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The onset of Darcy-Bénard convection in an inclined layer heated from below

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Summary

We present an, account of the linear instability of Darcy-Boussinesq convection in a uniform, unstably stratified porous layer at arbitrary inclinations α from the horizontal. A full numerical solution of the linearized disturbance equations is given and the detailed graphical results used to motivate various asymptotic analyses. A careful study shows that at large Rayleigh numbers two-dimensional instability can only arise when α≤31.30°. However it is also demonstrated that the maximum inclination below which this instability may be possible is the slightly greater value of 31.49° which corresponds to a critical Rayleigh number of 104.30.

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Author notes

  1. D. A. S. Rees

    Present address: Department of Mechanical Engineering, University of Bath, BA2 7AY, Claverton Down, Bath, U.K.

  2. A. P. Bassom

    Present address: School of Mathematical Sciences, University of Exeter, North Park Road, EX4 4QE, Exeter, Devon, U.K.

Authors and Affiliations

  1. New College, Anzac Parade, University of New South Wales, 2052, Sydney, Australia

    A. P. Bassom

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  1. D. A. S. Rees
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Rees, D.A.S., Bassom, A.P. The onset of Darcy-Bénard convection in an inclined layer heated from below. Acta Mechanica 144, 103–118 (2000). https://doi.org/10.1007/BF01181831

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  • DOI: https://doi.org/10.1007/BF01181831

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