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Transport in Porous Media

, Volume 85, Issue 2, pp 605–618 | Cite as

Darcy–Brinkman Flow Through a Corrugated Channel

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Abstract

A perturbation analysis is carried out to the second order to give effective equations for Darcy–Brinkman flow through a porous channel with slightly corrugated walls. The flow is either parallel or normal to the corrugations, and the corrugations of the two walls are either in phase or half-period out of phase. The present study is based on the assumptions that the corrugations are periodic sinusoidal waves of small amplitude, and the channel is filled with a sparse porous medium so that the flow can be described by the Darcy–Brinkman model, which approaches the Darcian or Stokes flow limits for small or large permeability of the medium. The Reynolds number is also assumed to be so low that the nonlinear inertia can be ignored. The effects of the corrugations on the flow are examined, quantitatively and qualitatively, as functions of the flow direction, the phase difference, and the wavelength of the corrugations, as well as the permeability of the channel. It is found that the corrugations will have greater effects when it is nearer the Stokes’ flow limit than the Darcian flow limit, and when the wavelength is shorter. For the same wavelength and phase difference, cross flow is more affected than longitudinal flow by the corrugations. Opposite effects can result from 180° out-of-phase corrugations, depending on the flow direction, the wavelength, as well as the permeability.

Keywords

Stokes flow Darcy–Brinkman Corrugated channel 
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Notes

Acknowledgments

The study was initiated by the second author when he was a William Mong Visiting Research Fellow associating with the first author in May, 2008. The financial support by the William M.W. Mong Engineering Research Fund of the University of Hong Kong is gratefully acknowledged. The study was also partly supported by the Research Grants Council of the Hong Kong Special Administrative Region, China, through Project No. HKU 715609E.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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© The Author(s) 2010

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringThe University of Hong KongHong KongHong Kong
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA

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