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Exact Solutions for Steady Convective Layered Flows with a Spatial Acceleration

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Abstract

In this paper, we study non-one-dimensional convective layered flows of a viscous incompressible fluid with a spatial acceleration. We perform the simulation on the base of thermal convection equations in the Boussinesq approximation. We seek for solutions to these equations in a generalized class of exact solutions, where all components of the velocity vector, the pressure, and the temperature represent complete linear forms of two Cartesian coordinates with nonlinear (with respect to to the third Cartesian coordinate) coefficients. We prove that the system of correlations that describe layered flows can be reduced to an overdetermined system of ordinary differential equations. We state and prove two theorems that justify the existence (under a special algebraic condition) and uniqueness of the solution to the resulting overdetermined system.

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Funding

This work was supported by the Russian Scientific Foundation (project no. 19-19-00571).

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Authors and Affiliations

  1. Institute of Engineering Science Ural Branch of the Russian Academy of Sciences, 34 Komsomolskaya st., 620049, Yekaterinburg, Russia

    N. V. Burmasheva & E. Yu. Prosviryakov

  2. Ural Federal University, 19 Mira str., 620002, Yekaterinburg, Russia

    N. V. Burmasheva & E. Yu. Prosviryakov

Authors
  1. N. V. Burmasheva
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  2. E. Yu. Prosviryakov
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Corresponding authors

Correspondence to N. V. Burmasheva or E. Yu. Prosviryakov.

Additional information

Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 7, pp. 12–22.

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Burmasheva, N.V., Prosviryakov, E.Y. Exact Solutions for Steady Convective Layered Flows with a Spatial Acceleration. Russ Math. 65, 8–16 (2021). https://doi.org/10.3103/S1066369X21070021

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  • DOI: https://doi.org/10.3103/S1066369X21070021

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