Channel model as a means for describing the hydrodynamics and heat transfer in porous media

Permeable porous media are widely occurring in nature and are frequently used in various apparatuses in the metallurgical, chemical, and electric-power industries. The heating and processing of bulk materials, the heating of charge in shaft furnaces, the processes of heat transfer in recuperators and heating furnaces, and modern high-intensity cooling systems employed in aviation-and-space engineering and in radio electronics make rather an incomplete list of applications associated with heat and mass transfer in permeable porous media. The theoretical description of these processes or the generalization of experimental data are usually based on a number of assumptions, of which the most important one is the introduction of one or several linear scales describing adequately the structure of a porous medium. It is the objective of this paper to critically analyze the problem of the choice of linear scale and assess the possibility of constructing a generalized model of hydrodynamics and heat transfer in permeable porous media within a deterministic approach.