated. In the Euler approach, a nonstationary closed-loop equation is derived for the probability density function of random particle temperatures, which is numerically integrated using an original conservative difference scheme. The calculation results for both approaches agree satisfactorily with each other. It is shown that a random temperature field of the medium qualitatively changes the dynamics of occurrence of a thermal explosion. In a random temperature field, a thermal explosion can occur provided that in a deterministic case, the system is absolutely stable.