@article{Tashev_Kazykhan_Aitbayeva_2023, title={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}, volume={117}, url={https://bm.kaznu.kz/index.php/kaznu/article/view/1158}, DOI={10.26577/JMMCS.2023.v117.i1.07}, abstractNote={<p>The article describes methods and computational algorithms for estimating the temperature<br>distribution law in the body of a rectangular parallelepiped shape under the influence of heat flow<br>and the presence of heat exchange. It is believed that one of the faces is amenable to heat flow, and<br>the other faces are insulated or are under the influence of the environment. To use the variational<br>approach, the total energy functional is calculated, taking into account the boundary conditions.<br>Minimizing the functional and equating it to zero, we obtain a system of linear equations, the<br>solution of which gives the temperature of a rectangular parallelepiped at the nodal points. Further,<br>substituting these nodal temperature values into the approximating function, we obtain the law of<br>temperature distribution in the body in the form of a rectangular parallelepiped. The temperature<br>distribution law is obtained by dividing a rectangular parallelepiped into one, two and three<br>elements. To speed up the process of calculating the temperature distribution law, an algorithm has<br>been developed that allows you to create a program code that increases the calculation efficiency by<br>an order of magnitude. This is achieved by the fact that the created code contains only a system<br>of linear equations, unlike the main program, which forms a general functional of full energies,<br>calculates derivatives of this functional and obtains a system of equations.</p>}, number={1}, journal={Journal of Mathematics, Mechanics and Computer Science}, author={Tashev, A. and Kazykhan, R. and Aitbayeva, B.}, year={2023}, month={Apr.} }