Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 165, Pages 63–72
DOI: https://doi.org/10.36535/0233-6723-2019-165-63-72 (Mi into467) 		 
Mathematical modeling of the free surface of a magnetic fluid surrounding a magnetized plate

A. Ya. Simonovskiia, O. A. Grishaninab, D. B. Litvinc

a North-Caucasus Federal University
b Moscow State Pedagogical University, Stavropol branch
c Stavropol State Agrarian University
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DOI: https://doi.org/10.36535/0233-6723-2019-165-63-72
Abstract: We propose a mathematical model that allows one to describe the shape of the free surface of a magnetic fluid surrounding a thin flat magnetized plate with infinite magnetic susceptibility. The Maxwell equations and the hydrostatics equations for magnetic fluid with the corresponding boundary conditions on the free surface of the magnetic fluid are solved. By methods of complex analysis, we find the distribution of the magnetic field and the pressure in the magnetic fluid surrounding the plate. An equation for the shape of the free surface of a magnetic fluid near the plate is written, and graphs of equilibrium shapes of the free surface of the magnetic fluid in a neighborhood of the plate are given for various volumes of the fluid and the angle between the plate and the vector of the external magnetic field.
Keywords: magnetic fluid, heat transfer, hydrodynamics, steel plate, magnetic field.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00037_а
This work was supported by the Russian Foundation for Basic Research (project No. 17-01-00037).
Bibliographic databases:
Document Type: Article
UDC: 517.958; 536.242
MSC: 49M30, 49М37
Language: Russian
Citation: A. Ya. Simonovskii, O. A. Grishanina, D. B. Litvin, “Mathematical modeling of the free surface of a magnetic fluid surrounding a magnetized plate”, Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics". Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 165, VINITI, Moscow, 2019, 63–72
Citation in format AMSBIB
\Bibitem{SimGriLit19}
\by A.~Ya.~Simonovskii, O.~A.~Grishanina, D.~B.~Litvin
\paper Mathematical modeling of the free surface of a~magnetic fluid surrounding a~magnetized plate
\inbook Proceedings of the IV International Scientific Conference "Actual Problems of Applied Mathematics".
Kabardino-Balkar Republic, Nalchik, Elbrus Region, May 22–26, 2018. Part I
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 165
\pages 63--72
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into467}
\crossref{https://doi.org/10.36535/0233-6723-2019-165-63-72}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4030611}
\elib{https://elibrary.ru/item.asp?id=42639618}
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