APPLICATION OF «MICRO-PROCESSES» METHOD FOR MODELING HEAT CONDUCTION AND DIFFUSION PROCESSES IN CANONICAL BODIES

Abstract

This paper shows that, in many technological processes, raw materials are subjected to high-temperature heat treatment and, in most cases, they have a geometric shape of the canonical form: a plate, a cylinder and a sphere. The convection drying process is considered as a typical heat and mass transfer process. The processes occurring under heat treatment conditions are reduced to transfer problems for an unbounded plate, cylinder, and ball with boundary conditions of the first kind, when the transfer potential (temperature, moisture content) is set on the surface of a solid. A number of expressions for calculations in the context of arbitrary distribution of initial values of transfer potentials as well as for uniform distributions are presented. It is shown that, when modeling heat and mass transfer processes in which the thermophysical characteristics of a solid body change significantly in the course of thermal treatment thereof, the use of already known solutions that have been previously developed becomes problematic. The «zonal» method and the «micro-processes» method are considered herein. It is shown that, for both methods, on the basis of experimental data referring to the dynamics of temperature and mass (moisture) content of the material over the course of the process, their dependences on the average (for the «zone» or «micro - process») temperatures and mass contents are determined. The next stage for calculations using the «zonal» method is formalization of the results obtained in the form of histograms of the values of mass conductivity coefficients from the average values of mass contents. For the «micro-processes» method, the kinetic curve can be used in calculations simultaneously. The smaller the range of measured values of temperatures and mass contents is the greater is the adequacy of calculated experimental data. It is emphasized that, under uneven initial conditions, analytical solutions to the heat transfer problem are usually presented in the form of infinite Fourier series. The convergence of the Fourier series deteriorates with decreasing time intervals. The great relevance of the application of the considered methods can be traced when modeling heat and mass transfer with intensive processes of phase transitions.