Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows
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| Автор |
Ershkov, S.
Burmasheva, N. Leshchenko, D. D. Prosviryakov, E. Y. |
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| Тематика |
CONVECTION
COUNTERFLOW DIFFUSION DUFOUR EFFECT EXACT SOLUTION OVERDETERMINED SYSTEM SORET EFFECT THERMAL DIFFUSION |
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| Описание |
We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in processes, and apparatuses of chemical technology. To describe the steady shear flows of an incompressible fluid, the system of Navier–Stokes equations in the Boussinesq approximation is redefined, so the construction of exact and numerical solutions to the equations of hydrodynamics is a very difficult and urgent task. A non-trivial exact solution is constructed in the Lin-Sidorov-Aristov class. For this class of exact solutions, the hydrodynamic fields (velocity field, pressure field, temperature field, and solute concentration field) were considered as linear forms in the x and y coordinates. The coefficients of linear forms depend on the third coordinate z. Thus, when considering a shear flow, the two-dimensional velocity field depends on three coordinates. It is worth noting that the solvability condition given in the article imposes a condition (relation) only between the velocity gradients. A theorem on the uniqueness of the exact solution in the Lin–Sidorov–Aristov class is formulated. The remaining coefficients of linear forms for hydrodynamic fields have functional arbitrariness. To illustrate the exact solution of the overdetermined system of Oberbeck–Boussinesq equations, a boundary value problem was solved to describe the complex convection of a vertical swirling fluid without its preliminary rotation. It was shown that the velocity field is highly stratified. Complex countercurrents are recorded in the fluid. © 2023 by the authors.
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| Дата |
2024-04-05T16:33:32Z
2024-04-05T16:33:32Z 2023 |
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| Тип |
Article
Journal article (info:eu-repo/semantics/article) |info:eu-repo/semantics/publishedVersion |
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| Идентификатор |
Ershkov, S, Burmasheva, N, Leshchenko, D & Prosviryakov, E 2023, 'Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows', Symmetry, Том. 15, № 9, 1730. https://doi.org/10.3390/sym15091730
Ershkov, S., Burmasheva, N., Leshchenko, D., & Prosviryakov, E. (2023). Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows. Symmetry, 15(9), [1730]. https://doi.org/10.3390/sym15091730 2073-8994 Final All Open Access, Gold, Green https://www.scopus.com/inward/record.uri?eid=2-s2.0-85172759221&doi=10.3390%2fsym15091730&partnerID=40&md5=ca392168ae974dcbfde0491c93ed7358 https://www.mdpi.com/2073-8994/15/9/1730/pdf?version=1694181123 http://elar.urfu.ru/handle/10995/130820 10.3390/sym15091730 85172759221 001074145300001 |
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| Язык |
en
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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 |
Multidisciplinary Digital Publishing Institute (MDPI)
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| Источник |
Symmetry
Symmetry |
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