Darcy-Bénard-Bingham convection

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Abstract

The present paper is the first to consider Darcy–Bénard–Bingham convection. A Bingham fluid saturates a horizontal porous layer that is subjected to heating from below. It is shown that this simple extension to the classical Darcy–Bénard problem is linearly stable to small-amplitude disturbances but nevertheless admits strongly nonlinear convection. The Pascal model for a Bingham fluid occupying a porous medium is adopted, and this law is regularized in a frame-invariant manner to yield a set of two-dimensional governing equations that are then solved numerically using finite difference approximations. A weakly nonlinear theory of the regularized Pascal model is used to show that the onset of convection is via a fold bifurcation. Some parametric studies are performed to show that this non-linear onset of convection arises at increasing values of the Darcy–Rayleigh number as the Rees–Bingham number increases and that, for a fixed Rees–Bingham number, the wavenumber at which the rate of heat transfer is maximized increases with the Darcy–Rayleigh number.
Original languageEnglish
Article number084107
Number of pages11
JournalPhysics of Fluids
Volume32
Issue number8
Early online date21 Aug 2020
DOIs
Publication statusPublished - 31 Aug 2020

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