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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, Volume 22, Number 3, Pages 532–548 (Mi vsgtu1638)  

This article is cited in 9 scientific papers (total in 9 papers)

Mathematical Modeling, Numerical Methods and Software Complexes

Couette–Hiemenz exact solutions for the steady creeping convective flow of a viscous incompressible fluid, with allowance made for heat recovery

V. V. Privalovaa*, E. Yu. Prosviryakovba

a Institute of Engineering Science, Urals Branch, Russian Academy of Sciences, Ekaterinburg, 620049, Russian Federation
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg, 620002, Russian Federation

Abstract: In this paper, we study the steady creeping convective flow of a viscous incompressible fluid in the thin infinite layer. The study of the fluid flow is based on the exact solutions class for the Oberbeck–Boussinesq equations in the Stokes approximation using. The velocity field is described by the Hiemenz exact solution. The temperature field and the pressure field linearly depend on the horizontal (longitudinal) coordinate, it corresponds to the Ostroumov–Birich exact solutions class. The convective motion of a viscous incompressible fluid was induced by tangential stresses on the upper permeable (porous) boundary and thermal source definition at the lower boundary. In addition, the heat exchange according to the Newton–Richmann law takes into account at the upper boundary. The obtained exact solutions describe counterflows in fluids. The stagnant points number in the fluid layer does not exceed three. The formation of counterflows in the fluid is accompanied by sucking and injection of the fluid through the permeable boundary. The larger number of stagnant points presence forms a cellular structure of the streamlines. In addition, the velocity field, which obtained in the solution of the boundary value problem is characterized by localization of the flow near the boundary of the fluid layer (boundary layer). The exact solutions obtained in this paper can be used for the nonlinear Oberbeck–Boussinesq system solving. The Grashof number can take large values, which depends on the geometric anisotropy index for the linearized Oberbeck–Boussinesq system.

Keywords: counterflow, exact solution, Stokes approximation, stagnation point

Funding Agency Grant Number
Russian Academy of Sciences - Federal Agency for Scientific Organizations АААА-А18-118020790140-5
The work was done within the state assignment from FASO Russia, theme No. АААА-А18-118020790140-5.

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.14498/vsgtu1638

Full text: PDF file (933 kB) (published under the terms of the Creative Commons Attribution 4.0 International License)
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Bibliographic databases:

UDC: 532.51, 517.958:531.3-324
MSC: 76F02, 76F45, 76M45, 76R05, 76U05
Received: July 25, 2018
Revised: August 21, 2018
Accepted: September 3, 2018
First online: October 4, 2018
Language:

Citation: 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. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:3 (2018), 532–548

Citation in format AMSBIB
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with allowance made for heat recovery
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
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\pages 532--548
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\crossref{https://doi.org/10.14498/vsgtu1638}
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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. N. V. Burmasheva, E. Yu. Prosviryakov, “Convective layered flows of a vertically whirling viscous incompressible fluid. Velocity field investigation”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:2 (2019), 341–360  mathnet  crossref  elib
    2. G. I. Kelbaliev, S. R. Rasulov, “Matematicheskoe modelirovanie protsessov koalestsentsii i drobleniya kapel i puzyrei v izotropnom turbulentnom potoke (obzor)”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 23:3 (2019), 541–581  mathnet  crossref  elib
    3. N. V. Burmasheva, E. Y. Prosviryakov, “Layered convective flows of vertically swirling incompressible fluid affected by tangential stresses” (Ekaterinburg, Russian Federation, 9–13 December 2019), AIP Conference Proceedings, 2176, 13th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures, MRDMS 2019 (2019), 030025  crossref  scopus
    4. N. V. Burmasheva, E. A. Larina, E. Y. Prosviryakov, “Unidirectional convective flows of a viscous incompressible fluid with slippage in a closed layer” (Ekaterinburg, Russian Federation, 9–13 December 2019), AIP Conference Proceedings, 2176, 13th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures, MRDMS 2019 (2019), 030023  crossref  scopus
    5. N. V. Burmasheva, E. Y. Prosviryakov, “Unidirectional thermocapillary flows of a viscous incompressible fluid with the Navier boundary condition” (Ekaterinburg, Russian Federation, 9–13 December 2019), AIP Conference Proceedings, 2176, 13th International Conference on Mechanics, Resource and Diagnostics of Materials and Structures, MRDMS 2019 (2019), 030002  crossref  scopus
    6. A. A. Domnich, E. S. Baranovskii, M. A. Artemov, “On a mathematical model of non-isothermal creeping flows of a fluid through a given domain”, Vestn. Samar. Gos. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 23:3 (2019), 417–429  crossref  zmath  isi  scopus
    7. Victor K. Andreev, Natalya L. Sobachkina, “Rotationally-axisymmetric motion of a binary mixture with a flat free boundary at small Marangoni numbers”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 197–212  mathnet  crossref
    8. J. Zhao, “Axisymmetric convection flow of fractional maxwell fluid past a vertical cylinder with velocity slip and temperature jump”, Chin. J. Phys., 67 (2020), 501–511  crossref  mathscinet  isi  scopus
    9. S. R. Rasulov, G. T. Hasanov, A. N. Zeynalov, “Acoustic testing of rheological properties of oil in orehole”, News Natl. Acad. Sci. Rep. Kazakstan-Ser. Geol. Tech. Sci., 2020, no. 2, 141–147  crossref  isi  scopus
  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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