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Degenerate onset of convection in vertical porous cylinders

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Abstract

The fourth-order Darcy–Bénard eigenvalue problem for the onset of thermal convection in vertical porous cylinders is investigated. With cylinder walls either impermeable/adiabatic or open/conducting, the thermomechanical fourth-order problem over the cylinder’s cross-section decouples into a second-order eigenvalue problem, so that each perturbation variable is governed by a single Helmholtz equation. The eigenvalues for the decoupled Helmholtz equation give discrete sample points on the continuous dispersion relation curve, where the smallest sampled Rayleigh number represents the convection onset. Exact analytical solutions are given for a triangular cross-section and circular geometries.

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Authors and Affiliations

  1. Faculty of Mathematical Sciences and Technology, Norwegian University of Life Sciences, 1432, Ås, Norway

    Peder A. Tyvand

  2. Department of Mathematics, University of Agder, 4604, Kristiansand, Norway

    Leiv Storesletten

Authors
  1. Peder A. Tyvand
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  2. Leiv Storesletten
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Correspondence to Peder A. Tyvand.

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Tyvand, P.A., Storesletten, L. Degenerate onset of convection in vertical porous cylinders. J Eng Math 113, 165–181 (2018). https://doi.org/10.1007/s10665-018-9979-1

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  • DOI: https://doi.org/10.1007/s10665-018-9979-1

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