Modeling of a temperature field for extruder body
DOI:
https://doi.org/10.20535/SRIT.2308-8893.2021.2.10Keywords:
equivalent simplification, extruder, induction heating, integral transformations, polymer, Bessel functionsAbstract
The paper considers the process of induction heating of the extruder body, the temperature of which determines the degree of heating of the polymer mixture in the zone of loading the dry mixture. A mathematical model of this process is formulated taking into account radiant heat transfer in the gap between the inductor and the case. An iterative numerical-analytical method is proposed for solving the corresponding nonlinear boundary value problem of housing heating, at the first iteration of which a linear boundary value problem is solved (without taking into account radiant heat transfer). At the subsequent stages, a nonlinear boundary value problem is solved. The iterative method is based on the application of integral transformations of the linear part of the problem, followed by an iterative scheme for finding a nonlinear problem. This scheme is based on the algorithms for the equivalent simplification of the expressions obtained by solving the problem. The results of mathematical modeling of the corresponding algorithms are presented.
References
A. Zhuchenko, A. Kubrak, and A. Dankevych, “Mathematical description of the thermal regime of the extruder”, Bulletin of NTUU “KPI”, Chemical Engineering, Ecology and Resource Conservation, pp. 11–22, 2016.
V. Pervadchuk, Processes of movement, heat exchange and phase transformations of non-Newtonian materials in screw devices: Dis. Dr. Tech. Sciences in special. Perm, 1984, 377 p.
E. Subbotin and R. Zinnatullin, “Experimental determination of rheological characteristics of polymer melt in numerical modeling of the extrusion process”, Nauch.-tehn. Bulletin of the Volga region, pp. 28–30, 2015.
N. Trufanova, A. Shcherbinin, and V. Yankov, Melting of polymers in extruders. Moscow-Izhevsk: Regular and chaotic dynamics, 2009, 336 p.
N. Trufanova, Polymer processing. Perm: Publishing House of Perm. State Tech. University, 2009, 158 p.
V. Mitroshin, “Structural modeling of the temperature field of the polymer melt in the dosing zone of a single-worm extruder”, Vestnik Samar. state tech. un-ta, ser.: Technical sciences, no. 41, pp.191–194, 2006.
K. Zelensky, V. Ignatenko, and O. Kots, Computer methods of applied mathematics. Kyiv: Akademperiodika, 2003, 480 p.
N. Zelenskaya and K. Zelensky, “Approximation of cylindrical functions by fractional-rational expressions”, Bulletin of the University “Ukraine”, series: Informatics, Computer Science and Cybernetics, no. 1, pp. 78–83, 2016.
