Nelineinaya Dinamika [Russian Journal of Nonlinear Dynamics]
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 Nelin. Dinam., 2018, Volume 14, Number 1, Pages 81–97 (Mi nd599)

Original papers

Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient

M. S. Deryabina, S. I. Martynov

Ugra State University, ul. Chekhova 16, Khanty-Mansiysk, 119991, Russia

Abstract: A procedure is proposed for constructing an approximate periodic solution to the equations of motion of a viscous fluid in an unbounded region in the class of piecewise smooth functions for a given gradient of pressure and temperature for small Reynolds numbers. The procedure is based on splitting the region of the liquid into cells, and finding a solution with boundary conditions corresponding to the periodic function. The cases of two- and three-dimensional flows of a viscous fluid are considered. It is shown that the solution obtained can be regarded as a flow through a periodic system of point particles placed in the cell corners. It is found that, in a periodic flow, the fluid flow rate per unit of cross-sectional area is less than that in a similar Poiseuille flow.

Keywords: viscous fluid, periodic solution, piecewise function, gradient, pressure, temperature

 Funding Agency Grant Number Russian Foundation for Basic Research 15-41-00077

DOI: https://doi.org/10.20537/nd1801008

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UDC: 532.529:541.182
MSC: 76D07, 76D09, 76D17
Accepted:06.03.2018

Citation: M. S. Deryabina, S. I. Martynov, “Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient”, Nelin. Dinam., 14:1 (2018), 81–97

Citation in format AMSBIB
\Bibitem{DerMar18} \by M.~S.~Deryabina, S.~I.~Martynov \paper Periodic flow of a viscous fluid with a predetermined pressure and temperature gradient \jour Nelin. Dinam. \yr 2018 \vol 14 \issue 1 \pages 81--97 \mathnet{http://mi.mathnet.ru/nd599} \crossref{https://doi.org/10.20537/nd1801008} \elib{https://elibrary.ru/item.asp?id=32773041} 

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This publication is cited in the following articles:
1. Privalova V.V. Prosviryakov E.Yu., “Couette-Hiemenz Exact Solutions For the Steady Creeping Convective Flow of a Viscous Incompressible Fluid With Allowance Made For Heat Recovery”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:3 (2018), 532–548
2. M. S. Deryabina, S. I. Martynov, “O techenii vyazkoi zhidkosti s zadannym gradientom davleniya cherez periodicheskie struktury”, Zhurnal SVMO, 21:2 (2019), 222–243
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