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 J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 4, Pages 404–413 (Mi jsfu925)

Solution of a two-layer flow problem with inhomogeneous evaporation at the thermocapillary interface

Victoria B. Bekezhanovaa, Olga N. Goncharovab, Ilya A. Sheferc

a Institute of Computational Modelling SB RAS, Krasnoyarsk, Russian Federation
b Altai State University, Barnaul, Russian Federation
c Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: The Ostroumov–Birikh type exact solution of thermodiffusion convection equations is constructed in the frame of mathematical model considering evaporation through the liquid–gas interface and the influence of direct and inverse thermodiffusion effects. It is interpreted as a solution describing steady flow of evaporating liquid driven by co-current gas-vapor flux on a working section of a plane horizontal channel. Functional form of required functions is presented. An algorithm for finding all the constants and parameters contained in the solution is outlined, and their explicit expressions are written. The solution is derived for the case of vapor absorption on the upper wall of the channel which is set with the help of the first kind boundary condition for the function of vapor concentration. Applicability field of the solution is briefly discussed.

Keywords: mathematical model, boundary value problem, exact solution, evaporative convection.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation 075-02-2020-1631FZMW-2020-0008 V. B. Bekezhanova and I. A. Shefer are thankful for the support provided by the Krasnoyarsk Mathematical Center and financed by the Ministry of Science and Higher Education of the Russian Federation in the framework of the establishment and development of regional Centers for Mathematics Research and Education (Agreement no. 075-02-2020-1631). The work of O. N. Goncharova was carried out in accordance with the State Assignment of the Russian Ministry of Science and Higher Education entitled "Modern methods of hydrodynamics for environmental management, industrial systems and polar mechanics" (Govt. contract code: FZMW-2020-0008).

DOI: https://doi.org/10.17516/1997-1397-2021-14-4-404-413

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UDC: 532.5.013.3
Accepted: 05.04.2021
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Citation: Victoria B. Bekezhanova, Olga N. Goncharova, Ilya A. Shefer, “Solution of a two-layer flow problem with inhomogeneous evaporation at the thermocapillary interface”, J. Sib. Fed. Univ. Math. Phys., 14:4 (2021), 404–413

Citation in format AMSBIB
\Bibitem{BekGonShe21} \by Victoria~B.~Bekezhanova, Olga~N.~Goncharova, Ilya~A.~Shefer \paper Solution of a two-layer flow problem with inhomogeneous evaporation at the thermocapillary interface \jour J. Sib. Fed. Univ. Math. Phys. \yr 2021 \vol 14 \issue 4 \pages 404--413 \mathnet{http://mi.mathnet.ru/jsfu925} \crossref{https://doi.org/10.17516/1997-1397-2021-14-4-404-413} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000684603900001}