Abstract:
The group properties of the thermal-diffusion equations for a binary mixture in plane flow are studied. Optimal systems of first-and second-order subalgebras are constructed for the admissible Lie operator algebra, which is infinite-dimensional. Examples of the exact invariant solutions are given, which are found by solving ordinary differential equations. Exact solutions are found that describe thermal diffusion in an inclined layer with a free boundary and in a vertical layer in the presence of longitudinal temperature and concentration gradients. The effect of the thermal-diffusion parameter on the flow regime is studied.
Keywords:
thermal diffusion, binary mixture, group analysis, invariant solutions.
Citation:
I. I. Ryzhkov, “Invariant solutions of the thermal-diffusion equations for a binary mixture in the case of plane motion”, Prikl. Mekh. Tekh. Fiz., 47:1 (2006), 95–108; J. Appl. Mech. Tech. Phys., 47:1 (2006), 79–90
\Bibitem{Ryz06}
\by I.~I.~Ryzhkov
\paper Invariant solutions of the thermal-diffusion equations for a binary mixture in the case of plane motion
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2006
\vol 47
\issue 1
\pages 95--108
\mathnet{http://mi.mathnet.ru/pmtf2115}
\elib{https://elibrary.ru/item.asp?id=16546838}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2006
\vol 47
\issue 1
\pages 79--90
\crossref{https://doi.org/10.1007/s10808-006-0011-6}
Linking options:
https://www.mathnet.ru/eng/pmtf2115
https://www.mathnet.ru/eng/pmtf/v47/i1/p95
This publication is cited in the following 2 articles:
I. I. Ryzhkov, I. V. Stepanova, “Group properties and exact solutions of equations for vibrational convection of a binary mixture”, J. Appl. Mech. Tech. Phys., 52:4 (2011), 560–570
Ilya I. Ryzhkov, “On double diffusive convection with Soret effect in a vertical layer between co-axial cylinders”, Physica D: Nonlinear Phenomena, 215:2 (2006), 191
Citation in format AMSBIB
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