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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Published in | Symmetry (Basel) Vol. 15; no. 10; p. 1825 |
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Format | Journal Article |
Language | English |
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Abstract | 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. |
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AbstractList | 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. |
Audience | Academic |
Author | Ershkov, Sergey V. Prosviryakov, Evgeniy Yu Christianto, Victor Burmasheva, Natalya V. |
Author_xml | – sequence: 1 givenname: Sergey V. orcidid: 0000-0002-6826-1691 surname: Ershkov fullname: Ershkov, Sergey V. – sequence: 2 givenname: Evgeniy Yu orcidid: 0000-0002-2349-7801 surname: Prosviryakov fullname: Prosviryakov, Evgeniy Yu – sequence: 3 givenname: Natalya V. orcidid: 0000-0003-4711-1894 surname: Burmasheva fullname: Burmasheva, Natalya V. – sequence: 4 givenname: Victor orcidid: 0000-0002-0478-2842 surname: Christianto fullname: Christianto, Victor |
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SubjectTerms | Analysis Book publishing Boussinesq approximation Convection exact solution Exact solutions Fluid flow Fluid mechanics hydrodynamical system of equations Incompressible flow Incompressible fluids Inhomogeneity inhomogeneous fluid flows Momentum transfer non-stationary solution stability of flow Temperature distribution Thermal diffusion Velocity Velocity distribution Viscosity Vortices |
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Title | Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review |
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