ANALYTICAL SOLUTIONS AND NEUTRAL CURVES OF STATIONARY LINEAR RAYLEIGH PROBLEMS FOR CYLINDRICAL CONVECTIVE CELLS WITH SOLID AND MIXED BOUNDARY CONDITIONS

image_print

J. of Mech. Eng., 2017, vol. 20, no. 1, pp. 17-22

DOI:   https://doi.org/10.15407/pmach2017.01.017

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 20, no. 1, 2017 (March)
Pages 17–22

 

Authors

O. L. Andreyeva, 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: andreevaoksana@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

This paper proposes an analytical solution to the stationary linear Rayleigh problem for a convective cell in a cylindrical geometry with solid boundary conditions. On its basis, analytical expressions for neutral curves in the case of solid and mixed boundary conditions are constructed. It is shown that the neutral curves correspond to the numerical calculations obtained by other authors with a sufficient degree of accuracy.

 

Keywords: Rayleigh stationary linear problem, cylindrical geometry, solid or mixed boundary conditions, analytical solution, neutral curves

 

References

  1. Chandrasekhar, S. (1970). Hydrodynamic and hydromagnetic stability. Oxford: University Press, 657 p.
  2. Neklyudov, I. M., Borts, B. V., & Tkachenko, V. I. (2012). Opisanie Lengmurovskih cirkulyaciy uporyadochennim naborom konvektivnih kubicheskih yacheek. [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).
  3. Shchuka, A. A. (2012). Nanoelektronika. Moscow: Binom. Laboratoriya znaniy, 342 p.
  4. Sazhin, B. S. & Reutskiy, V. A. (1990). Sushka i promivka tekstilnih materialov: teoriya i raschet processov. Moscow: Legpromizdat, 224 p.
  5. Muller, G. (1991) Virashchivanie kristalov iz rasplava. Moscow: Mir, 143 p. https://doi.org/10.1007/978-3-642-84552-9_93
  6. Rykalin, N. N., Uglov, A. A., & Kоkоra, A. N. (1975). Lazernaya obrabotka materialov. Moscow: Mashinostroenie, 296 p.
  7. Gershuny, G. Z. & Zhuhovickiy, E. M. (1972). Convective stability of incompressible fluid. Moscow: Nauka, 393 p.
  8. 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
  9. 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
  10. Patochkina, O. L., Borts, B. V., & Tkachenko, V. I. (2015). Elementary Convection Cell in the Horizontal Layer of Viscous Incompressible Liquid with Rigid and Mixed Boundary Conditions. East-European J. of Phys., vol. 2, no. 1, pp. 23–31. https://doi.org/10.26565/2312-4334-2015-1-03
  11. Bozbey, L. S. (2014). Elementary convective cell in the layer of incompressible, viscous liquid and its physical properties. International conference MSS-14 «Mode conversion, coherent structures and turbulence», Space Research Institute, Moscow, pp. 322–328.

 

Received 09 February 2017