RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Archive
Impact factor
Guidelines for authors

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



J. Sib. Fed. Univ. Math. Phys.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


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

This article is cited in 5 scientific papers (total in 5 papers)

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.

Full text: PDF file (347 kB)
References: PDF file   HTML file
UDC: 532.517
Received: 10.08.2008
Received in revised form: 10.10.2008
Accepted: 06.11.2008
Language:

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}


Linking options:
  • http://mi.mathnet.ru/eng/jsfu41
  • http://mi.mathnet.ru/eng/jsfu/v1/i4/p410

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    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  crossref  mathscinet  zmath  adsnasa  isi  elib
    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  crossref  isi  elib
    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  crossref  mathscinet  zmath  isi
    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  mathnet  crossref
    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  crossref  mathscinet  zmath  isi  scopus
  • Журнал Сибирского федерального университета. Серия "Математика и физика"
    Number of views:
    This page:228
    Full text:91
    References:33

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2021