Inhomogeneous Nusselt–Couette–Poiseuille Flow

Burmasheva, N. V.; Prosviryakov, E. Yu.

doi:10.1134/s0040579522050207

Cited by 7 publications

(1 citation statement)

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“…The theory of hydrodynamics stability has been developed for a long time as a theory of stability of exact solutions (Couette, Hagen-Poiseuille and its analogue, the Nusselt solution) [24][25][26][27]. In a recent survey on exact methods of integrating the Navier-Stokes equations [7], all known classes of exact solutions of equations were given.…”

Section: The Path From the Simplest Exact Solutions To Classes Of Exa...mentioning

confidence: 99%

Solving the Hydrodynamical System of Equations of Inhomogeneous Fluid Flows with Thermal Diffusion: A Review

Ershkov,

Prosviryakov,

Burmasheva

et al. 2023

Symmetry

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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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Section: The Path From the Simplest Exact Solutions To Classes Of Exa...mentioning

confidence: 99%