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Journal of Porous Media

ISSN for PRINT: 1091-028X

Institutional price:	$713.00
Issues per year:	8

Best Paper Award Selection - Editorial Board Site

2008, Volume11

96 pages

Issue price - $107.00

Effects of Combined Horizontal and Vertical Heterogeneity on the Onset of Transient Convection in a Porous Medium

D. A. Nield
Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland, New Zealand

A. V. Kuznetsov
Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910, USA

ABSTRACT

The effects of both horizontal and vertical hydrodynamic and thermal heterogeneity on the onset of convection in a horizontal layer of a saturated porous medium, uniformly heated from below but with a nonuniform basic temperature gradient resulting from transient heating or otherwise, are studied analytically using linear stability theory for the case of weak heterogeneity. 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.