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 J. Sib. Fed. Univ. Math. Phys., 2021, Volume 14, Issue 1, Pages 57–68 (Mi jsfu891)

Construction of exact solution describing three-layer flows with evaporation in a horizontal channel

Ekaterina V. Rezanova

Altai State University, Barnaul, Russian Federation

Abstract: The paper considers the flow in a three-layer system "liquid–liquid–gas" in a horizontal channel with solid impermeable walls.The evaporation process at the thermocapillary interface of the liquid and gas is taken into account. The Soret and Dufour effects are taken into account in the upper layer filled with a gas-vapor mixture. The system of Navier-Stokes equations in the Boussinesq approximation is used as a mathematical model. A temperature regime is set on the channel walls. Liquid evaporation is modeled using the conditions at the liquid-gas interface. Exact solution of a special type describing the flow in a three-layer system is constructed. The velocity profiles are presented on the example of the "silicone oil–water–air" system for various values of gas flow rate, longitudinal temperature gradients at the system boundaries, thicknesses of liquid and gas-vapor layers.

Keywords: three-layer system, exact solutions, evaporation, Soret effect, Dufour effect.

 Funding Agency Grant Number Ministry of Science and Higher Education of the Russian Federation FZMW-2020-0008 The work 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, 24 January 2020).

DOI: https://doi.org/10.17516/1997-1397-2021-14-1-57-68

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UDC: 536.25
Accepted: 26.10.2020
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Citation: Ekaterina V. Rezanova, “Construction of exact solution describing three-layer flows with evaporation in a horizontal channel”, J. Sib. Fed. Univ. Math. Phys., 14:1 (2021), 57–68

Citation in format AMSBIB
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