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Exact Solutions to the Navier–Stokes Equations with the Boussinesq Approximation for Describing Binary Fluid Flows

  • AERO- AND GAS-DYNAMICS OF FLIGHT VEHICLES AND THEIR ENGINES
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Abstract

A new class of exact solutions of the Oberbeck–Boussinesq equations is constructed to describe diffusion convective flows of incompressible media taking into account mass forces, concentration sources (sinks), and Joule’s dissipation. The velocity field is described by quadratic forms with respect to two spatial coordinates. The announced exact solution generalizes the class of Lin–Sidorov–Aristov exact solutions. The solute concentration, pressure, and mass force field are described by nonlinear fourth-degree forms.

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ACKNOWLEDGEMENTS

We are grateful to the untimely deceased Sergei Anatol’evich Mikhailov for many years of joint scientific work.

The work was performed in the framework of the state task of the Ministry of Science and High Education of the Russian Federation, theme no. 123030100016-5, FZSU-2023-0005.

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Authors and Affiliations

  1. Tupolev Kazan National Research Technical University, ul. K. Marksa 10, 420111, Kazan, Russia

    E. Yu. Prosviryakov, S. A. Mikhailov & O. A. Ledyankina

  2. Institute of Engineering Science, Ural Branch of the RAS, ul. Komsomolskaya 34, 620049, Ekaterinburg, Russia

    E. Yu. Prosviryakov & L. S. Goruleva

  3. Ural Federal University, ul. Mira, 19, 620002, Ekaterinburg, Russia

    L. S. Goruleva

Authors
  1. E. Yu. Prosviryakov
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  2. S. A. Mikhailov
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  3. O. A. Ledyankina
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  4. L. S. Goruleva
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Corresponding author

Correspondence to E. Yu. Prosviryakov.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Aviatsionnaya Tekhnika, 2023, No. 3, pp. 77 – 84.

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Prosviryakov, E.Y., Mikhailov, S.A., Ledyankina, O.A. et al. Exact Solutions to the Navier–Stokes Equations with the Boussinesq Approximation for Describing Binary Fluid Flows. Russ. Aeronaut. 66, 500–509 (2023). https://doi.org/10.3103/S106879982303011X

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  • DOI: https://doi.org/10.3103/S106879982303011X

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