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

Modern intensification of materials processing technology leads to an increase in the role of non-stationary interconnected exchange processes compared to stationary unconnected interconnected exchange processes compared to stationary unconnected. This fact is still insufficiently reflected in the field of solving energy and mass transfer problems (EMT) at small Fourier numbers (Fourier numbers ≤0.1) at short-term phase contact (SPC). In this article, a generalized mathematical model of interconnected non-stationary irregular energy and mass transfer mode at short-term contact across a boundary with selective permeability of phases is formalized. In vector-matrix form, a conjugate mixed boundary value problem is solved with excitation in each of the phases of flows of substances absent in the other phase. By analogy with heat exchange and mass exchange, matrices of potential assimilation of phases and a contact matrix are introduced, which allows obtaining a uniform solution for a number of special cases and especially simplified the entry for the vector of interphase flow densities. The mathematical notation of the solutions of the considered parabolic system of partial differential equations of the second order for intensive irreversible processes (Fourier numbers ≤0.1) are written in vector-matrix form and are close to the scalar Higbee theory for mass transfer.

The paper considers an analytical method for solving systems of equations of conjugate non-stationary heat and mass transfer with account of volumetric negative or positive heat sources (and steam generation aswell). The obtained data can be used to find integral kinetic dependencies of heat and mass exchange processes, analytical formulas for calculating heat and mass transfer coefficients and other derivative quantities necessary for engineering calculations of processes and devices in chemical technology, biotechnology, industrial heat power engineeringand other industries.

For various canonical forms (plane, cylinder, ball, etc.), a generalized mathematical model (MM) of a nonlinear steady-state process of molecular heat transfer (or moisture diffusion) through enclosing structures (ES) is proposed, taking into account infiltration or exfiltration of a vapor-air (gas) mixture and the presence of various internal or surface positive (moisture condensation) or negative (evaporation of moisture) of heat sources (HS). The mathematical formalization of the posed boundary value problem (BVP) of transfer and its general solution are given, on the basis of which, under various specified conditions of unambiguity, solutions of specific physical processes with constant or variable thermophysical characteristics and HS are constructed and analyzed. For large-scale transitions, the short-circuit problem is posed and solved under various boundary conditions (BVC), written in a criterion form as dependences of the dimensionless temperature T(R-, Pe, Po) on the dimensionless thermal resistance (R-) of the heat exchange criteria for the similarity of Pecle (Pe) and Pomerantsev (Po).

The problems of heat and moisture transfer, air permeability in single and enclosure constructions (EC) of buildings, facilities and heat, engineering and electrical networks under the influence of environmental factors and the work of heating, ventilation and air conditioning has been analyzed. A general definition of the problem taking into account the transfer processes of internal voluminous or local heat source (drainage) has been considered. A generalized mathematical model (MM) of unsteady heat and mass transfer process for bodies of different canonical form (half-plate, hollow cylinder and sphere) and their analogues has been developed. In particular cases of the mathematical model, the dependence of the physical characteristics of the (solid isotropic) medium, the boundary conditions parameters, the capacity of the mass substance transfer sources (drains) from the transfer potentials (temperature, moisture content) or the space-time continuum has been taken into consideration. The analytical solution of the generalized non-stationary and stationary heat and mass transfer problem under the general boundary conditions of different (first, second, third and mixed) kind on the outline of the researched area has been scrutinized. For constant system parameters of non-stationary transfer processes an algorithm for solving differential transfer equations using Fourier transformation with variable parameters of different kind of boundary conditions has been shown. For large-scale transitions, practical applications, parametric analysis of the solutions obtained, setting optimization and automation tasks for process control systems, the obtained MM, analytical and approximate solutions of direct transfer short circuits are given a criterion form convenient for these purposes.