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Nelin. Dinam., 2018, Volume 14, Number 1, Pages 69–79 (Mi nd598)  

This article is cited in 1 scientific paper (total in 1 paper)

Original papers

Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer

V. V. Privalovaa, E. Yu. Prosviryakovba

a Institute of Ingineering Science UB RAS, ul. Komsomolskaya 34, Yekaterinburg, 620049, Russia
b Kazan National Research Technical University named after A.N. Tupolev, ul. Karla Marksa 10, Kazan, 420111, Russia

Abstract: This paper presents an exact solution to the Oberbeck Ц Boussinesq system which describes the flow of a viscous incompressible fluid in a plane channel heated by a linear point source. The exact solutions obtained generalize the isothermal Couette flow and the convective motions of Birikh Ц Ostroumov. A characteristic feature of the proposed class of exact solutions is that they integrate the horizontal gradient of the hydrodynamic fields. An analysis of the solutions obtained is presented and thus a criterion is obtained which explains the existence of countercurrents moving in a nonisothermal viscous incompressible fluid.

Keywords: Couette flow, Birikh Ц Ostroumova flow, planar Rayleigh Ц Benard convection, quadratic heating, exact solution, counterflow

DOI: https://doi.org/10.20537/nd1801007

Full text: PDF file (356 kB)
References: PDF file   HTML file

UDC: 532.51
MSC: 76F02, 76F45, 76M45, 76R05, 76U05
Received: 28.06.2017
Accepted:23.10.2017

Citation: V. V. Privalova, E. Yu. Prosviryakov, “Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer”, Nelin. Dinam., 14:1 (2018), 69–79

Citation in format AMSBIB
\Bibitem{PriPro18}
\by V.~V.~Privalova, E.~Yu.~Prosviryakov
\paper Steady convective Coutte flow for quadratic heating of the lower boundary fluid layer
\jour Nelin. Dinam.
\yr 2018
\vol 14
\issue 1
\pages 69--79
\mathnet{http://mi.mathnet.ru/nd598}
\crossref{https://doi.org/10.20537/nd1801007}
\elib{http://elibrary.ru/item.asp?id=32773040}


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    Citing articles on Google Scholar: Russian citations, English citations
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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  crossref  zmath  isi
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