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.
|Number of pages||11|
|Journal||Physics of Fluids|
|Early online date||21 Aug 2020|
|Publication status||Published - 31 Aug 2020|