Local thermal non-equilibrium effects in the Darcy-Benard instability with isoflux boundary conditions


Barletta, A. and Rees, D. A. S., 2012. Local thermal non-equilibrium effects in the Darcy-Benard instability with isoflux boundary conditions. International Journal of Heat and Mass Transfer, 55 (1-3), pp. 384-394.

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    The Darcy-Benard problem with constant heat flux boundary conditions is studied in a regime where the fluid and solid phases are in local thermal non-equilibrium. The onset conditions for convective instability in the plane porous layer are investigated using a linear stability analysis. Constant heat flux boundary conditions are formulated according to the Amiri-Vafai-Kuzay Model A, where the boundary walls are assumed as impermeable and with a high thermal conductance. The normal mode analysis of the perturbations imposed on the basic state leads to a one-dimensional eigenvalue problem, solved numerically to determine the neutral stability condition. Analytical solutions are found for the limit of small wave numbers, and in the regime where the conductivity of the solid phase is much larger than the conductivity of the fluid phase. A comparison with the corresponding results under conditions of local thermal equilibrium is carried out. The critical conditions for the onset of convection correspond to a zero wave number only when the inter-phase heat transfer coefficient is sufficiently large. Otherwise, the critical conditions correspond to a nonzero wave number.


    Item Type Articles
    CreatorsBarletta, A.and Rees, D. A. S.
    Uncontrolled Keywordsbuoyancy-induced instability, local thermal non-equilibrium, darcy-benard problem, porous medium, constant heat flux
    DepartmentsFaculty of Engineering & Design > Mechanical Engineering
    Research CentresAerospace Engineering Research Centre
    Publisher StatementRees_IJHMT_2012_55_1-3_384.pdf: NOTICE: this is the author’s version of a work that was accepted for publication in International Journal of Heat and Mass Transfer. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in International Journal of Heat and Mass Transfer, vol 55, issue 1-3, 2012, DOI 10.1016/j.ijheatmasstransfer.2011.09.031
    ID Code27964


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