V. K. Andreev, E. N. Cheremnykh, “A joint creeping motion of three fluids in a flat layer: a priori estimates and convergence to a stationary regime”, Sib. Zh. Ind. Mat., 19:1 (2016), 3–17; J. Appl. Industr. Math., 10:1 (2016), 7

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Sibirskii Zhurnal Industrial'noi Matematiki, 2016, Volume 19, Number 1, Pages 3–17
DOI: https://doi.org/10.17377/sibjim.2016.19.101 (Mi sjim907)

This article is cited in 10 scientific papers (total in 10 papers)

A joint creeping motion of three fluids in a flat layer: a priori estimates and convergence to a stationary regime

V. K. Andreev^ab, E. N. Cheremnykh^ab

^a Institute of Computational Modeling SB RAS, 50/44 Akademgorodok, 660036 Krasnoyarsk
^b Siberian Federal University, 79 Svobodnyi av., 660041 Krasnoyarsk

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DOI: https://doi.org/10.17377/sibjim.2016.19.101

Abstract: We study a partially invariant solution of rank 2 and defect 3e to the equations of a viscous heat-conducting fluid. It is interpreted as a two-dimensional motion of three immiscible fluids in a flat channel bounded by solid walls for which the distribution of temperature is known. From a mathematical point of view, the resulting initial boundary value problem is nonlinear and inverse. Under some assumptions (often fulfilled in practical applications), the problem is replaced by a linear one. We obtain a priori estimates as well as the exact stationary solution and prove that, the solution tends to a stationary regime if the temperatures of the walls stabilize with time.

Keywords: thermocapillarity, a priori estimate, conjugate boundary value problem, asymptotic behavior.

Funding agency	Grant number
Russian Foundation for Basic Research	14-01-00067

Received: 16.05.2015

English version:
Journal of Applied and Industrial Mathematics, 2016, Volume 10, Issue 1, Pages 7–20
DOI: https://doi.org/10.1134/S1990478916010026

Bibliographic databases:

Document Type: Article

UDC: 517.941.1+532.529.5

Language: Russian

Citation: V. K. Andreev, E. N. Cheremnykh, “A joint creeping motion of three fluids in a flat layer: a priori estimates and convergence to a stationary regime”, Sib. Zh. Ind. Mat., 19:1 (2016), 3–17; J. Appl. Industr. Math., 10:1 (2016), 7–20

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Linking options:

https://www.mathnet.ru/eng/sjim907

https://www.mathnet.ru/eng/sjim/v19/i1/p3

This publication is cited in the following 10 articles:

L. S. Goruleva, E. Yu. Prosviryakov, “A New Class of Exact Solutions to Magnetohydrodynamics Equations for Describing Convective Flows of Binary Fluids”, Tech. Phys., 68:10 (2023), 292
Sergey V. Ershkov, Evgeniy Yu. Prosviryakov, Natalya V. Burmasheva, Victor Christianto, “Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review”, Symmetry, 15:10 (2023), 1825
Larisa Goruleva, Evgenii Prosviryakov, “A New Class of Exact Solutions for Magnetohydrodynamics Equations to Describe Convective Flows of Binary Liquids”, HFIM, 25:4 (2023)
M V Efimova, “The effect of interfacial heat transfer energy on a two-layer creeping flow in a flat channel”, J. Phys.: Conf. Ser., 1268:1 (2019), 012022
E. N. Cheremnykh, “A Priori Estimates of the Solution of the Problem of the Unidirectional Thermogravitational Motion of a Viscous Liquid in the Plane Channel”, Math. Notes, 103:1 (2018), 145–154
M. V. Efimova, N. Darabi, “Thermal-concentration convection in a system of viscous liquid and binary mixture in a plane channel with small Marangoni numbers”, J. Appl. Mech. Tech. Phys., 59:5 (2018), 847–856
E. N. Cheremnykh, “Unidirectional heat-gravitational motion of viscous fluid in a flat channel with a given flow rate”, J. Appl. Mech. Tech. Phys., 59:3 (2018), 416–421
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. Tekhnicheskogo Univ.-Ser. Fiz.-Mat. Nauka, 22:3 (2018), 532–548
E. V. Rezanova, I. A. Shefer, “Influence of the thermal load on the characteristics of a flow with evaporation”, J. Appl. Industr. Math., 11:2 (2017), 274–283
V. K. Andreev, E. N. Cheremnykh, “The unidirectional motion of two heat-conducting liquids in a flat channel”, All-Russian Conference With International Participation Modern Problems of Continuum Mechanics and Explosion Physics Dedicated to the 60th Anniversary of Lavrentyev Institute of Hydrodynamics SB RAS, Journal of Physics Conference Series, 894, eds. Chesnokov A., Pruuel E., Shelukhin V., IOP Publishing Ltd, 2017, UNSP 012106

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Сибирский журнал индустриальной математики

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