Geodesic
Construction of exact solution describing three-layer flows with evaporation in a horizontal channel
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 57-68

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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, evaporation, Soret effect
Mots-clés : exact solutions, Dufour effect. 
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     author = {Ekaterina V. Rezanova},
     title = {Construction of exact solution describing three-layer flows with evaporation in a horizontal channel},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {57--68},
     publisher = {mathdoc},
     volume = {14},
     number = {1},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_1_a6/}
}
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Ekaterina V. Rezanova. Construction of exact solution describing three-layer flows with evaporation in a horizontal channel. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 1, pp. 57-68. http://geodesic.mathdoc.fr/item/JSFU_2021_14_1_a6/