Exact Solutions to the Navier–Stokes Equations for Describing the Flow of Multicomponent Fluids with Internal Heat Generation

Prosviryakov, E. Yu.; Ledyankina, O. A.; Goruleva, L. S.

doi:10.3103/s1068799824010070

Russ. Aeronaut.

2024

DOI: 10.3103/s1068799824010070

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Exact Solutions to the Navier–Stokes Equations for Describing the Flow of Multicomponent Fluids with Internal Heat Generation

E. Yu. Prosviryakov,

O. A. Ledyankina,

L. S. Goruleva

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2024

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Mathematical Analysis of the Poiseuille Flow of a Fluid with Temperature-Dependent Properties

Baranovskii,

Domnich,

Artemov

2024

Mathematics

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This article is devoted to the mathematical analysis of a heat and mass transfer model for the pressure-induced flow of a viscous fluid through a plane channel subject to Navier’s slip conditions on the channel walls. The important feature of our work is that the used model takes into account the effects of variable viscosity, thermal conductivity, and slip length, under the assumption that these quantities depend on temperature. Therefore, we arrive at a boundary value problem for strongly nonlinear ordinary differential equations. The existence and uniqueness of a solution to this problem is analyzed. Namely, using the Galerkin scheme, the generalized Borsuk theorem, and the compactness method, we proved the existence theorem for both weak and strong solutions in Sobolev spaces and derive some of their properties. Under extra conditions on the model data, the uniqueness of a solution is established. Moreover, we considered our model subject to some explicit formulae for temperature dependence of viscosity, which are applied in practice, and constructed corresponding exact solutions. Using these solutions, we successfully performed an extra verification of the algorithm for finding solutions that was applied by us to prove the existence theorem.

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Mathematical Analysis of the Poiseuille Flow of a Fluid with Temperature-Dependent Properties

Baranovskii,

Domnich,

Artemov

2024

Mathematics

View full text Add to dashboard Cite

show abstract

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Exact Solutions to the Navier–Stokes Equations for Describing the Flow of Multicomponent Fluids with Internal Heat Generation

Cited by 1 publication

References 32 publications

Mathematical Analysis of the Poiseuille Flow of a Fluid with Temperature-Dependent Properties

Mathematical Analysis of the Poiseuille Flow of a Fluid with Temperature-Dependent Properties

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