Ignition of porous materials by gas filtration (unsteady downstream filtration)

The wave theory of ignition is used to create an analytic method for calculating the temporal characteristics of ignition in porous samples by a flow of hot gas into the material (unsteady downstream filtration). When classical dimensionless variables are used, characteristic ignition times are found to have an anomalous dependence on the parameter $\beta=RT_{ign}/E$: as $\beta$ is increased, the duration of the ignition stages is reduced and does not increase, as it does for conductive heating of the material. A scale is found for the gas density, such that the temporal ignition characteristics have the customary dependence on $\beta$ when it is used. It is shown that the equations for isothermal filtration can be used to determine the mass feed rate of the gas. Numerical calculations confirm the validity of the basic assumptions of the theory regarding the existence of stages in the ignition process and the wave mechanism for heating the material. Good quantitative agreement is obtained between an approximate analysis and the numerical calculations. The error in determining the time to develop a zero temperature gradient at the sample boundary and the thermal explosion time is less than 50%.