Abstract
The forced flow through a channel with bumpy walls which sandwich a porous medium is studied. The problem models micro-fluidics where, due to the small size of the channel width, the surface roughness of the walls is amplified. The Darcy-Brinkman equation is solved analytically through small perturbations on the ratio of bump amplitude to the half width of the channel. The first- order perturbation solutions give the three-dimensional velocity effects of the bumpiness and the second-order perturbation solutions give the increased resistance due to roughness. The problem depends heavily on the non-dimensional porous medium parameter \(k\) which represents the importance of length scale to the square root of permeability. Our solutions reduce to the clear fluid limit when \(k\) is zero and to the Darcy limit when \(k\) approaches infinity.
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Yu, L., Wang, C. Darcy-Brinkman Flow Through a Bumpy Channel. Transp Porous Med 97, 281–294 (2013). https://doi.org/10.1007/s11242-013-0124-3
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DOI: https://doi.org/10.1007/s11242-013-0124-3