The onset of convection in a shallow box occupied by a heterogeneous porous medium with constant flux boundaries |
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Authors: | D A Nield A V Kuznetsov |
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Institution: | (1) Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand;(2) Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA |
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Abstract: | The effects of hydrodynamic and thermal heterogeneity, for the case of variation in both the horizontal and vertical directions,
on the onset of convection in a horizontal layer of a saturated porous medium uniformly heated from below, are studied analytically
using linear stability theory for the case of weak heterogeneity. Attention is focused on the case of constant flux upper
and lower boundaries, a case for which the critical horizontal wavenumber is zero, and attention is also concentrated on the
case of a shallow layer. It is found that the effect of such heterogeneity on the critical value of the Rayleigh number Ra
based on mean properties is of second order if the properties vary in a piecewise constant or linear fashion. The effects
of horizontal heterogeneity and vertical heterogeneity are then comparable once the aspect ratio is taken into account, and
to a first approximation are independent. The combination of permeability heterogeneity and conductivity heterogeneity can
be either stabilizing or destabilizing for the present case. |
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Keywords: | Natural convection Heterogeneity Instability Horton– Rogers– Lapwood problem |
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