ELEMENTARY CONVECTIVE CELL IN AN INCOMPRESSIBLE VISCOUS FLUID LAYER AND ITS PARAMETERS

Authors

L. S. Bozbey, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), National Science Center Kharkov Institute of Physics and Technology (1, Akademicheskaya St., Kharkov, 61108, Ukraine), e-mail: bozbiei@kipt.kharkov.ua

A. O. Kostikov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), V. N. Karazin Kharkiv National University (4, Svobody Sq., Kharkiv, 61022, Ukraine), e-mail: kostikov@ipmach.kharkov.ua, ORCID: 0000-0001-6076-1942

V. I. Tkachenko, National Science Center Kharkov Institute of Physics and Technology (1, Akademicheskaya St., Kharkov, 61108, Ukraine),  V. N. Karazin Kharkiv National University (4, Svobody Sq., Kharkiv, 61022, Ukraine), e-mail: tkachenko@kipt.kharkov.ua, ORCID: 0000-0002-1108-5842

Abstract

The principle of formation of convective structures in a layer of a viscous incompressible fluid with a uniform heating from below is considered. The energy principle of using a cylindrical elementary convective cell of a cylindrical shape was proposed and implemented. Its parameters and thermal properties are determined. Experimental studies of the thermophysical properties of an elementary convective cell are carried out, and numerical data processing is performed.

Keywords: elementary convective cell, free boundaries, convective processes, heat transfer, temperature gradient

References

1. Benard, H. (1900). Les tourbillons cellulaires dans une nappe liquide. Description générale des phénomènes. Revue générale des Sciences pures et appliqués, vol. 11, no. 24, 1261–1271.
2. Benard, H. (1900). Les tourbillons cellulaires dans une nappe liquide. Procédés mécaniques et optiques d’examen lois numériques des phénomènes. Revue générale des Sciences pures et appliqués, vol. 11, 24, pp. 1309–1328.
3. Strutt, J. W. (Lord Rayleigh). (1916). On convection currents in a horizontal layer of fluid when the higher temperature is on the under side.  Phil. Mag., vol. 32, pp. 529–546. https://doi.org/10.1080/14786441608635602
4. Thomson, J. (1882). On a changing tesselated structure in certain liquid. Glasgow Philos. Soc., vol. 13, pp. 464–468.
5. http://www.ivanov-portal.ru/astron/30.htm
6. Shishkin, N. S. (1991). Education cellular structures in a liquid or gas layers. Uspekhi phizicheskih nauk – Successes of physical sciences, vol. 31, no. 4, pp. 462–490 (in Russian).
7. http://lifeglobe.net/blogs/details?id=860
8. http://p-i-f.dreamwidth.org/351593.html
9. Ray, R. J., Krantz, W. B., Caine, T. N., & Gunn, R. D. (1983). A model for sorted patterned-ground regularity. of Glaciology, vol. 29, no. 102, pp. 317–337. https://doi.org/10.1017/S0022143000008376
10. Rychkova, E. V. & Tychkov, S. A. (1997). Numerical model of thermal convection in the upper mantle of the earth under continental lithosphere. Vyichislitelnyie tehnologii, vol. 2, no. 5, 66–81. (in Russian).
11. http://en.wikipedia.org/wiki/Supergranulation
12. Pikel’ner, S. B. (1966). Dynamics of the solar atmosphere. Uspekhi phizicheskih nauk – Successes of physical sciences, vol. 88, no. 3, 505–523. (in Russian). https://doi.org/10.3367/UFNr.0088.196603f.0505
13. http://opensky.library.ucar.edu/collections/SOARS-000-000-000-268 .
14. Rieutord, M. & Rincon, F. (2010). The Sun’s Supergranulation. Living Rev. Sol. Phys., vol. 7, no. 2, pp. 84. https://doi.org/10.12942/lrsp-2010-2
15. Gershuni, G. Z. & Zhukhovitskii, E. M. (1972). Convective stability of incompressible fluid. Moscow: Nauka, 393 p. (in Russian).
16. Chandrasekhar, S. (1970). Hydrodynamic and hydromagnetic stability. Oxford: University Press, 657 p.
17. Getling, A. V. (1991). Spatial patterns formed by Rayleigh-Benard convection. Uspekhi phizicheskih nauk, vol. 161, no. 9, pp. 1–80. (in Russian). https://doi.org/10.3367/UFNr.0161.199109a.0001
18. Bozbiei, L. S. (2013). An elementary convective cell in layer of incompressible viscous fluid. Conference of young scientists and specialists. Kharkov: A. Podgorny Institute of Mechanical Engineering Problems of NASU, pp. 29. (in Russian).
19. Bozbey, L. S., Kostikov, A. O., & Tkachenko, V. I. (2014). Elementary convective cell and its thermal properties. Proc. conf. “Physical and technical problems of energy and ways of their solution in 2014”. Kharkov, Ukraine, on 25-26 June 2014, pp. 6. (in Russian).
20. Nekludov, I. M., Bortz, B. V., & Tkachenko, V. I. (2012). Description of the Langmuir circulations by the ordered set of convective bicubic cells. Prikladnaya gidromehanika – Applied hydromechanics, vol. 14 (86), no. 2, pp. 29–40 (in Russian).
21. Van Dyke, M. (1986). Atlas flow of liquids and gases. Moscow: Mir, 184 p. (in Russian).
22. Koschmieder, E. L. (1993). Bénard cells and Taylor vortices. Cambridge etc., Cambridge University Press, 337 p. https://doi.org/10.1002/zamm.19940741005
23. Adelman, E. D. (1996). Effect of liquid film thickness to cell size ratio convection. Zhurnal tehnicheskoy fiziki, vol. 68, no. 11, pp. 7–11. (in Russian).
24. Eckert, K., Bestehorn, M., & Thess, A. E. (1998). Square cells in surface-tension-driven Bernard convection: experiment and theory. J. Fluid Mech., vol. 356, pp. 155–197. https://doi.org/10.1017/S0022112097007842
25. Bozbiei, L. S., Borts, B. V., Kazarinov, U. G., Kostikov, A. O., & Tkachenko, V. I. (2015). Experimental study of liquid movement in free elementary convective cells. Energetika, vol. 61, no. 2, pp. 45–56.  https://doi.org/10.6001/energetika.v61i2.3132
26. (1960). Royal Society Mathematical Tables. Vol. 7. Bessel functions. Cambridge University Press, 140 p.
27. Zierep, J. (1958). Über rotationssymmetrische Zellularkonvektionsströmungen.  Z. Agev. Mah. Mech., Bd. 39, no. 7/8, pp. 329–333. https://doi.org/10.1002/zamm.19580380746
28. Zierep, J. (1958). Eine rotationssymmetrische Zellularkonvektionsstromun. Beitr.  Phys. Atmos., vol. 30, pp. 215–222.
29. Korn, G. & Korn, T. (1968). Mathematical Handbook for Scientists and Engineers. Moscow: Nauka, 720 p. (in Russian).

Received 01 August 2016

Published 30 September 2016