Geodesic
Two-dimensional plane thermocapillary flow of two immiscible liquids
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 310-316 Cet article a éte moissonné depuis la source Math-Net.Ru

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The problem of two-dimensional stationary flow of two immiscible liquids in a plane channel with rigid walls is considered. A temperature distribution is specified on one of the walls and another wall is heat-insulated. The interfacial energy change is taken into account on the common interface. The temperature in liquids is distributed according to a quadratic law. It agrees with velocities field of the Hiemenz type. The corresponding conjugate boundary value problem is nonlinear and inverse with respect to pressure gradients along the channel. The Tau method is used for the solution of the problem. Three different solutions are obtained. It is established numerically that obtained solutions converge to the solutions of the slow flow problem with decreasing the Marangoni number. For each of the solutions the characteristic flow structures are constructed.
Keywords: thermocapillary, inverse problem, Tau method.
Mots-clés : interface 
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Elena N. Lemeshkova. Two-dimensional plane thermocapillary flow of two immiscible liquids. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 12 (2019) no. 3, pp. 310-316. http://geodesic.mathdoc.fr/item/JSFU_2019_12_3_a4/

[1] V.K. Andreev, V.E. Zahvataev, E.A. Ryabitskii, Thermocapillary Instability, Nauka, Sibirskoe otdelenie, Novosibirsk, 2000 (in Russian) | MR

[2] F.E. Torres, E. Helborzheimer, “Temperature gradients and drag effects produced by convection of interfacial internal energy around bubbles”, Phys. Fluids A, 5:3 (1993), 537–549 | DOI | MR | Zbl

[3] K. Hiemenz, “Die Grenzschicht an einem in den gleichförmigen Flüssigkeitsstrom eingetauchten geraden Kreiszylinder”, Dinglers Poliytech. J., 326 (1911), 321–440

[4] R.Kh. Zeytounian, “The Benard-Marangoni thermocapillary-instability problem”, Physics-Uspekhi, 41:3 (1998), 241–267 | DOI

[5] V.K. Andreev, “The solutions properties of conjugated nonlinear boundary value problem describing a stationary flow of a two liquids in the channel”, Some actual problems of modern mathematics and mathematical education, Herzen readings, Scientific conference materials, 2018, 18–23

[6] C.A.J. Fletcher, Computational Galerkin method, Springer-Verlag, 1984 | MR

[7] Gabor Szego, Orthogonal polynomials, American Mathematical Society Colloquium Publications, 23, Revised ed., American Mathematical Society, Providence, R.I., 1959 | MR | Zbl