Abstract:
Properties of an invariant solution of thermodiffusion equations in a planar layer are investigated in the case when the surface tension on the surface of two mixtures depends linearly on temperature and concentration. For the arising adjoint initial-boundary value problem, a priori estimates of perturbations of velocity and temperature fields are obtained. The estimates show that perturbations converge exponentially to stationary values as time increases. Concentration perturbations also settle into a stationary regime; this is proved by means of the Laplace transformation.
Citation:
V. K. Andreev, “On properties of solution of a boundary value problem describing simultaneous flow of two binary mixtures”, Trudy Inst. Mat. i Mekh. UrO RAN, 13, no. 4, 2007, 14–26; Proc. Steklov Inst. Math. (Suppl.), 261, suppl. 1 (2008), S1–S14
\Bibitem{And07}
\by V.~K.~Andreev
\paper On properties of solution of a boundary value problem describing simultaneous flow of two binary mixtures
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2007
\vol 13
\issue 4
\pages 14--26
\mathnet{http://mi.mathnet.ru/timm114}
\elib{https://elibrary.ru/item.asp?id=12040794}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2008
\vol 261
\issue , suppl. 1
\pages S1--S14
\crossref{https://doi.org/10.1134/S008154808050015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-66149173398}
Linking options:
https://www.mathnet.ru/eng/timm114
https://www.mathnet.ru/eng/timm/v13/i4/p14
This publication is cited in the following 4 articles:
Victor K. Andreev, Ilya I. Ryzhkov, “On thermocapillary instability of a liquid column with a co-axial gas flow”, Zhurn. SFU. Ser. Matem. i fiz., 6:1 (2013), 3–17
Ryzhkov I.I., Shevtsova V.M., “Thermocapillary instabilities in liquid columns under co - and counter-current gas flows”, Int J Heat Mass Transfer, 55:4 (2012), 1236–1245
Sobachkina N.L., “O sovmestnom dvizhenii binarnoi smesi i vyazkoi zhidkosti v teploizolirovannoi tsilindricheskoi trube”, Vychislitelnye tekhnologii, 16:4 (2011), 120–133
Ryzhkov I.I., “Thermocapillary convection stability in a cylindrically-symmetric two-phase system”, Fluid Dynamics, 45:6 (2010), 866–879
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