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 J. Sib. Fed. Univ. Math. Phys., 2008, Volume 1, Issue 4, Pages 410–431 (Mi jsfu41)

Symmetry Analysis of Equations for Convection in Binary Mixture

Ilya I. Ryzhkov

Institute of Computational Modelling SB RAS

Abstract: 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.

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

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UDC: 532.517
Accepted: 06.11.2008
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Citation: Ilya I. Ryzhkov, “Symmetry Analysis of Equations for Convection in Binary Mixture”, J. Sib. Fed. Univ. Math. Phys., 1:4 (2008), 410–431

Citation in format AMSBIB
\Bibitem{Ryz08} \by Ilya~I.~Ryzhkov \paper Symmetry Analysis of Equations for Convection in Binary Mixture \jour J. Sib. Fed. Univ. Math. Phys. \yr 2008 \vol 1 \issue 4 \pages 410--431 \mathnet{http://mi.mathnet.ru/jsfu41} 

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This publication is cited in the following articles:
1. Stepanova I.V., “Group Classification for Equations of Thermodiffusion in Binary Mixture”, Commun. Nonlinear Sci. Numer. Simul., 18:6 (2013), 1341–1346
2. Ryzhkov I.I., “The Extended Graetz Problem with Specified Heat Flux for Multicomponent Fluids with Soret and Dufour Effects”, Int. J. Heat Mass Transf., 66 (2013), 461–471
3. Stepanova I.V., “The Invariant Solution of Thermal Diffusion Equations for a Non-Linear Buoyancy Force”, Pmm-J. Appl. Math. Mech., 77:3 (2013), 330–337
4. Victoria B. Bekezhanova, Olga N. Goncharova, Ilia A. Shefer, “Analysis of an exact solution of problem of the evaporative convection (review). Part I. Plane case”, Zhurn. SFU. Ser. Matem. i fiz., 11:2 (2018), 178–190
5. Stepanova I.V., “Symmetry of Heat and Mass Transfer Equations in Case of Dependence of Thermal Diffusivity Coefficient Either on Temperature Or Concentration”, Math. Meth. Appl. Sci., 41:8 (2018), 3213–3226
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