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Stability of a fluid-saturated porous medium contained in a vertical cylinder heated from below by forced convection

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An Erratum to this article was published on 26 June 2013

Abstract

A linear stability analysis determining the critical Rayleigh number R c for onset of convection in a bounded vertical cylinder containing a fluid-saturated porous medium is performed for insulated sidewalls, isothermal top surface, and bottom surface heated by forced convection. This Newtonian heating of the bottom surface involves a Biot number Bi that allows consideration of the continuum of boundary conditions ranging from constant heat flux, with global minimum R min=27.096 found as Bi→0, to isothermal, with global minimum R min=4π2 found as Bi→ ∞. In both cases and for most cylinder aspect ratios, incipient convection sets in as an asymmetric mode, though islands of aspect ratio exist where the onset mode is symmetric. Sample three-dimensional renderings of disturbance temperature distributions showing preferred modes at onset of convection for fixed Bi are provided and an analytical fit to R min as a function of Bi is given.

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Acknowledgements

P.D.W. extends his gratitude to Professor Bruno Keller for his gracious hospitality and support as Gastprofessor in the Department of Building Physics at ETH Zürich during the period this paper was written.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Colorado, UCB 427, Boulder, CO, 80309-0427, USA

    Joseph P. Kubitschek & Patrick D. Weidman

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  1. Joseph P. Kubitschek
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  2. Patrick D. Weidman
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Correspondence to Joseph P. Kubitschek.

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An erratum to this article is available at http://dx.doi.org/10.1007/s00231-013-1193-0.

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Kubitschek, J.P., Weidman, P.D. Stability of a fluid-saturated porous medium contained in a vertical cylinder heated from below by forced convection. Heat Mass Transfer 42, 789–794 (2006). https://doi.org/10.1007/s00231-005-0045-y

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  • DOI: https://doi.org/10.1007/s00231-005-0045-y

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