DEVELOPMENT OF METHODS AND ALGORITHMS FOR ESTIMATING THE TEMPERATURE DISTRIBUTION IN THE BODY OF A RECTANGULAR PARALLELEPIPED SHAPE UNDER THE INFLUENCE OF HEAT FLOW AND THE PRESENCE OF HEAT EXCHANGE

Authors

• A. Tashev Institute of Information and Computing Technologies of the KN MES RK
• R. Kazykhan Al-Farabi Kazakh National University
• B. Aitbayeva Al-Farabi Kazakh National University

84 84

Keywords:

variational approach, thermal conductivity, heat flow, rectangular parallelepiped, heat exchange, temperature

Abstract

The article describes methods and computational algorithms for estimating the temperature
distribution law in the body of a rectangular parallelepiped shape under the influence of heat flow
and the presence of heat exchange. It is believed that one of the faces is amenable to heat flow, and
the other faces are insulated or are under the influence of the environment. To use the variational
approach, the total energy functional is calculated, taking into account the boundary conditions.
Minimizing the functional and equating it to zero, we obtain a system of linear equations, the
solution of which gives the temperature of a rectangular parallelepiped at the nodal points. Further,
substituting these nodal temperature values into the approximating function, we obtain the law of
temperature distribution in the body in the form of a rectangular parallelepiped. The temperature
distribution law is obtained by dividing a rectangular parallelepiped into one, two and three
elements. To speed up the process of calculating the temperature distribution law, an algorithm has
been developed that allows you to create a program code that increases the calculation efficiency by
an order of magnitude. This is achieved by the fact that the created code contains only a system
of linear equations, unlike the main program, which forms a general functional of full energies,
calculates derivatives of this functional and obtains a system of equations.

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2023-04-07

How to Cite

Tashev, A., Kazykhan, R., & Aitbayeva, B. (2023). DEVELOPMENT OF METHODS AND ALGORITHMS FOR ESTIMATING THE TEMPERATURE DISTRIBUTION IN THE BODY OF A RECTANGULAR PARALLELEPIPED SHAPE UNDER THE INFLUENCE OF HEAT FLOW AND THE PRESENCE OF HEAT EXCHANGE. Journal of Mathematics, Mechanics and Computer Science, 117(1). https://doi.org/10.26577/JMMCS.2023.v117.i1.07

Section

Applied Mathematics