International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

Calculation of thermal diffusion and filtration fluxes at the interface by “traditional” methods requires preliminary determination of the potential values (concentration, moisture content, temperature, pressure) in the four-dimensional space of events. Such methods for solving boundary value problems, which provide “extra” information for technical calculations, are usually very laborous and require the use of numerical methods that are not always convenient in engineering practice. The proposed fieldless calculation method allows one to determine on the boundary of the region the gradients from the transfer potentials and, consequently, energy and material flows in the form of a known functional of the potentials at the interface at their short-term contact directly on the matrix of transfer coefficients of the formalized boundary value problem. This method uses the fractional index differentiation operation (fractional differentiation) and is convenient for solving limiting boundary value problems, i.e. when the characteristic size of the contacting phases in the boundary conditions of boundary value problems tends to infinity or the time of their interaction tends to zero.

Using the methods of systemic, mathematical and numerical analysis, as well as general physicochemical and thermodynamic laws, a complex of theoretical and experimental studies of transfer processes during short-term contact of phases has been carried out. These studies made it possible to fully reveal the regularities of external and internal heat and mass transfer, to find scientifically grounded ways to intensify the processes of vacuum, conductive and combined drying methods. Within the framework of linear nonequilibrium thermodynamics, a mathematical model of filtration-diffusion energy and mass transfer has been developed with a correct estimate of the orders of the terms in the system of differential equations of energy and mass transfer, taking into account the composition of the vapor-air mixture in the capillary-porous body. The limits of applicability of the hypothesis of short-term contact of phases according to the Fourier criterion for the transfer inside and outside the surfaces of the canonical shape (plate, cylinder, sphere) and wedge are estimated from the standpoint of the accuracy of calculating interphase flows. It is shown that in a number of cases the contact is not short-lived due to the curvature and the presence of angles on the contact surface, and not due to the finiteness of the dimensions of the contacting phases.