Research methods of the process of heat and mass transfer in different media with diffusion and subdiffusion

The problem of studying the laws governing the formation of the radon environment is not new. The development of the mining industry (to study the regularities of the formation of the radon environment in mine workings, it was necessary to simulate the flux of radon density, which led to the construction of various models of radon transfer), became the main catalyst for in-depth research in this direction. It should also be noted that according to the RF radiation safety standards (NRB-99), the average annual equivalent equilibrium volumetric activity (concentration) of radon in the air of residential and public buildings should not exceed the established limit. To implement this decree, various models of mass transfer (radon) were built. Most of these models are based on the advection-diffusion equation, which simulates the processes of mass transfer of matter or heat transfer in a medium with fractal geometry (in particular, in porous media). Moreover, the order of the fractional time derivative in this equation corresponds to the proportion of channels (the system described by this equation is open, that is, it is connected to the outside world either by a finite or infinite number of communication channels) open for flow in a fractal (porous) medium. This process is non-local in time. And the environment in which this process takes place will be an environment with memory. In this paper, we analyze boundary value problems for the considered equation. A method based on the separation of variables is presented, while the solution of the problems posed is written out in the form of an infinite series in the eigenfunctions of the operator generated by an ordinary differential expression of the fractional order (the order of the fractional derivative is greater than one but less than two) and boundary conditions of the Sturm-Liouville type.