Journal of Siberian Federal University. Engineering & Technologies / Simulation and Calculation of Heat Transfer in Multilayer Wall Structures Based on Iterative Models

Full text (.pdf)
Issue
Journal of Siberian Federal University. Engineering & Technologies. 2022 15 (5)
Authors
Zhakatayev, Toksan; Kakimova, Klara; Taukenova, Liazat; Serikov, Tansaule
Contact information
Zhakatayev, Toksan: Turan-Astana University Nur-Sultan, Kazakhstan; ; Kakimova, Klara: Karaganda State Technical University Karaganda, Kazakhstan; Taukenova, Liazat: Turan-Astana University Nur-Sultan, Kazakhstan; Serikov, Tansaule: S. Seifullin Agrotechnical Universit Nur-Sultan, Kazakhstan
Keywords
wall many layers; heat transfer; nonlinear boundary conditions; iterative calculations; systems of equations; heat flows
Abstract

Through heat transfer is considered: heat carrier, liquid medium 1 – wall of arbitrary n layers – liquid external medium 2, cooler. For heat flows, a system of (n + 1) nonlinear equations is considered. The method of excluding unknowns sequentially calculates all values of tw, i. The design scheme allows iterative calculations of wall temperature from one to three layers and, accordingly, five heat flows. The novelty of the solution is that the temperature of the first wall tw,1 and the last wall tw, n+1 are not set, but are unknown. They are calculated using an iterative scheme. If you further increase the number of wall layers, the calculations become cumbersome. We are talking about the explicit expression of all tw, i through formulas based on the manual transformation of equations. Optimally bringing the problem to a closed and defined system (n + 1) of equations for (n + 1) unknown wall temperatures tw, i. This system of equations is easily calculated in mass accessible packets, to which Matlab belongs. The advantage is a matrix solution of the entire system at once. In the case of a system of cylindrical and spherical walls, the problem is also solvable. New coefficients have been established for these systems of equations. Which allows you to save balance equations for heat flows

Pages
622–633
DOI
10.17516/1999-494X‑0410
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/148774

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