One-dimensional stationary conditions of gas filtration through layer of motionless condensed substance with heat evolution

A gas flow through solid porous motionless homogeneous medium with heat evolution is considered. Such movement may arise from filtration cooling of fuel elements. Similar model was suggested in [1] for description the cooling process of destroyed block of Chernobyl atomic power station.
The system of equations, describing stationary conditions of cooling of homogeneous fuel element by air, is solved taking into account heat conductivity and gravity. A solution for special case, when the gravity is negligible, is presented too.
Then the problem about filtration cooling of fuel element with porous inert heap, situated over the fuel element, is solved. A critical heap height, at which a stationary solution exists, is determined.