Heat transfer in the thermo-electro-hydrodynamic convection under microgravity conditions

  • M. Tadie Fogaing
  • H. N. Yoshikawa
  • O. Crumeyrolle
  • I. MutabaziEmail author
Regular Article
Part of the following topical collections:
  1. Irreversible Dynamics: A topical issue dedicated to Paul Manneville


This article deals with the thermal convection in a dielectric fluid confined in a finite-length plane capacitor with a temperature gradient under microgravity conditions. The dielectrophoretic force resulting from differential polarization of the fluid plays the role of buoyancy force associated with an electric effective gravity. It induces the convection when the Rayleigh number based on this electric gravity exceeds a critical value. Two-dimensional numerical simulation for a geometry with a large aspect ratio is used to determine the convective flow in the saturated state. The Nusselt number Nu is computed for a wide range of Prandtl number (0.01 ≤ Pr ≤ 103) and its dependence on the distance from the critical condition is determined. A correlation between Nu and Pr in the vicinity of criticality is obtained and compared with that of the Rayleigh-Bénard convection. The behavior of the convection is analyzed in detail from an energetic viewpoint: electrostatic energy, power inputs by different components of the electric gravity and viscous and thermal dissipations are computed.

Graphical abstract


Topical issue: Irreversible Dynamics: A topical issue dedicated to Paul Manneville 


  1. 1.
    P. Manneville, Structures Dissipatives Chaos et Turbulence (CEA, Gif-sur-Yvette, 1991).Google Scholar
  2. 2.
    P. Bergé, Y. Pomeau, C. Vidal, Order within Chaos: Towards a Deterministic Approach to Turbulence (John Wiley & Sonc Inc., 1986).Google Scholar
  3. 3.
    M.C. Cross, P.C. Hohenberg, Rev. Mod. Phys. 65, 851 (1993).ADSCrossRefGoogle Scholar
  4. 4.
    R. Tagg, P.D. Weidman, Z. Angew. Math. Phys. 58, 431 (2007).zbMATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    B. Chandra, D.E. Smylie, Geophys. Fluid Dyn. 3, 211 (1972).ADSCrossRefGoogle Scholar
  6. 6.
    P.H. Roberts, Q. J. Mech. Appl. Math. 22, 211 (1969).zbMATHCrossRefGoogle Scholar
  7. 7.
    R.J. Turnbull, Phys. Fluids 12, 1809 (1969).ADSCrossRefGoogle Scholar
  8. 8.
    P.J. Stiles, Chem. Phys. Lett. 179, 311 (1991).ADSCrossRefGoogle Scholar
  9. 9.
    B.L. Smorodin, Tech. Phys. Lett. 27, 1062 (2001).ADSCrossRefGoogle Scholar
  10. 10.
    H.N. Yoshikawa, M.T. Fogaing, O. Crumeyrolle, I. Mutabazi, Phys. Rev. E 87, 043003 (2013).ADSCrossRefGoogle Scholar
  11. 11.
    L.D. Landau, E.M. Lifshitz, Electrodynamics of Continuous Media, Vol. 8 of Landau and Lifshitz Course of Theoretical Physics, 2nd edition (Elsevier Butterworth-Heinemann, Burlington, Massachusetts, 1984).Google Scholar
  12. 12.
    J.R. Melcher, Continuum Electromechanics (The MIT Press, 1981).Google Scholar
  13. 13.
    T.B. Jones, Adv. Heat Transfer 14, 107 (1979).CrossRefGoogle Scholar
  14. 14.
    M. Takashima, H. Hamabata, J. Phys. Soc. Jpn 53, 1728 (1984).ADSCrossRefGoogle Scholar
  15. 15.
    S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability (Dover, New York, 1961).Google Scholar
  16. 16.
    P.J. Stiles, F. Lin, P.J. Blennerhassett, Phys. Fluids A 5, 3273 (1993).ADSzbMATHCrossRefGoogle Scholar
  17. 17.
    H.N. Yoshikawa, O. Crumeyrolle, I. Mutabazi, Phys. Fluids 25, 024106 (2013).ADSCrossRefGoogle Scholar
  18. 18.
    M. Takashima, Q. J. Mech. Appl. Math. 33, 93 (1980).zbMATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    B.L. Smorodin, M.G. Velarde, J. Electrostatics 50, 205 (2001).CrossRefGoogle Scholar
  20. 20.
    I.M. Yavorskaya, N.I. Fomina, Y.N. Belyaev, Acta Astronaut. 11, 179 (1984).ADSzbMATHCrossRefGoogle Scholar
  21. 21.
    A. Schlüter, D. Lortz, F. Busse, J. Fluid Mech. 23, 129 (1965).ADSzbMATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    E.D. Siggia, Annu. Rev. Fluid Mech. 26, 137 (1994).ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    B.I. Shraiman, E.D. Siggia, Phys. Rev. A 42, 3650 (1990).ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • M. Tadie Fogaing
    • 1
  • H. N. Yoshikawa
    • 1
  • O. Crumeyrolle
    • 1
  • I. Mutabazi
    • 1
    Email author
  1. 1.Laboratoire Ondes et Milieux Complexes, UMR 6294 CNRSUniversité du HavreLe Havre CedexFrance

Personalised recommendations