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Sibirskii Zhurnal Industrial'noi Matematiki, 2022, Volume 25, Number 2, Pages 5–20
DOI: https://doi.org/10.33048/SIBJIM.2021.25.201
(Mi sjim1168)
 

The heat convection in a rotating tube

V. K. Andreevab, I. V. Vakhràmeevb, E. P. Magdenkoba

a Institute of Computational Modeling SB RAS, Akademgorodok 50/44, Krasnoyarsk 660036, Russia
b Institute of Mathematics and Fundamental Informatics Siberian Federal University, pr. Svobodny 79, Krasnoyarsk 660041, Russia
References:
Abstract: The unsteady boundary value fluid motion problem in the rotating cylindrical tube is investigated. There are no mass forces, since it is assumed that the angular velocity of the cylinder rotation is high enough. The Oberbeck—Boussinesq equations are used to describe the fluid motion. From the mathematical point of view, the problem is inverse with respect to the pressure gradients along the cylinder axis. Based on the priori estimates, conditions are obtained under which the stationary inverse problem solution is exponentially stable. In Laplace images, the solution is found in the form of quadratures. Sufficient conditions are given for the non-stationary problem solution to reach the stationary mode with increasing time.
Keywords: convection, inverse problem, priori estimates, asymptotic behavior, Laplace transform. .
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1384
Received: 17.11.2021
Revised: 30.12.2021
Accepted: 13.01.2022
Document Type: Article
UDC: 532.5.013.4
Language: Russian
Citation: V. K. Andreev, I. V. Vakhràmeev, E. P. Magdenko, “The heat convection in a rotating tube”, Sib. Zh. Ind. Mat., 25:2 (2022), 5–20
Citation in format AMSBIB
\Bibitem{AndVakMag22}
\by V.~K.~Andreev, I.~V.~Vakhràmeev, E.~P.~Magdenko
\paper The~heat convection in~a~rotating tube
\jour Sib. Zh. Ind. Mat.
\yr 2022
\vol 25
\issue 2
\pages 5--20
\mathnet{http://mi.mathnet.ru/sjim1168}
\crossref{https://doi.org/10.33048/SIBJIM.2021.25.201}
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