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Journal of Porous Media

Published 12 issues per year

ISSN Print: 1091-028X

ISSN Online: 1934-0508

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

Volume 11, Issue 4, 2008, pp. 377-387
DOI: 10.1615/JPorMedia.v11.i4.40
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D. A. Nield
Department of Engineering Science, University of Auckland, Auckland, New Zealand

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.

CITED BY

  1. Nield D. A., Kuznetsov A. V., Simmons Craig T., The Effect of Strong Heterogeneity on the Onset of Convection in a Porous Medium: 2D/3D Localization and Spatially Correlated Random Permeability Fields, Transport in Porous Media, 83, 3, 2010. Crossref

  2. Kuznetsov A. V., Nield D. A., Simmons Craig T., The Effect of Strong Heterogeneity on the Onset of Convection in a Porous Medium: Periodic and Localized Variation, Transport in Porous Media, 81, 1, 2010. Crossref

  3. Nield D. A., Kuznetsov A. V., Simmons Craig T., The Effect of Strong Heterogeneity on the Onset of Convection in a Porous Medium, Transport in Porous Media, 77, 2, 2009. Crossref

  4. Simmons Craig T., Kuznetsov A. V., Nield D. A., Effect of strong heterogeneity on the onset of convection in a porous medium: Importance of spatial dimensionality and geologic controls, Water Resources Research, 46, 9, 2010. Crossref

  5. Nield D. A., Kuznetsov A. V., The Onset of Convection in a Heterogeneous Porous Medium with Transient Temperature Profile, Transport in Porous Media, 85, 3, 2010. Crossref

  6. Kuznetsov A. V., Nield D. A., The Effects of Combined Horizontal and Vertical Heterogeneity on the Onset of Convection in a Porous Medium with Vertical Throughflow, Transport in Porous Media, 90, 2, 2011. Crossref

  7. Nield D.A., Kuznetsov A.V., The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium with horizontal throughflow, International Journal of Heat and Mass Transfer, 54, 25-26, 2011. Crossref

  8. Shivakumara I. S., Ng Chiu-On, Ravisha M., Ferromagnetic Convection in a Heterogeneous Darcy Porous Medium Using a Local Thermal Non-equilibrium (LTNE) Model, Transport in Porous Media, 90, 2, 2011. Crossref

  9. Kuznetsov A. V., Nield D. A., The Effect of Strong Heterogeneity and Strong Throughflow on the Onset of Convection in a Porous Medium: Periodic and Localized Variation, Transport in Porous Media, 92, 2, 2012. Crossref

  10. Nield D. A., Kuznetsov A. V., The Effect of Strong Heterogeneity and Strong Throughflow on the Onset of Convection in a Porous Medium: Non-Periodic Global Variation, Transport in Porous Media, 91, 3, 2012. Crossref

  11. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2013. Crossref

  12. Nield Donald A., Bejan Adrian, Internal Natural Convection: Heating from Below, in Convection in Porous Media, 2017. Crossref

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