The convection of a Bingham fluid in a differentially-heated porous cavity

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Abstract

Purpose – The purpose is to determine the manner in which a yield-stress fluid begins convecting when it saturates a porous medium. A sidewall-heated rectangular cavity is selected as the testbed for this pioneering work.

Design/methodology/approach – Steady solutions are obtained using (i) a second-order accurate finite difference method, (ii) line relaxation based on the Gauss-Seidel smoother, (iii) a Full Approximation Scheme multigrid algorithm with V-cycling and (iv) a regularization of the Darcy-Bingham model to smooth
the piecewise linear relation between the Darcy flux and the applied body forces.

Findings – While Newtonian fluids always convect whenever the Darcy-Rayleigh number is nonzero, Bingham fluids are found to convect only when the Darcy-Rayleigh number exceeds a value which is linearly dependent on both the Rees-Bingham number and the overall perimeter of the rectangular cavity.
Stagnation is always found in the centre of the cavity and in regions close to the four corners. Care must be taken over the selection of the regularization constant.

Research limitations/implications – The Darcy-Rayleigh number is restricted to values which are at or below 200.

Originality/value – This is the first investigation of the effect of yield stress on nonlinear convection in porous media.
Original languageEnglish
Pages (from-to)879-896
Number of pages18
JournalInternational Journal for Numerical Methods in Heat and Fluid Flow
Volume26
Issue number3/4
DOIs
Publication statusPublished - May 2016

Keywords

  • Porous media, convection, stagnation, nonlinear flow, rectangular cavity, Bingham fluid.

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