Mathematical model of heat and mass transfer in a bidisperse porous material

Abstract

A model of heat and mass processes in a body with two types of pores is considered. This model describes the initial stage of substance penetration into the porous system (or the inverse process, namely, substance extraction from the system) and takes into account convective transport in large channels. A kinetic function of impregnation (extraction) of the porous medium and the substance flux density are found for a problem with additional conditions. Introduction.A two-component transport model is usually used to describe a number of heat-and masstransfer processes, including convective motion of the transported substance. This model can be derived from the condition of heat and mass balance in two continua with specific laws of energy and mass transfer and with a postulated law of energy and mass exchange between the components (see, e.g., [1][2][3][4][5][6][7]). A more generic approach is the use of methods of mechanics of continuous media for finding relations between interpenetrating continua, where the necessary closing relations are found from the corresponding problems with microscopic scales for the basic variables (see, e.g., [8][9][10][11]). A two-component (bidisperse) model of heat and mass transfer is usually used when the results predicted by a simpler one-component model differ significantly from experimental data because of an oversimplified presentation of the medium in the form of a homogeneous continuum or when the physical phenomenon has an essentially two-component character. Specific features of hydrodynamics of transport process and chemical kinetics can be often explained by using a model of a body containing pores of difference sizes (fissuredporous systems) [12,13]. For instance, mass transfer in some media forms zones with quantitatively and qualitatively different mass exchange with the ambient medium (cavities, pockets, stagnant zones, etc.). Despite the large variety of transport phenomena (washing of sediments, desalinization of soils, heat transfer in a heterogeneous medium, filtration in bidisperse or fissured-porous media, adsorption, etc.), the models have much in common, which allows one to use the results for studying similar processes.The solution of problems of this class is usually based on equations that describe processes occurring within sufficiently large time intervals, whereas the behavior of the heat-and mass-transfer characteristics at the initial stage (short times) has not been adequately studied. Moreover, the problem considered usually involves several dimensionless parameters (criteria) and characteristic times; therefore, the analysis is rather complicated. The initial stage of the process evolution is analyzed in the present work on the basis of a two-component model, and analytical solutions are found.Construction of the Model and Formulation of the Problem. Construction of models of hydrodynamics and heat and mass transfer in multispecies media usually involves averaging, for instance, over the volume [8] or over the ensemble of system configurations [10]...