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Thermal Cnvection of Two Immiscible Liquids in a 3D Channel with a Velocity Field of a Special Type
- Authors: Andreev V.K.1, Lemeshkova E.N.1
-
Affiliations:
- Institute of Computational Modelling SB RAS
- Issue: Vol 87, No 2 (2023)
- Pages: 200-210
- Section: Articles
- URL: https://ruspoj.com/0032-8235/article/view/675141
- DOI: https://doi.org/10.31857/S0032823523020029
- EDN: https://elibrary.ru/TYSYHA
- ID: 675141
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Abstract
The three-dimensional stationary flow of two immiscible liquids in a layer bounded by solid parallel walls is investigated. The upper wall is thermally insulated, and the lower one has a temperature field quadratic in horizontal coordinates. Velocity fields in liquids have a special form: their horizontal components are linear in the coordinates of the same name. The resulting conjugate boundary value problem in the framework of the Oberbeck–Boussinesq model is inverse and is reduced to a system of ten integro-differential equations. For small Marangoni numbers (creeping current), the problem is solved analytically. The nonlinear problem is solved by the tau method. It is shown that the solution of the nonlinear problem with a decrease in the Marangoni number is approximated by the solution of the creeping flow problem. The analysis of the influence of physical and geometric parameters, as well as the behavior of temperature on the substrate, on the structure of convection in layers is carried out.
About the authors
V. K. Andreev
Institute of Computational Modelling SB RAS
Author for correspondence.
Email: andr@icm.krasn.ru
Russia, Krasnoyarsk
E. N. Lemeshkova
Institute of Computational Modelling SB RAS
Author for correspondence.
Email: elena_cher@icm.krasn.ru
Russia, Krasnoyarsk
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