Journal of Siberian Federal University. Mathematics & Physics / Symmetry Analysis of Equations for Convection

Full text (.pdf)
Issue
Journal of Siberian Federal University. Mathematics & Physics. 2008 1 (4)
Authors
Ryzhkov, Ilya I.
Contact information
Ilya I.Ryzhkov: Institute of Computational Modelling SB RAS Krasnoyarsk, 660036 Russia, e-mail:
Keywords
Lie symmetry group; equivalence transformation; binary mixture; convection; Soret and Dufour
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.

Pages
410-431
Paper at repository of SibFU
https://elib.sfu-kras.ru/handle/2311/829