Filtration combustion in the closed volume of an SHS reactor

We propose a two-dimensional mathematical model of filtration combustion of a charge layer in an SHS reactor, in which the variation in the temperature and pressure of the gas in the reactor during the synthesis is taken into account. For a kinetic combustion regime, we have constructed an approximate analytical solution, which is in satisfactory agreement with the results of a numerical calculation. Heating of the gas in the reactor volume is shown to lead to acceleration of reaction-front propagation, whereas the moment of attainment of maximum pressure in the reactor, which allows one to judge, in practice, the cessation of the synthesis, does not always coincide with cessation of combustion.