TY - JOUR
AU - Tashev, A.
AU - Kazykhan, R.
AU - Aitbayeva, B.
PY - 2023/04/07
Y2 - 2024/09/10
TI - 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
JF - Journal of Mathematics, Mechanics and Computer Science
JA - JMMCS
VL - 117
IS - 1
SE - Applied Mathematics
DO - 10.26577/JMMCS.2023.v117.i1.07
UR - https://bm.kaznu.kz/index.php/kaznu/article/view/1158
SP -
AB - <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>
ER -