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Nelin. Dinam., 2016, Volume 12, Number 2, Pages 167–178 (Mi nd519)  

This article is cited in 4 scientific papers (total in 4 papers)

Original papers

Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer

S. N. Aristova, V. V. Privalovab, E. Yu. Prosviryakovcb

a Institute of Continuous Media Mechanics UB RAS, 1, Ak. Koroleva str., Perm, 614013
b Institute of Ingineering Science UB RAS, 34, Komsomolskaya str., Yekaterinburg, 620049
c Kazan National Research Technical University named after A.N.Tupolev, 10, Karl Marx str., Kazan, Russia, 420111

Abstract: A new exact solution of the two-dimensional OberbeckBoussinesq equations has been found. The analytical expressions of the hydrodynamic fields, which have been obtained, describe convective Couette flow. Fluid flow occurs in the case of nonuniform distribution of velocities and the quadratic heat source at the upper boundary of an infinite layer of viscous incompressible fluid. Two characteristic scales have been introduced for finding the exact solutions of the OberbeckBoussinesq equations. Using the anisotropic layer allows one to explore large-scale flows of liquids for large values of the Grashof number. A connection is shown between solutions describing the quadratic heating of boundaries with boundary problems concerned with motions of fluids in which the temperature is distributed linearly. Analysis of polynomial solutions describing the natural convection of the fluid is presented. The existence of points at which the hydrodynamic fields vanish inside the fluid layer. Thus, the above class of exact solutions allows us to describe the counterflows in the fluid and the separations of pressure and temperature fields.

Keywords: Couette flow, linear heating, quadratic heating, convection, exact solution, polynomial solution

Funding Agency Grant Number
Foundation for Assistance to Small Innovative Enterprises in Science and Technology


Full text: PDF file (301 kB)
References: PDF file   HTML file
UDC: 532.51
MSC: 76F02, 76F45, 76M45, 76R05, 76U05
Received: 22.06.2015
Revised: 14.05.2016

Citation: S. N. Aristov, V. V. Privalova, E. Yu. Prosviryakov, “Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer”, Nelin. Dinam., 12:2 (2016), 167–178

Citation in format AMSBIB
\Bibitem{AriPriPro16}
\by S.~N.~Aristov, V.~V.~Privalova, E.~Yu.~Prosviryakov
\paper Stationary nonisothermal Couette flow. Quadratic heating of the upper boundary of the fluid layer
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 2
\pages 167--178
\mathnet{http://mi.mathnet.ru/nd519}
\elib{http://elibrary.ru/item.asp?id=26193555}


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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. V. V. Privalova, E. Yu. Prosviryakov, “Statsionarnoe konvektivnoe techenie KuettaKhimentsa pri kvadratichnom nagreve nizhnei granitsy sloya zhidkosti”, Nelineinaya dinam., 14:1 (2018), 69–79  mathnet  crossref  elib
    2. E. Yu. Prosviryakov, “Dynamic equilibria of a nonisothermal fluid”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:4 (2018), 735–749  mathnet  crossref  elib
    3. V. V. Privalova, E. Yu. Prosviryakov, “Couette–Hiemenz exact solutions for the steady creeping convective flow of a viscous incompressible fluid, with allowance made for heat recovery”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 22:3 (2018), 532–548  mathnet  crossref  zmath  isi  elib
    4. V. V. Privalova, E. Yu. Prosviryakov, M. A. Simonov, “Nonlinear Gradient Flow of a Vertical Vortex Fluid in a Thin Layer”, Nelineinaya dinam., 15:3 (2019), 271–283  mathnet  crossref  mathscinet
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