On a~convective flow of a~binary mixture in a~vertical flume
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 1, pp. 17-26.

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Under study is an invariant solution of the equations of thermal diffusive convection which describes a stationary process of a binary mixture flow in a vertical layer under the action of the pressure gradient and the buoyancy force that depends nonlinearly on temperature and concentration. Some general properties of this solution are established and an existence theorem is proved. Analysis of the numerical solution of the problem is carried out in the cases of a power-law and exponential dependence of the buoyancy force on its argument.
Keywords: binary mixture
Mots-clés : heat diffusion, invariant solution.
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V. K. Andreev; I. V. Stepanova. On a~convective flow of a~binary mixture in a~vertical flume. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 1, pp. 17-26. http://geodesic.mathdoc.fr/item/SJIM_2011_14_1_a1/

[1] Gebkhart B., Dzhaluriya I., Makhadzhan R., Sammakiya B., Svobodnokonvektivnye techeniya, teplo- i massoobmen, v. 1, Mir, M., 1991

[2] Bryan K., Cox M. D., “An approximate equation of state for numerical models of ocean circulation”, J. Phys. Oceanography, 2 (1972), 510–514 | 2.0.CO;2 class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI

[3] Marchuk G. I., Sarkisyan A. S., Matematicheskoe modelirovanie tsirkulyatsii okeana, Nauka, M., 1988 | MR

[4] Gebhart B., Mollendorf J., “Buoyancy-induced flows in water under conditions in which density extrema may arise”, J. Fluid Mech., 89:4 (1978), 673–707 | DOI | Zbl

[5] Ovsyannikov L. V., Gruppovoi analiz differentsialnykh uravnenii, Nauka, M., 1978 | MR | Zbl

[6] Andreev V. K., Stepanova I. V., “Simmetriya uravnenii termodiffuzii pri nelineinoi zavisimosti sily plavuchesti ot temperatury i kontsentratsii”, Vych. tekhnologii, 15:4 (2010), 47–55

[7] Trenogin V. A., Funktsionalnyi analiz, Nauka, M., 1980 | MR | Zbl

[8] Andreev V. K., “Ob invariantnykh resheniyakh uravnenii termodiffuzii”, Tr. 3 Mezhdunar. konf. “Simmetriya i differentsialnye uravneniya”, izd. Krasnoyar. gos. un-ta, Krasnoyarsk, 2002, 13–17

[9] Ryzhkov I. I., “Ob invariantnykh resheniyakh uravnenii termodiffuzii binarnoi smesi v sluchae ploskogo dvizheniya”, Prikl. mekhanika i tekhn. fizika, 47:1 (2006), 95–108 | MR | Zbl

[10] Gershuni G. Z., Zhukhovitskii E. M., Sorokin L. E., “Ob ustoichivosti konvektivnogo techeniya binarnoi smesi s termodiffuziei”, Prikl. matematika i mekhanika, 46:1 (1982), 66–71 | Zbl