Numerical-Analytical Method for Reducing Problems of Non-Stationary Heat Conduction with Boundary Conditions of the III Kind to Problems with Conditions of the I Kind

In the technological problems of construction, problems often arise associated with the development of mathematical models for the processes of heat treatment of solids. It should be noted that the solution to the problems of developing mathematical models of such processes and the development of methods for optimizing the operation of equipment is the formulation and solution of boundary value problems of non-stationary heat and moisture transfer in the “gas-solid body” system. Modern software and hardware systems will make it possible to create mathematical models of building structures of complex geometric shapes. At the same time, simplification of both mathematical models of complex systems and calculation methods becomes acceptable. With this approach, complex geometric shapes such as two-layer cylinders and spheres, which are technological equipment, can be considered as a plate for modeling purposes, since the ratio of the thickness of the material layer to the radius of the cylinder (ball) is less than 0.5. It should also be noted that in real heat treatment processes, all thermophysical characteristics depend on temperature and, accordingly, change their values during the process. The thermophysical characteristics of the environment in which the material is processed (temperature and humidity parameters) also change with the time of the process. An approach is outlined below, the essence of which is to use the numerical-analytical method of “microprocesses”. The main advantage of the proposed approach in relation to the problem under consideration is the “avoidance” of the need to search for the roots of the transcendental characteristic equation, since the roots of the characteristic equations acquire a simplified form.

S.V. FEDOSOV¹, Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.);
V.N. FEDOSEEV², Doctor of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.),
V.A. VORONOV², Candidate of Sciences (Engineering) (This email address is being protected from spambots. You need JavaScript enabled to view it.)

¹ National Research Moscow State University of Civil Engineering (26, Yaroslavskoe Highway, Moscow, 129337, Russian Federation)
² Ivanovo State Polytechnic University (21, Sheremetevsky Avenue, Ivanovo, 153000, Russian Federation)

1. Lykov A.V., Mikhailov Yu.A. Teoriya perenosa energii i veshchestva [Theory of energy and substance transfer] Minsk: Acad. Sciences of the BSSR. 1959. 332 p.
2. Lykov A.V. Teoriya teploprovodnosti [Theory of thermal conductivity]. Moscow: Higher school, 1967. 600 p.
3. Rudobashta S.P. Mass transfer in a solid phase system [Mass transfer in a system with a solid phase]. Moscow: Khimiya. 1980. 248 p.
4. Rudobashta S.P., Kartashov E.M. Diffuziya v khimiko-tekhnologicheskikh protsessakh [Diffusion in chemical-technological processes]. Moscow: KolosS, 2010. 478 p.
5. Kartashov E.M. Analiticheskie metody v teorii teploprovodnosti tverdykh tel [Analytical methods in the theory of thermal conductivity of solids]. Moscow: Vysshaya shkola. 2001. 480 p.
6. Fedosov S.V. Teplomassoperenos v tekhnologicheskikh protsessa stroitel’noy industrii: monografiya [Heat and mass transfer in the technological process of the construction industry]. Ivanovo: IPK “PresSto”. 2010. 363 p.
7. Carslow G., Eger R. Teploprovodnost’ tverdykh tel [Thermal conductivity of solids]. Moscow: Nauka. 1964. 488 p.
8. Kudinov I.V., Stefanuk E.V. Teoreticheskie osnovy teplotekhniki. Chast’ 1. Termodinamika: uchebnoe posobie. [Theoretical foundations of heat engineering. Part 1. Thermodynamica: textbook]. Samara: SGASU. 2013. 172 p.
9. Fedosov S.V., Bakanov M.O. Modeling of non-stationary heat conduction and diffusion processes in canonical bodies using the “microprocesses” method. Collection of scientific papers of the International Scientific and Technical Symposium of the III International Kosygin Forum “Modern problems of engineering sciences”. Moscow. 2021, pp. 25–30.
10. Fedosov S.V., Bakanov M.O Modeli i metody vysokotemperaturnoy termicheskoy obrabotki v tekhnologii penostekla [Models and methods of high-temperature heat treatment in foam glass technology]. Moscow: Sputnik+, 2021. 302 p.