Exact Solution of the Couette–Poiseuille Type for Steady Concentration Flows
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Exact Solution of the Couette–Poiseuille Type for Steady Concentration Flows
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| Автор |
Burmasheva, N. V.
Prosviryakov, E. Yu. |
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| Тематика |
COUETTE–POISEUILLE FLOW
EXACT SOLUTION SOLUTAL CONVECTION |
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| Описание |
This article presents a new exact solution for predicting the properties of the velocity field, pressure, and impurity distribution in steady shear flows of viscous incompressible fluids in an extended horizontal layer. The solutal convection was described using a mathematical model based on the Oberbeck–Boussinesq equations with a linear dependence of density on concentration. It was assumed that the layer at one of its boundaries (the lower one) is im-permeable to the substance (impurity) dissolved in the fluid so that the fluid-sticking effect applies to it. It was demonstrated that the flow is induced by an inhomogeneous distribution of impurities and pressure at the upper boundary of the layer. A uniform distribution of velocities is set at the upper boundary. The obtained solution belongs to the Ostroumov–Birikh and Lin–Sidorov–Aristov classes. The velocity field was described by the two-dimensional Couette profile, i.e., both velocity components depend on the vertical transverse coordinate. The concentration and pressure were described by linear forms relative to horizontal (longitudinal) coordinates, with coefficients depending on the third coordinate. The structure of the exact solution is such that the incompressibility equation is identically satisfied. Thus, an overdeter-mined, quadratically nonlinear partial differential system was resolved. After the substitution in the stationary system of the Oberbeck–Boussinesq equations supplemented by the equations of diffusion and incompressibility, the unknown functions that determine the hydrodynamic fields were found by integrating the system of ordinary differential equations. This system is of the 13th order and admits an exact polynomial solution that can be used to describe the occurrence of several counterflow zones and the nonmonotonic nature of the specific kinetic energy with up to two zeros. The obtained exact solutions illustrate the multiple stratifica-tions of the shear stress, pressure, and concentration fields. Therefore, hydrodynamic fields have a complex topology defined by the dependence of velocities, pressure, and concentration on the transverse coordinate. © 2022, Kazan Federal University. All rights reserved.
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| Дата |
2024-04-08T11:07:50Z
2024-04-08T11:07:50Z 2022 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) Published version (info:eu-repo/semantics/publishedVersion) |
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| Идентификатор |
Бурмашева, НВ & Просвиряков, ЕЮ 2022, 'ТОЧНОЕ РЕШЕНИЕ ТИПА КУЭТТА - ПУАЗЕЙЛЯ ДЛЯ УСТАНОВИВШИХСЯ КОНЦЕНТРАЦИОННЫХ ТЕЧЕНИЙ', Ученые записки Казанского университета. Серия: Физико-математические науки, Том. 164, № 4, стр. 285-301. https://doi.org/10.26907/2541-7746.2022.4.285-301
Бурмашева, Н. В., & Просвиряков, Е. Ю. (2022). ТОЧНОЕ РЕШЕНИЕ ТИПА КУЭТТА - ПУАЗЕЙЛЯ ДЛЯ УСТАНОВИВШИХСЯ КОНЦЕНТРАЦИОННЫХ ТЕЧЕНИЙ. Ученые записки Казанского университета. Серия: Физико-математические науки, 164(4), 285-301. https://doi.org/10.26907/2541-7746.2022.4.285-301 2541-7746 Final All Open Access; Gold Open Access https://kpfu.ru/portal/docs/F1032482895/164_4_phys_mat_2.pdf https://kpfu.ru/portal/docs/F1032482895/164_4_phys_mat_2.pdf http://elar.urfu.ru/handle/10995/131523 50729892 10.26907/2541-7746.2022.4.285-301 85160063549 000982627500001 |
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| Язык |
ru
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by https://creativecommons.org/licenses/by/4.0/ |
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| Формат |
application/pdf
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| Издатель |
Kazan Federal University
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| Источник |
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki
Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki |
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