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Entropy 2007, 9(3), 118-131; doi:10.3390/e9030118

On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders

Department of Mechanical & Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, U.S.A.
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Received: 12 December 2006 / Accepted: 5 September 2007 / Published: 11 September 2007
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Abstract

Effects of the bounding solid walls are examined numerically for slow flow overregular, square arrays of circular cylinders between two parallel plates. A local magnitudeof the rate of entropy generation is used effectively to determine the flow region affected bythe presence of the solid boundary. Computed axial pressure gradients are compared to thecorresponding solution based on the Darcy-Brinkman equation for porous media in whichthe effective viscosity appears as an additional property to be determined from the flowcharacteristics. Results indicate that, between two limits of the Darcian porous medium andthe viscous flow, the magnitude of μ (the ratio of the effective viscosity to the fluid ˆviscosity) needs to be close to unity in order to satisfy the non-slip boundary conditions atthe bounding walls. Although the study deals with a specific geometric pattern of the porousstructure, it suggests a restriction on the validity of the Darcy-Brinkman equation to modelhigh porosity porous media. The non-slip condition at the bounding solid walls may beaccounted for by introducing a thin porous layer with μ = 1 near the solid walls. ˆ
Keywords: entropy generation; porous media; Darcy-Brinkman equation; effective viscosity. entropy generation; porous media; Darcy-Brinkman equation; effective viscosity.
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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MDPI and ACS Style

Liu, H.; Patil, P.R.; Narusawa, U. On Darcy-Brinkman Equation: Viscous Flow Between Two Parallel Plates Packed with Regular Square Arrays of Cylinders. Entropy 2007, 9, 118-131.

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