Layered Marangoni convection with the Navier slip condition
Электронный научный архив УРФУ
Информация об архиве | Просмотр оригинала| Поле | Значение | |
| Заглавие |
Layered Marangoni convection with the Navier slip condition
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| Автор |
Burmasheva, N. V.
Privalova, V. V. Prosviryakov, E. Y. |
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| Тематика |
EXACT SOLUTION
MARANGONI FLOW SLIPPING CONDITION VISCOUS FLOW VORTEX BOUNDARY CONDITIONS BOUNDARY VALUE PROBLEMS CAPILLARY FLOW GRAVITATION GEOMETRIC ANISOTROPY LONGITUDINAL VELOCITY NAVIER-SLIP CONDITIONS TEMPERATURE AND PRESSURES THERMOCAPILLARY FLOW THERMOGRAVITATIONAL FLOWS TRANSVERSE COORDINATE VISCOUS INCOMPRESSIBLE FLUIDS VELOCITY |
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| Описание |
A new exact solution to the problem of Marangoni layered convection is obtained. This solution describes a layered steady-state flow of a viscous incompressible fluid at varying gradients of temperature and pressure. The velocity components depend only on the transverse coordinate; the temperature and pressure fields are three-dimensional. The Marangoni effect is observed on the upper free surface of the fluid layer. On the lower solid surface of the fluid layer, three different cases of defining boundary conditions are considered: the no-slip condition, the perfect slip condition and the Navier slip condition. The obtained exact solution is determined by the interaction of three flows: a flow caused by pressure drop (the Poiseuille flow), a flow caused by heating/cooling and the effect of the gravity force (the thermogravitational flow), and a flow caused by heating/cooling and the fluid surface tension effect (the thermocapillary flow). The obtained exact solutions in the case of each of the three types of boundary conditions specified on the lower surface are analyzed in detail. It has been proved that, when certain ratios of the boundary value problem parameters are fulfilled, the velocity components may acquire stagnation points, this being indicative of the presence of counterflow areas in the fluid layer under consideration. In particular, the presence of up to two stagnation points in each of the two longitudinal velocity components may cause a stratification of the velocity field in more than two regions. The obtained exact solution of the Marangoni layered convection problem can describe flows in thin films through the variation of the geometric anisotropy factor. © 2021, Indian Academy of Sciences.
CICECO-Aveiro Institute of Materials Israeli Ministry of Science with the Russian Foundation for Basic Research Fundação para a Ciência e a Tecnologia, FCT Russian Foundation for Basic Research, РФФИ, (19‐52‐06004 MHTИ_a, 3‐16492) Israel Science Foundation, ISF, (1898/22) Ministerstwo Edukacji i Nauki, MNiSW, (N 075‐15‐2021‐677, UIDB/50011/2020, UIDP/50011/2020) Ural Federal University, UrFU Ministry of Science and Higher Education of the Russian Federation, (FEUZ-2020-0054) Funding text 1: This work was supported by the collaborative program of the Israeli Ministry of Science with the Russian Foundation for Basic Research (RFBR), grant #3‐16492. Russian partners thank RFBR for the financial support within the project #19‐52‐06004 MHTИ_a. The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University (Reg. N 2968) was used with the financial support of the Ministry of Science and Higher Education of the RF (Project N 075‐15‐2021‐677). This work was developed within the scope of project CICECO‐Aveiro Institute of Materials (UIDB/50011/2020 & UIDP/50011/2020) financed by national funds through the FCT—Foundation for Science and Technology (Portugal). IL thank the Israel Science Foundation for the financial support (#1898/22). The research made possible due to historic generosity of the Harold Perlman Family. VS is grateful for financial support of the Ministry of Science Higher Education of the Russian Federation (state task FEUZ‐2020‐0054). o o Funding text 2: This work was supported by the collaborative program of the Israeli Ministry of Science with the Russian Foundation for Basic Research (RFBR), grant #3-16492. Russian partners thank RFBR for the financial support within the project #19-52-06004 MHTИ_a. The equipment of the Ural Center for Shared Use “Modern nanotechnology” Ural Federal University (Reg. No 2968) was used with the financial support of the Ministry of Science and Higher Education of the RF (Project No 075-15-2021-677). This work was developed within the scope of project CICECO-Aveiro Institute of Materials (UIDB/50011/2020 & UIDP/50011/2020) financed by national funds through the FCT—Foundation for Science and Technology (Portugal). IL thank the Israel Science Foundation for the financial support (#1898/22). The research made possible due to historic generosity of the Harold Perlman Family. VS is grateful for financial support of the Ministry of Science Higher Education of the Russian Federation (state task FEUZ-2020-0054). |
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| Дата |
2024-04-22T15:53:26Z
2024-04-22T15:53:26Z 2021 |
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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 |
Burmasheva, NV, Privalova, VV & Prosviryakov, EY 2021, 'Layered Marangoni convection with the Navier slip condition', Sadhana - Academy Proceedings in Engineering Sciences, Том. 46, № 1, 55. https://doi.org/10.1007/s12046-021-01585-5
Burmasheva, N. V., Privalova, V. V., & Prosviryakov, E. Y. (2021). Layered Marangoni convection with the Navier slip condition. Sadhana - Academy Proceedings in Engineering Sciences, 46(1), [55]. https://doi.org/10.1007/s12046-021-01585-5 0256-2499 Final All Open Access; Bronze Open Access https://link.springer.com/content/pdf/10.1007/s12046-021-01585-5.pdf https://link.springer.com/content/pdf/10.1007/s12046-021-01585-5.pdf http://elar.urfu.ru/handle/10995/132439 46756751 10.1007/s12046-021-01585-5 85102725509 630356100001 |
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| Язык |
en
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| Права |
Open access (info:eu-repo/semantics/openAccess)
cc-by |
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| Формат |
application/pdf
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| Издатель |
Springer
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| Источник |
Sādhanā
Sadhana - Academy Proceedings in Engineering Sciences |
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