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ЖУРНАЛЫ // Журнал Сибирского федерального университета. Серия «Математика и физика» // Архив

Журн. СФУ. Сер. Матем. и физ., 2008, том 1, выпуск 4, страницы 410–431 (Mi jsfu41)

Эта публикация цитируется в 6 статьях

Symmetry Analysis of Equations for Convection in Binary Mixture

Ilya I. Ryzhkov

Institute of Computational Modelling SB RAS

Аннотация: The differential equations describing convection in binary mixture with Soret and Dufour effects are considered. The symmetry classification of these equations with respect to the constant parameters is made. It is shown that a generator producing equivalence transformations of constants is defined accurately up to a factor arbitrarily depending on these constants. The equivalence group admitted by the governing equations is calculated. Using this group, a transformation connecting the systems with and without Soret and Dufour terms is derived. In pure Soret case, it reduces to a linear change of temperature and concentration. The presence of Dufour effect requires an additional change of thermal diffusivity and diffusion coefficient. A scheme for reducing an initial and boundary value problem for Soret–Dufour equations to a problem for the system without these effects is proposed.

Ключевые слова: Lie symmetry group, equivalence transformation, binary mixture, convection, Soret and Dufour effects.

УДК: 532.517

Получена: 10.08.2008
Исправленный вариант: 10.10.2008
Принята: 06.11.2008

Язык публикации: английский



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