High-temperature processes in a porous medium

A study is made into a nonlinear filtration problem on the flow of gas in a porous weakly conducting medium, which simulates the process of superheating in a reactor. Explicit estimates are obtained of two critical values of the similarity parameter of the problem, which define the condition of existence of the steady-state mode of cooling a system open to the atmosphere and the condition of global superheating. The second one of these critical values is also the bifurcation point for the input set of equations. It is found that a thin layer forms at high temperatures corresponding to this point, in which the thermal energy is concentrated. A simultaneous radical variation of the physical process of heat transfer occurs, namely, convection is replaced by molecular heat conduction.