Abstract
Equations of thermal vibrational convection of an inhomogeneously heated liquid are analytically solved for arbitrary orientation of vectors determining the heating direction, force of gravity, and vibrations in a closed cavity in the shape of an infinite horizontal cylinder. It is demonstrated that for any orientation of these vectors in the plane perpendicular to the cylinder, the gravitational and vibrational convection mechanisms can completely compensate each other. The ratio is determined between the vibrational and the gravitational Grashof numbers such that mechanical equilibrium conditions are satisfied. This ratio is proved by direct numerical calculation of complete equations of thermal vibrational convection.
Similar content being viewed by others
References
A. V. Zyuzgin, G. F. Putin, N. G. Ivanova, A. V. Chudinov, A. I. Ivanov, A. V. Kalmykov, V. I. Polezhaev, and V. M. Emelianov, Adv. Space Res. 32, 205 (2003).
V. A. Demin, G. Z. Gershuni, and I. V. Verholantsev, Int. J. Heat Mass Transfer 39, 1979 (1996).
E. M. Zhukhovitskis-, Prikl. Mat. Mekh. 18, 205 (1954).
S. M. Zen’kovskaya and I. B. Simonenko, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 51 (1966).
G. Z. Gershuni and E. M. Zhukhovitskis-, Dokl. Akad. Nauk SSSR 249(1-3), 580 (1979) [Sov. Phys. Dokl. 24 (11), 894 (1979)].
G. Z. Gershuni and E. M. Zhukhovitskis-, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 12 (1981).
G. Z. Gershuni, E. M. Zhukhovitskis-, and A. N. Sharifulin, Chislennye Metody Mekh. Sploshnos- Sredy 14, 21 (1983).
A. N. Sharifulin, Convective Flows (Perm State Pedagogical Institute, Perm, Soviet Union, 1981), p. 22 [in Russian].
J. P. McHugh, Q. Appl. Math. LVIII, 425 (2000).
G. Z. Gershuni and E. M. Zhukhovitskis-, Convective Stability of an Incompressible Liquid (Nauka, Moscow, 1972) [in Russian].
V.I. Chernatynskis- and M. I. Shliomis, Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 1, 64 (1973).
A. I. Nikitin and A. N. Sharifulin, in Processes of Heat and Mass Transfer of an Viscous Liquid (Ural Scientific Centre, Academy of Sciences of the Soviet Union, Sverdlovsk, Soviet Union, 1986), p. 32 [in Russian]; A. I. Nikitin and A. N. Sharifulin, Heat Transfer-Sov. Res. 21, 213 (1989).
A. N. Sharifulin, in Hydrodynamic and Convective Stability of an Incompressible Liquid (Ural Scientific Centre, Academy of Sciences of the Soviet Union, Sverdlovsk, Soviet Union, 1984), p. 27 [in Russian]; A. N. Sharifulin, Fluid Mech.-Sov. Res. 15, 28 (1986).
F. T. Ferguson and L. U. Lilleleht, Int. J. Heat Mass Transfer 39, 2895(1996). Translated by E. Baudina
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © A.N. Sharifulin, 2010, published in Zhurnal Éksperimental’noĭ i Teoreticheskoĭ-Fiziki, 2010, Vol. 137, No. 1, pp. 177–182.
Rights and permissions
About this article
Cite this article
Sharifulin, A.N. Controllable equilibrium of an inhomogeneously heated liquid in a vibrational field. J. Exp. Theor. Phys. 110, 157–161 (2010). https://doi.org/10.1134/S1063776110010188
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063776110010188