Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review
The present review analyzes classes of exact solutions for the convection and thermal diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck–Boussinesq equations for convection and thermal diffusion is more difficult than for the Navier–Stokes equations. It has be...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-09-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/10/1825 |
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| author | Sergey V. Ershkov Evgeniy Yu. Prosviryakov Natalya V. Burmasheva Victor Christianto |
| author_facet | Sergey V. Ershkov Evgeniy Yu. Prosviryakov Natalya V. Burmasheva Victor Christianto |
| author_sort | Sergey V. Ershkov |
| collection | DOAJ |
| description | The present review analyzes classes of exact solutions for the convection and thermal diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck–Boussinesq equations for convection and thermal diffusion is more difficult than for the Navier–Stokes equations. It has been shown that the exact integration of the thermal diffusion equations is carried out in the Lin–Sidorov–Aristov class. This class of exact solutions is a generalization of the Ostroumov–Birikh family of exact solutions. The use of the class of exact solutions by Lin–Sidorov–Aristov makes it possible to take into account not only the inhomogeneity of the pressure field, the temperature field and the concentration field, but also the inhomogeneous velocity field. The present review shows that there is a class of exact solutions for describing the flows of incompressible fluids, taking into account the Soret and Dufour cross effects. Accurate solutions are important for modeling and simulating natural, technical and technological processes. They make it possible to find new physical mechanisms of momentum transfer for the design of new types of equipment. |
| first_indexed | 2024-03-10T20:52:14Z |
| format | Article |
| id | doaj.art-e2a134158cf84819aeb5eb38d1010a2e |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:52:14Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e2a134158cf84819aeb5eb38d1010a2e2023-11-19T18:17:18ZengMDPI AGSymmetry2073-89942023-09-011510182510.3390/sym15101825Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A ReviewSergey V. Ershkov0Evgeniy Yu. Prosviryakov1Natalya V. Burmasheva2Victor Christianto3Department of Scientific Researches, Plekhanov Russian University of Economics, Scopus Number 60030998, 36 Stremyanny Lane, 117997 Moscow, RussiaSector of Nonlinear Vortex Hydrodynamics, Institute of Engineering Science of Ural Branch of the Russian Academy of Sciences, 34 Komsomolskaya st., 620049 Ekaterinburg, RussiaSector of Nonlinear Vortex Hydrodynamics, Institute of Engineering Science of Ural Branch of the Russian Academy of Sciences, 34 Komsomolskaya st., 620049 Ekaterinburg, RussiaSatyabhakti Advanced School of Theology—Jakarta Chapter, 10410 Jakarta, IndonesiaThe present review analyzes classes of exact solutions for the convection and thermal diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck–Boussinesq equations for convection and thermal diffusion is more difficult than for the Navier–Stokes equations. It has been shown that the exact integration of the thermal diffusion equations is carried out in the Lin–Sidorov–Aristov class. This class of exact solutions is a generalization of the Ostroumov–Birikh family of exact solutions. The use of the class of exact solutions by Lin–Sidorov–Aristov makes it possible to take into account not only the inhomogeneity of the pressure field, the temperature field and the concentration field, but also the inhomogeneous velocity field. The present review shows that there is a class of exact solutions for describing the flows of incompressible fluids, taking into account the Soret and Dufour cross effects. Accurate solutions are important for modeling and simulating natural, technical and technological processes. They make it possible to find new physical mechanisms of momentum transfer for the design of new types of equipment.https://www.mdpi.com/2073-8994/15/10/1825hydrodynamical system of equationsinhomogeneous fluid flowsthermal diffusionnon-stationary solutionstability of flowexact solution |
| spellingShingle | Sergey V. Ershkov Evgeniy Yu. Prosviryakov Natalya V. Burmasheva Victor Christianto Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review Symmetry hydrodynamical system of equations inhomogeneous fluid flows thermal diffusion non-stationary solution stability of flow exact solution |
| title | Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review |
| title_full | Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review |
| title_fullStr | Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review |
| title_full_unstemmed | Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review |
| title_short | Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review |
| title_sort | solving the hydrodynamical system of equations of inhomogeneous fluid flows with thermal diffusion a review |
| topic | hydrodynamical system of equations inhomogeneous fluid flows thermal diffusion non-stationary solution stability of flow exact solution |
| url | https://www.mdpi.com/2073-8994/15/10/1825 |
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