Influence of temperature fluctuations on the thermal explosion of a single particle

A statistical approach is used to study the influence of a random field of temperature in the ambient medium on the thermal stability limits of a particle with an exothermal chemical reaction. Temperature fluctuations in the ambient medium are modeled with a spatially uniform, statistically stationary, random Gaussian process with a finite time of autocorrelation function decay. A closed equation for the particle temperature probability density is derived by the method of functional differentiation. Stochastic drift of the particle in the temperature space, which makes the particle reach the critical temperature of the thermal explosion, is studied with the use of the Kolmogorov backward equation for the transition probability density. On the basis of the numerical solution of the equation for the particle temperature probability density, the stationary distribution of this probability is demonstrated to have a bimodal structure. The influence of the time of thermal relaxation of the particle and the integral time scale of temperature fluctuations in the ambient medium on the loss of thermal stability of the particle with volume heat release is examined.