Abstract:
In the work the 3D two-layer motion of liquids, the velocity field of which has a special form, is considered. The arising conjugate initial boundary value problem for the Oberbek–Boussinesq model is reduced to a system of ten integrodifferential equations with full conditions on a flat interface. It is shown that for small Marangoni numbers the stationary problem can have up to two solutions. The case when the stationary flow arises due to a change in the internal interphase energy is analyzed separately.
This research was supported by the Russian Foundation for Basic Research (20-01-00234) and Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement no. 075-02-2020-1631).
Received: 22.06.2020 Received in revised form: 02.07.2020 Accepted: 20.09.2020
Bibliographic databases:
Document Type:
Article
UDC:
517.977.55:536.25
Language: English
Citation:
Viktor K. Andreev, “On a creeping 3D convective motion of fluids with an isothermal interface”, J. Sib. Fed. Univ. Math. Phys., 13:6 (2020), 661–669
\Bibitem{And20}
\by Viktor~K.~Andreev
\paper On a creeping 3D convective motion of fluids with an isothermal interface
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2020
\vol 13
\issue 6
\pages 661--669
\mathnet{http://mi.mathnet.ru/jsfu871}
\crossref{https://doi.org/10.17516/1997-1397-2020-13-6-661-669}
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This publication is cited in the following 4 articles:
Viktor K. Andreev, “Thermocapillary convection of immiscible liquid in a three-dimensional layer at low Marangoni numbers”, Zhurn. SFU. Ser. Matem. i fiz., 17:2 (2024), 195–206
V. K. Andreev, E. N. Lemeshkova, “Thermal Cnvection of Two Immiscible Liquids in a 3D Channel with a Velocity Field of a Special Type”, Prikladnaya matematika i mekhanika, 87:2 (2023), 200
V. K. Andreev, E. N. Lemeshkova, “Thermal Convection of Two Immiscible Fluids in a 3D Channel with a Velocity Field of a Special Type”, Fluid Dyn, 58:7 (2023), 1246
A. A. Azanov, E. N. Lemeshkova, “Kachestvennye svoistva resheniya odnoi sopryazhennoi zadachi teplovoi konvektsii”, Uchen. zap. Kazan. un-ta. Ser. Fiz.-matem. nauki, 165, no. 4, Izd-vo Kazanskogo un-ta, Kazan, 2023, 326–343
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