Geodesic
Viscous fluid flow between plane walls in presence of temperature gradient
Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 26-38 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Slow flow of incompressible viscous fluid confined by two parallel planes is studied in the paper. The flow is caused either by motion of one plane with respect to another or by pressure drop along the planes. It is supposed that fluid viscosity is the first-order polynomial of temperature and that its gradient is constant in the entire domain under study. These two reasons cause the flow to be disturbed (compared with isothermal case). Dependence of these disturbances on the type of flow and on the orientation of temperature gradient with respect to the flow is investigated by asymptotic methods. Temperature drop on distances equal to the gap between planes is supposed to be small during the investigation. It is shown that both fluid velocity and pressure may be disturbed. In the last case additional lift or drag force may act on the alien particles suspended in the fluid (if it contains any).
Mots-clés : viscous fluid
Keywords: Stokes approximation, variable viscosity, temperature gradient. 
@article{VTPMK_2021_2_a2,
     author = {A. O. Syromyasov and T. V. Menshakova},
     title = {Viscous fluid flow between plane walls in presence of temperature gradient},
     journal = {Vestnik Tverskogo gosudarstvennogo universiteta. Seri\^a Prikladna\^a matematika},
     pages = {26--38},
     year = {2021},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a2/}
}
TY  - JOUR
AU  - A. O. Syromyasov
AU  - T. V. Menshakova
TI  - Viscous fluid flow between plane walls in presence of temperature gradient
JO  - Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
PY  - 2021
SP  - 26
EP  - 38
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a2/
LA  - ru
ID  - VTPMK_2021_2_a2
ER  - 
%0 Journal Article
%A A. O. Syromyasov
%A T. V. Menshakova
%T Viscous fluid flow between plane walls in presence of temperature gradient
%J Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika
%D 2021
%P 26-38
%N 2
%U http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a2/
%G ru
%F VTPMK_2021_2_a2
A. O. Syromyasov; T. V. Menshakova. Viscous fluid flow between plane walls in presence of temperature gradient. Vestnik Tverskogo gosudarstvennogo universiteta. Seriâ Prikladnaâ matematika, no. 2 (2021), pp. 26-38. http://geodesic.mathdoc.fr/item/VTPMK_2021_2_a2/

[1] Landau L. D., Lifshitz E. M., Fluid Mechanics, 2nd ed., Butterworth–Heinemann, Waltham, Massachusetts, 1986, 736 pp. | MR

[2] Vargaftik N. B., Handbook of thermophysical properties of gases and liquids, Second Edition, Nauka. Glavnaya redaktsiya fiziko-matematicheskoj literatury, Moscow, 1972, 720 pp. (in Russian)

[3] Malai N. V., “Thermophoresis of a Rigid Spherical Particle in a Fluid”, Fluid Dynamics, 38:6 (2003), 954–962 | DOI | Zbl

[4] Glushak A. V., Malaj N. V., Mironova N. N., “Boundary value problem for the Navier–Stokes equations linearized in rate in the case of non-isothermal flow of heated gaseous medium spheroid”, Journal of computational mathematics and mathematical physics, 52:5 (2012), 946–959 (in Russian) | Zbl

[5] Glushak A. V., Malai N. V., Shchukin E. R., “Solution of a boundary value problem for velocity-linearized Navier–Stokes equations in the case of a heated spherical solid particle settling in fluid”, Journal of computational mathematics and mathematical physics, 58:7 (2018), 1132–1141 | DOI | MR | Zbl

[6] Felderhof B. U., “Thermocapillary mobility of bubbles and electrophoretic motion of particles in a fluid”, Journal of Engineering Mathematics, 30 (1996), 299–305 | DOI | MR | Zbl

[7] Morris S., “The effects of a strongly temperature-dependent viscosity on a slow flow past a hot sphere”, Journal of Fluid Mechanics, 124 (1982), 1–26 | DOI | Zbl

[8] Ansari A., Morris S., “The effects of a strongly temperature-dependent viscosity on Stokes’s drag law: experiments and theory”, Journal of Fluid Mechanics, 159 (1985), 459–476 | DOI | Zbl

[9] Muskat M., Physical Principles of Oil Production, McGraw-Hill, New York, Izhevsk, 1949, 606 pp.

[10] Abramov A. A., Abramov F. A., Butkovskii A. V., Chernyshev S. L., “Effect of Viscous Friction Reduction by Blocking Dissipation”, Fluid Dynamics, 55:6 (2020), 743–750 | DOI

[11] Lojtsyanskij L. G., Fluid and Gas Mechanics, Drofa Publ., Moscow, 1987, 840 pp. (in Russian)

[12] Happel J., Brenner H., Low Reynolds-number hydrodynamics, Prentice-Hall, New Jersey, 1965, 632 pp. | MR

[13] Sedov L. I., Mechanics of Continuous Media, v. 1, World Scientific Publishing Company, New Jersey, 1997, 528 pp. | MR | Zbl