5d62206f-eb2b-4bcf-89d5-fd2c6c7df8c020230710084602691naun:naunmdt@crossref.orgMDT DepositInternational Journal of Mechanics1998-444810.46300/9104http://www.naun.org/cms.action?id=28283320233320231710.46300/9104.2023.17https://npublications.com/journals/mechanics/2023.phpDevelopment of Methods and Computational Algorithms Parallelepiped in the Presence of Temperature and Heat ExchangeKazykhanRysgulAl-Farabi Kazakh National University, 050040, Almaty, KazakhstanTashevAzatInstitute of Information and Computing Technologies Committee of Science MON RK, 050040, Almaty, KazakhstanAitbayevaRakhatayAl-Farabi Kazakh National University, 050040, Almaty, KazakhstanKudaykulovAnarbayInstitute of Information and Computing Technologies Committee of Science MON RK, 050040, Almaty, KazakhstanKunelbayevMuratInstitute of Information and Computing Technologies Committee of Science MON RK, 050040, Almaty, KazakhstanMukaddasArshidinovaAl-Farabi Kazakh National University, 050040, Almaty, KazakhstanZhunusovaAliyaNarkhoz University, 050040, Almaty, KazakhstanKazangapovaBayanAlmaty Technological University, 050040, Almaty, KazakhstanThe article describes computational algorithms for estimating the law of distribution of body temperature in the form of a rectangular parallelepiped. The case is studied when a conditioned temperature is maintained on one of the boundaries of a rectangular parallelepiped, and heat exchange with the environment occurs on the opposite side. In addition, there are cases when other faces of the parallelepiped are thermally insulated or are under the influence of the environment. A polynomial is chosen as the approximating function. In accordance with the proposed layout, a function is formed that considers temperature, heat exchange with the environment, and insulation of the faces of a rectangular parallelepiped. The temperatures at the nodal points are determined by minimizing the function. Further, the temperature distribution law is determined according to the proposed approximating polynomial. The estimation of temperature distribution law is calculated for different amounts of partitioning into elements of a rectangular parallelepiped.7102023710202357639https://npublications.com/journals/mechanics/2023/a182003-009(2023).pdf10.46300/9104.2023.17.9https://npublications.com/journals/mechanics/2023/a182003-009(2023).pdfJ. L. Segerlind, “Applied finite element analysis”, New York-London-Sydney-Toronto, Jonh Wiley and Song, 1976. 10.1515/eng-2018-0020A. Kudaykulov, A.A. Tashev, A. Askarova, “Computational algorithm and the method of determining the temperature field along the length of the rod of variable cross section”, Open Engineering, vol.8, 2018, pp. 170-175. J. L. Segerlind, “Applied finite element analysis”, New York-London-Sydney-Toronto, Jonh Wiley and Song, 1976. 10.1109/icisce.2018.00080Arshidinova М, Begaliyeva K, Kudaykulov А, Tashev А, “Numerical Modeling Of Nonlinear Thermomechanical Processes in a rod of variable cross section in the presence of heat flow”, International Conference on Information Science and Control Engineering,2018, pp. 351-354. 10.1016/j.ijheatmasstransfer.2004.04.021J. V. Beck, “Verification solution for partial heating of rectangular solids”, International Journal of Heat and Mass Transfer”, vol. 47, 2004, pp. 4243–4255. 10.1016/j.ijheatmasstransfer.2006.06.032J. V. Beck, K. D. Cole, “Improving convergence of summations in heat conduction, International Journal of Heat and Mass Transfer”, vol. 50, 2007, pp. 257–268. 10.1016/0017-9310(69)90136-7Y. O. Nurettin, «General solution to a class of unsteady heat conduction problems in a rectangular parallelepiped», International Journal of Heat and Mass, vol. 12, 1969, pp 393-411. 10.1007/978-1-4471-1915-9_6J. W. Vergnaud, J. Bouzon, «Heat conduction n a Rectangular parallelepiped», Cure pf thermosetting Resins, pp 89-93. 10.3390/axioms11090488D. Kumar, F. Y. Ayant, C. Cesarano, «Analytical Solutions of Temperature Distribution in a Rectangular Parallelepiped», Axioms, vol. 11, 2022, pp 488. 10.46793/kgjmat2103.439kD. Kumar, F. Y. Ayant, «Application of Jacobi Polynomial and Multivariable Aleph-Fuctional in heat conduction in Non-Homogeneous moving rectangular parallelepiped» Kragujevac Journal of Mathematics, vol 45, 2021, pp439-448. 10.46300/9104.2022.16.8A. A. Tashev, A. K. Kudaykulov, R. K. Kazykhan, R. B. Aitbayeva, M. Arshidinova, M. M. Kunelbayev, D. A. Kuanysh, “Variational approach for estimating the temperature distribution in the body of a rectangular parallelepiped shape”, Vol. 16, pp. 10, (2022).