Ячеечная модель теплопроводности в многослойной среде с переменным числом слоев

Abstract

The heat conduction is an important part of heat transfer processes in power engineering, civil engineering, chemical technologies, etc. Variety of researches is devoted to theoretical and experimental study of the heat transfer by the heat conduction. At present, the considerable attention is concentrated on the heat conduction in media with variable boundaries (the so-called Stephan’s problem). A reason of a boundary motion can be burning-out of material, its wear, its melting with carry-over of a melt, other physic-chemical processes. Analytical solutions to the Stephan’s problem exist only after far-going assumptions, which lead to the loss of their practical value. The development of effective numerical methods of its solution becomes an actual scientific and practical problem. Such methods are to combine universality and physical clearness and convenience for engineering practice. In order to solve the problem, the method of mathematical modeling is used. The model uses the mathematical tools of the theory of Markov chains. It is adapted to the cell model of a medium, in which the number of cells can vary due to this or that mechanism of the edge cells interaction with outside medium. The heat transfer by the heat conduction and the heat interaction with the heat sources are described by the classical heat balance equations. The study of the influence of parameters on the process is performed by numerical methods. A mathematical model that allows describing transient heat processes in a multi-layer medium with variable number of layers is developed. The results of heat process calculation inside a plane wall with the moving boundary form the heat source side due to the boundary thermal distruction at a certain critical temperature are presented. The obtained results are physically consistent and approve the model workability. The principle differences between the heat processes in the walls with immovable and movable boundaries are found. It is shown that the temperature in a wall with moving boundary does not overbalance the critical temperature of the thermal distraction when the wall still exists, and the rate of the wall dimension decrease is growing with its dimension decrease.