Geodesic
On motion of a flooded jet of binary mixture in a viscous fluid
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 3, pp. 308-319

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The invariant solution to the problem of motion of a flooded jet of binary mixture in a viscous heatconducting fluid is investigated. The motion is induced by longitudinal pressure gradient in a mixture. The problem reduces to solving a conjugate initial-boundary value problem for parabolic equations. Stationary solution of problem is determined and it is shown that this solution is not the limiting one at different pressure gradients values. Using Laplace transformation properties the exact analytical solution was obtained. Some examples of numerical reconstruction of the velocities, temperatures and concentration fields depending on geometric and physical parameters were considered.
Keywords: binary mixture, flooded jet, stationary solution
Mots-clés : pressure gradient, Laplace transformation. 
Victor K. Andreev; Natalya L. Sobachkina. On motion of a flooded jet of binary mixture in a viscous fluid. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 4 (2011) no. 3, pp. 308-319. http://geodesic.mathdoc.fr/item/JSFU_2011_4_3_a4/
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[1] V. K. Andreev, Yu. A. Gaponenko, Matematicheskoe modelirovanie konvektivnykh techenii, Uchebnoe posobie, KrasGU, Krasnoyarsk, 2006

[2] V. K. Andreev, V. E. Zakhvataev, E. A. Ryabitskii, Termokapillyarnaya neustoichivost, Nauka, Novosibirsk, 2000 | MR | Zbl

[3] V. K. Andreev, N. L. Sobachkina, Svoistva reshenii nachalno-kraevoi zadachi, voznikayuschei pri dvizhenii binarnoi smesi v tsilindricheskoi trube, Preprint No 1, IVM SO RAN, Krasnoyarsk, 2009, 40 pp.

[4] N. L. Sobachkina, “O sovmestnom dvizhenii binarnoi smesi i vyazkoi zhidkosti v teploizolirovannoi tsilindricheskoi trube”, Vychislitelnye tekhnologii, 2011 (to appear)