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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Bergles A.E.: Some perspectives on enhanced heat-transfer—2nd generation heat-transfer technology. J. Heat Transf. 110, 1082–1096 (1988)
Brinkman H.C.: A calculation of the viscous force exerted by a flowing fluid in a dense swarm of particles. Appl. Sci. Res. A1, 27–34 (1947)
Chow, J.C.F., Soda, K., Dean, C.: On laminar flow in wavy channels. Proc. 12th Midwestern Mech. Conf. 6, 247–253 (1971)
Elshafei E.A.M., Awad M.M., El-Negiry E., Ali A.G.: Heat transfer and pressure drop in corrugated channels. Energy 35, 101–110 (2010)
Howells I.D.: Drag due to the motion of a Newtonian fluid through a sparse random array of small fixed rigid objects. J. Fluid Mech. 64, 449–475 (1974)
Ingham D.B., Pop I.: Transport in Porous Media. Pergamon, Oxford (2002)
Kaviany M.: Principles of Heat Transfer in Porous Media. Springer, New York (1991)
Khanafer K., Al-Azmi B., Marafie A., Pop I.: Non-Darcian effects on natural convection heat transfer in a wavy porous enclosure. Int. J. Heat Mass Transf. 52, 1887–1896 (2009)
Lundgren T.S.: Slow flow through stationary random beds and suspensions of spheres. J. Fluid Mech. 51, 273–299 (1972)
Luo H., Blyth M.G., Pozrikidis C.: Two-layer flow in a corrugated channel. J. Eng. Math. 60, 127–147 (2008)
Malevich A.E., Mityushev V.V., Adler P.M.: Couette flow in channels with wavy walls. Acta Mech. 197, 247–283 (2008)
Nield D.A., Bejan A.: Convection in Porous Media. 3rd edn. Springer, New York (2006)
Pozrikidis C.: Creeping flow in two-dimensional channels. J. Fluid Mech. 180, 495–514 (1987)
Scholle M., Haas A., Aksel N., Wilson M.C.T., Thompson H.M., Gaskell P.H.: Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films. Phys. Fluids 20, 123101 (2008)
Szumbarski J., Floryan J.M.: Transient disturbance growth in a corrugated channel. J. Fluid Mech. 568, 243–272 (2006)
Tam C.K.W.: The drag on a cloud of spherical particles in low Reynolds number flow. J. Fluid Mech. 38, 537–546 (1969)
Wang C.Y.: Parallel flow between corrugated plates. J. Eng. Mech. 102, 1088–1090 (1976)
Wang C.Y.: On Stokes flow between corrugated plates. J. Appl. Mech. 46, 462–464 (1979)
Wang H., Wang Y.: Flow in microchannels with rough walls: flow pattern and pressure drop. J. Micromech. Microeng. 17, 586–596 (2007)
Zhou H., Khayat R.E., Martinuzzi R.J., Straatman A.G.: On the validity of the perturbation approach for the flow inside weakly modulated channels. Int. J. Numer. Methods Fluids 39, 1139–1159 (2002)
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Ng, CO., Wang, C.Y. Darcy–Brinkman Flow Through a Corrugated Channel. Transp Porous Med 85, 605–618 (2010). https://doi.org/10.1007/s11242-010-9580-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-010-9580-1