Unsteady concentration field of reacting gas in the vicinity of a burning coal particle

The article deals with a boundary value problem of mathematical physics describing the unsteady process of diffusion of a reacting gas to a spherical coal particle located in the atmosphere of a mine. The solution of the boundary value problem is based on self-similar transformations which are a special case of group analysis. Formulas for determining the concentrations of the reacting gas in the vicinity of the coal particle and on its surface are obtained. Graphs of the dependencies of the burn-out time of the coal particle on a number of its parameters are constructed, and the fields of the reacting gas concentration at various stages of combustion of the coal particle are revealed.