A progressive asymptotic approach procedure for simulating steady-state natural convective problems in fluid-saturated porous media

Chongbin Zhao, Bruce E. Hobbs, Alison Ord

    Research output: Chapter in Book/Conference paperChapter

    Abstract

    In a fluid-saturated porous medium, a change in medium temperature may lead to a change in the density of pore-fluid within the medium. This change can be considered as a buoyancy force term in the momentum equation to determine pore-fluid flow in the porous medium using the Oberbeck-Boussinesq approximation model. The momentum equation used to describe pore-fluid flow in a porous medium is usually established using Darcy's law or its extensions. If a fluid-saturated porous medium has the geometry of a horizontal layer, and is heated uniformly from the bottom of the layer, then there exists a temperature difference between the top and bottom boundaries of the layer. Since the positive direction of the temperature gradient due to this temperature difference is opposite to that of the gravity acceleration, there is no natural convection for a small temperature gradient in the porous medium. In this case, heat energy is solely transferred from the high temperature region (the bottom of the horizontal layer) to the low temperature region (the top of the horizontal layer) by thermal conduction. However, if the temperature difference is large enough, it may trigger natural convection in the fluid-saturated porous medium. This problem was first treated analytically by Horton and Rogers (1945) as well as Lapwood (1948), and is often called the Horton-Rogers-Lapwood problem.

    Original languageEnglish
    Title of host publicationFundamentals of Computational Geoscience
    Subtitle of host publicationNumerical Methods and Algorithms
    EditorsChongbin Zhao, Bruce Hobbs, Alison Ord, Alison Ord
    PublisherSpringer-Verlag Wien
    Pages7-36
    Number of pages30
    ISBN (Print)9783540897422
    DOIs
    Publication statusPublished - 7 May 2009

    Publication series

    NameLecture Notes in Earth Sciences
    Volume122
    ISSN (Print)0930-0317

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  • Cite this

    Zhao, C., Hobbs, B. E., & Ord, A. (2009). A progressive asymptotic approach procedure for simulating steady-state natural convective problems in fluid-saturated porous media. In C. Zhao, B. Hobbs, A. Ord, & A. Ord (Eds.), Fundamentals of Computational Geoscience: Numerical Methods and Algorithms (pp. 7-36). (Lecture Notes in Earth Sciences; Vol. 122). Springer-Verlag Wien. https://doi.org/10.1007/978-3-540-89743-9_2