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

Purpose – The purpose of this paper 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 usin...

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Veröffentlicht in:International journal of numerical methods for heat & fluid flow Jg. 26; H. 3/4; S. 879 - 896
1. Verfasser: Rees, D. Andrew S
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Bradford Emerald Group Publishing Limited 03.05.2016
Schlagworte:
Approximation
Computational fluid dynamics
Convection
Engineering
Finite difference method
Fluid flow
Fluids
Forces (mechanics)
Holes
Mathematical analysis
Mechanical engineering
Newtonian fluids
Numerical analysis
Permeability
Porous media
Rayleigh number
Regularization
Shear stress
Solutions
Stagnation
Viscosity
Yield strength
Yield stress
Yields
Porous media
Bingham fluid
Nonlinear flow
Rectangular cavity
Stagnation
Convection
ISSN:0961-5539, 1758-6585
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Zusammenfassung:Purpose – The purpose of this paper 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 a second order accurate finite difference method, line relaxation based on the Gauss-Seidel smoother, a Full Approximation Scheme multigrid algorithm with V-cycling and 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.
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ISSN:0961-5539
1758-6585
DOI:10.1108/HFF-09-2015-0383