Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 10
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Pérez-Reyes, I. and Dávalos-Orozco, L.A. 2011. Effect of thermal conductivity and thickness of the walls in the convection of a viscoelastic Maxwell fluid layer. International Journal of Heat and Mass Transfer, Vol. 54, Issue. 23-24, p. 5020.

    Münch, A and Wagner, B 2008. Galerkin method for feedback controlled Rayleigh–Bénard convection. Nonlinearity, Vol. 21, Issue. 11, p. 2625.

    Remillieux, Marcel C. Zhao, Hui and Bau, Haim H. 2007. Suppression of Rayleigh-Bénard convection with proportional-derivative controller. Physics of Fluids, Vol. 19, Issue. 1, p. 017102.

    Or, A. C. and Speyer, J. L. 2006. Robust control for convection suppression in a fluid layer: The effects of boundary properties, actuator lag, and major parameter uncertainties. Physical Review E, Vol. 73, Issue. 4,

    Zhao, Hui and Bau, Haim H. 2006. Limitations of linear control of thermal convection in a porous medium. Physics of Fluids, Vol. 18, Issue. 7, p. 074109.

    da Silva, A.K. and Gosselin, L. 2005. Optimal geometry of L and C-shaped channels for maximum heat transfer rate in natural convection. International Journal of Heat and Mass Transfer, Vol. 48, Issue. 3-4, p. 609.

    Or, A. C. and Speyer, J. L. 2005. Gain-scheduled controller for the suppression of convection at high Rayleigh number. Physical Review E, Vol. 71, Issue. 4,

    INABA, Hideo DAI, Chuanshan and HORIBE, Akihiko 2004. The Convective Instability in a Microemulsion Phase-Change-Material Slurry Layer. JSME International Journal Series B, Vol. 47, Issue. 1, p. 126.

    Grigoriev, Roman O. 2002. Control of evaporatively driven instabilities of thin liquid films. Physics of Fluids, Vol. 14, Issue. 6, p. 1895.

    Pabiou, Hervé Liu, Jun and Bénard, Christine 2002. Linear Stability Analysis for the Wall Temperature Feedback Control of Planar Poiseuille Flows. Journal of Dynamic Systems, Measurement, and Control, Vol. 124, Issue. 4, p. 617.

  • Journal of Fluid Mechanics, Volume 411
  • May 2000, pp. 39-58

The effect of boundary properties on controlled Rayleigh–Bénard convection

  • DOI:
  • Published online: 01 May 2000

We investigate the effect of the finite horizontal boundary properties on the critical Rayleigh and wave numbers for controlled Rayleigh–Bénard convection in an infinite horizontal domain. Specifically, we examine boundary thickness, thermal diffusivity and thermal conductivity. Our control method is through perturbation of the lower-boundary heat flux. A linear proportional-differential control method uses the local amplitude of a shadowgraph to actively redistribute the lower-boundary heat flux. Realistic boundary conditions for laboratory experiments are selected. Through linear stability analysis we examine, in turn, the important boundary properties and make predictions of the properties necessary for successful control experiments. A surprising finding of this work is that for certain realistic parameter ranges, one may find an isola to time-dependent convection as the primary bifurcation.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *