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.