Abstract
The effect of strong heterogeneity on the onset of convection induced by a vertical density gradient in a saturated porous medium governed by Darcy’s law is investigated. The general case, where there is heterogeneity in both the vertical and horizontal directions, and where there is heterogeneity in permeability, thermal conductivity, and applied temperature gradient, is considered. A computer package has been developed to implement an algorithm giving a criterion for instability, and this is now employed to investigate the case where the variation is of a periodic or localized nature.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Beck J.L.: Convection in a box of porous material saturated with fluid. Phys. Fluids 15, 1377–1383 (1977). doi:10.1063/1.1694096
Kuznetsov A.V., Nield D.A.: The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium: double diffusive case. Transp. Porous Media 72, 157–170 (2008). doi:10.1007/s11242-007-9141-4
Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (1992)
Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (1999)
Nield D.A., Bejan A.: Convection in Porous Media. Springer, New York (2006)
Nield D.A., Kuznetsov A.V.: The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium. Int. J. Heat Mass Transf. 50, 1909–1915 (2007a). doi:10.1016/j.ijheatmasstransfer.2006.09.023 Erratum, 4512–4512
Nield D.A., Kuznetsov A.V.: The onset of convection in a shallow box occupied by a heterogeneous porous medium with constant flux boundaries. Transp. Porous Media 67, 441–451 (2007b). doi:10.1007/s11242-006-9035-x
Nield D.A., Kuznetsov A.V.: The effects of combined horizontal and vertical heterogeneity and anisotropy on the onset of convection in a porous medium. Int. J. Therm. Sci. 46, 1211–1218 (2007c). doi:10.1016/j.ijthermalsci.2007.01.005
Nield D.A., Kuznetsov A.V.: The effects of combined horizontal and vertical heterogeneity on the onset of convection in a bidisperse porous medium. Int. J. Heat Mass Transf. 50, 3329–3339 (2007d). doi:10.1016/j.ijheatmasstransfer.2007.01.027
Nield D.A., Kuznetsov A.V.: The onset of convection in a porous medium occupying an enclosure of variable width. ASME J. Heat Transf. 129, 1714–1718 (2007e). doi:0.1115/1.2768097
Nield D.A., Kuznetsov A.V.: The effects of combined horizontal and vertical heterogeneity on the onset of transient convection in a porous medium. J. Porous Media 11, 377–387 (2008a). doi:10.1615/JPorMedia.v11.i4.40
Nield D.A., Kuznetsov A.V.: The effects of combined horizontal and vertical heterogeneity on the onset of convection in a porous medium: Moderate heterogeneity. Int. J. Heat Mass Transf. 50, 1909–1915 (2008b). doi:10.1016/j.ijheatmasstransfer.2006.09.023
Nield D.A., Kuznetsov A.V., Simmons C.T.: The effect of strong heterogeneity on the onset of convection in a porous Medium. Transp. Porous Media 77, 169–186 (2009). doi:10.1007/s11242-008-9297-6
Nield D.A., Simmons C.T.: A discussion on the effect of heterogeneity on the onset of convection in a porous medium. Transp. Porous Media 68, 413–421 (2007). doi:10.1007/s11242-006-9045-8
Prasad A., Simmons C.T.: Unstable density-driven flow in heterogeneous porous media: a stochastic study of the Elder [1967b] “short heater” problem. Water Resour. Res. 39(1), #1007 (2003)
Simmons C.T., Fenstemaker T.R., Sharp J.M.: Variable-density flow and solute transport in heterogeneous porous media: approaches, resolutions, and future challenges. J. Contam. Hydrol. 52, 245–275 (2001). doi:10.1016/S0169-7722(01)00160-7
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kuznetsov, A.V., Nield, D.A. & Simmons, C.T. The Effect of Strong Heterogeneity on the Onset of Convection in a Porous Medium: Periodic and Localized Variation. Transp Porous Med 81, 123–139 (2010). https://doi.org/10.1007/s11242-009-9390-5
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-009-9390-5