К РЕШЕНИЮ ЗАДАЧ НЕСТАЦИОНАРНОЙ ДИФФУЗИИ В СЛОИСТЫХ СРЕДАХ

Abstract

The issues of nonstationary diffusion in layered structures are considered. When designing the devices for implementing mass transfer processes, it is necessary to take into account the properties of the substance and the nature of the processes. Design time reduces significantly and the efficiency of the devices is higher if a good physical model is built and a mathematical analysis with kinetics of the processes is applied. The difficulties of theoretical analysis and calculation of mass transfer are determined by the complexity of the transfer mechanism to and from the phase boundary. Therefore, simplified models of mass transfer processes are used in which the mass transfer mechanism is characterized by a combination of molecular and convective mass transfer. Many important practical problems involve the calculation of nonstationary diffusion (Fick's second law of diffusion) for a certain volume of substance (substances). For qualitative evaluation of processes, in the case of symmetry, volumetric issues can be considered as one-dimensional tasks, i.e. dependent on one coordinate. The general solution of the non-stationary diffusion equation for layered environments is proposed. The case of non-stationary boundary conditions of the third kind on the external surface and boundary conditions of the fourth kind conjugation for contiguous layers has been considered. The solution is obtained by separating the Fourier variables by the eigenfunctions of the problem using the Duhamel integral. The proposed solution is explicit and due to the recurrent form of the basic relations can be useful in numerical calculations