Geodesic
Comparative analysis of the analytical and numerical solution of the problem of thermocapillary convection in a rectangular channel
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 48-55.

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The paper compares the exact solution of one-dimensional and two-dimensional stationary convective flow equations with a free boundary for a flat liquid channel. Constant temperature gradient is set on the bottom solid wall. On the upper free boundary the surface tension coefficient is linearly dependent on temperature. Zero heat flux and velocities are set on the side walls of the two-dimensional problem. The deviation of the one-dimensional exact solution is determined for different aspect ratio and Marangoni number.
Keywords: thermocapillary, Marangoni number.
Mots-clés : interface 
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Viktor K. Andreev; Artem I. Pyanykh. Comparative analysis of the analytical and numerical solution of the problem of thermocapillary convection in a rectangular channel. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 16 (2023) no. 1, pp. 48-55. http://geodesic.mathdoc.fr/item/JSFU_2023_16_1_a4/

[1] R.V.Birikh, “Thermocapillary convection in a horizontal layer of liquid”, J. Appl. Mech. Tech. Phys., 5 (1966), 69–72

[2] A.G.Kirdyashkin, “Thermogravitational and thermocapillary flows in a horizontal liquid layer under the conditions of a horizontal temperature gradient”, Int. J. Heat Mass Transfer, 27:8 (1984), 1205–1218

[3] A.G.Kirdyashkin, “Thermocapillary and thermogravitational convection in a horizontal liquid layer”, Hydromechanics and transfer processes in weightlessness, UC AS USSR, Sverdlovsk, 1983, 81–86 (in Russian)

[4] A.G.Kirdyashkin, Thermocapillary periodic flows, Preprint No 8, IGG SB AS USSR, Novosibirsk, 1985 (in Russian)

[5] M.K.Smith, S.H.Davies, “Instabilities of dynamic thermocapillary liquid layers. Part 1. Convective instabilities”, Jour. Fluid Mech., 132 (1983), 119–144

[6] J.-J.Xu, S.H.Davis, “Liquid bridges with thermocapillarity”, Physics of Fluids, 26:10 (1983), 2880–2886

[7] V.B.Bekezhanova, “Convective instability of a two-layer fluid flow on an inclined plane”, Abstracts of the Russian Conference “New Mathematical Models of Continuum Mechanics: Construction and Study”, Lavrentiev Institute of Hydrodynamics SB RAS, Novosibirsk, 2009, 32–33 (in Russian)