ELEMENTARY CONVECTION CELL IN THE HORIZONTAL LAYER OF VISCOUS INCOMPRESSIBLE LIQUID WITH RIGID AND MIXED BOUNDARY CONDITIONS

  • О. L. Patochkina National Science Center «Kharkov Institute Of Physics And Technology» The National Academy of Science of Ukraine 61108, Kharkov, Akademicheskaya str., 1, phone/fax 8-057-335-08-47«The A.N. Podgorny Institute for Mechanical Engineering Problems» The National Academy of Science of Ukraine61046, Kharkov, Dmitriy Pozharskiy str., 2/10, phone/fax 8-057-294-46-35
  • B. V. Borts V.N. Karazin Kharkov National University 61022, Kharkov, Svoboda square, 4, phone/fax 8-057-705-14-05
  • Viktor I. Tkachenko National Science Center «Kharkov Institute Of Physics And Technology» The National Academy of Science of Ukraine 61108, Kharkov, Akademicheskaya str., 1, phone/fax 8-057-335-08-47V.N. Karazin Kharkov National University61022, Kharkov, Svoboda square, 4, phone/fax 8-057-705-14-05 https://orcid.org/0000-0002-1108-5842
DOI: https://doi.org/10.26565/2312-4334-2015-1-03

Abstract

The result of experimental study of convection cells formation of vacuum oil with mixed boundary conditions is presented. The adding small amounts of dispersed phase (aluminum powder) the viscosity and density of the oil didn’t change and under such conditions the boundary conditions for liquid velocity on a rigid boundary can be applied is shown. The experiments demonstrated that exceeding the certain temperature of the container bottom cells of cylindrical shape start to appear in the oil layer with small addition of dispersed phase (oil paint or aluminum powder). The process of appearing of cells finished when the number of cells increases up to the complete filling of oil volume. When amount of the added dispersed phase are small regardless of the its type a rigid boundary conditions can be applied for the lower boundary, i.e. the mixed boundary conditions are present in the layer is shown. The diameter of cells with the mixed boundary conditions varies from 2,65 to 2,83 mm, which is less than the diameter of a cell with free boundary conditions. For a special case there were obtained the analytical solutions of Navier–Stokes equation with rigid boundaries when Rayleigh number is R ≈ 7124.78 and wave number is 7 r k ≈π . The expressions of distribution for perturbed velocity and temperature in cylindrical convection cell were received. This distributions were compared to similar property for free convective cell for the main mode n = 1. It is demonstrated that the diameter of convective cell is inversely related to the 
value of minimal wave number of the corresponding boundary value problem, i.e. the diameter of a cell with the mixed boundary conditions is less than the diameter of a cell with free boundary conditions, but it’s larger than the diameter of a cell with rigid boundary conditions.

Downloads

Download data is not yet available.

Author Biographies

О. L. Patochkina, National Science Center «Kharkov Institute Of Physics And Technology» The National Academy of Science of Ukraine 61108, Kharkov, Akademicheskaya str., 1, phone/fax 8-057-335-08-47«The A.N. Podgorny Institute for Mechanical Engineering Problems» The National Academy of Science of Ukraine61046, Kharkov, Dmitriy Pozharskiy str., 2/10, phone/fax 8-057-294-46-35
 
B. V. Borts, V.N. Karazin Kharkov National University 61022, Kharkov, Svoboda square, 4, phone/fax 8-057-705-14-05
 
Viktor I. Tkachenko, National Science Center «Kharkov Institute Of Physics And Technology» The National Academy of Science of Ukraine 61108, Kharkov, Akademicheskaya str., 1, phone/fax 8-057-335-08-47V.N. Karazin Kharkov National University61022, Kharkov, Svoboda square, 4, phone/fax 8-057-705-14-05

tkachenko@kipt.kharkov.ua 

 

References

Chandrasekhar S. Hydrodynamic and hydromagnetic stability. – Oxford: University Press, 1970. - 657 p.

Necklyudov I.M.., Borts B.V., Tkachenko V.I. Description of the Langmuir circulations by the ordered set of convective bicubic cells // Applied hydromechanics. – 2012. - Vol. 14(86). – No.2.- P. 29–40.

Schuka A.A. Nanoelectronics. - M.: Fizmatkniga, 2007. – 465 p.

Sazhin B.S., Reutsky V.A. Washing and drying of textile materials: theory and calculation processes. - M.: Fizmatkniga, 1990. – 17-66p.

Muller G. Cultivation of crystals from the melt. - M.: Fizmatkniga, 1991. – 143p.

Rykalin N.N. Laser processing of materials. – M.: Mechanical Engineering, 1975. – 296p.

Gershuni G.Z., Zhuxovickij E.M. Convective stability of incompressible fluid. – М: Science, 1972. – 393 p.

Strutt J. W. (Lord Rауlеigh). On convection currents in a horizontal layer of fluid when the higher temperature is on the under side // Phil. Mag. – 1916. – Vol.32. – P.529–546.

Getling A.V. Formation of spatial structures of Rayleigh-Benard convection // UFN. – 1991. – Vol. 161. – Issue.9. – P.1–80.

Bozbei L.S., Kostikov A.O., Tkachenko V.I. Elementary convective cell in incompressible viscous fluid and its physical properties // Conf. Proc. Int. Conf. MSS-14: Mode Conversion, Coherent Structures and Turbulence, 2014. – 448 p.

Hodakov G.S. Geology of suspensions. Phase flow theory and its experimental validation // Ros. Chem. G. – 2003. - Vol.31. – No.2. – P.33-44.

Silveston P.L. Warmedurchgang in waagerechten Flussigkeitsschichten //Forsch. Ing. Wes. – 1958. – Vol.29. – P.59-69.

Published
2015-06-13
Cited
How to Cite
PatochkinaО. 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 Journal of Physics, 2(1), 23-31. https://doi.org/10.26565/2312-4334-2015-1-03
Issue
Vol. 2 No. 1 (2015): East European Journal of Physics
Section
Original Papers

Authors who publish with this journal agree to the following terms:

    • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
    • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
    • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).