Abstract
The analytical study of the processes of thermal conductivity at high intensity heating of dense bodies, similar to clay and plastic materials, was conducted. The conditions of applicability for the hyperbolic and parabolic equation of thermal conductivity for the composition of mathematical models of high intensity heating were explored. It was found that for the small Fourier numbers, the solution of hyperbolic equation of thermal conductivity makes it possible to determine thickness of the thermal layer and its change over time. Based on the example of manufacturing technical ceramics, it was demonstrated that the possible heating rates are considerably below the boundary rate, within which the velocity of heat propagation may be accepted as infinitely high. The conclusion was drawn that in the course of construction of mathematical models for the processes of thermal treatment in the technologies for the production of technical ceramics and the products similar to them in the intensity of heating, it is rational to take the thermal conductivity equation of parabolic type as the basis. The analytical solution, which makes it possible to calculate temperature field of the semirestricted array under conditions of microwave heating, was obtained on the basis of the equation of thermal conductivity with internal heat sources, taking into consideration heat exchange with the environment. Results of computational experiment testify to the correctness of the proposed dependency.
Highlights
The application of methods of high-energy influence and their combining with the traditional technologies of thermal treatment of clay and plastic materials sets the aim of obtaining the assigned working properties and characteristics: the degree of resistance to wear and cracking, resistance to the influence of high temperatures, and the required mechanical and physical internal structure
The efficiency of obtaining such materials depends on the special features of forming the temperature field in a body, and obtaining data about it requires reliable mathematical models
The purpose of the work is to build up mathematical models of high intensity heating of dense bodies, the properties of which are similar to clay materials and plastics, used in the production of technical ceramics and different compositional articles
Summary
The application of methods of high-energy influence and their combining with the traditional technologies of thermal treatment of clay and plastic materials sets the aim of obtaining the assigned working properties and characteristics: the degree of resistance to wear and cracking, resistance to the influence of high temperatures, and the required mechanical and physical internal structure. Such materials find their use in machine building, microelectronics, biomechanics, power engineering, as well as in the aerospace and transport industry [1,2,3]. Analytical solutions give the opportunity to carry out computational experiments and, as a result, to obtain new knowledge about the influence of a wide spectrum of parameters of the process on the thermal state of the body
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