A note on flow reversal in a wavy channel filled with anisotropic porous material

• Published in: Proceedings of the Royal Society. A, Mathematical, physical, and engineering sciences Vol. 473; no. 2203; p. 20170193
• Main Authors: Karmakar, Timir, Raja Sekhar, G. P.
• Format: Journal Article
• Language: English
• Published: London The Royal Society Publishing 01.07.2017
• Edition: Royal Society (Great Britain)
• Subjects: Anisotropic Ratio; Anisotropy; Brinkman Equation; Circulation; Porous materials; Porous media; Separation; Viscosity; Viscous flow
• ISSN: 1364-5021; 1471-2946
• DOI: 10.1098/rspa.2017.0193

Viscous flow through a symmetric wavy channel filled with anisotropic porous material is investigated analytically. Flow inside the porous bed is assumed to be governed by the anisotropic Brinkman equation. It is assumed that the ratio of the channel width to the wavelength is small (i.e. δ2≪1). The problem is solved up to O(δ2) assuming that δ2λ2≪1, where λ is the anisotropic ratio. The key purpose of this paper is to study the effect of anisotropic permeability on flow near the crests of the wavy channel which causes flow reversal. We present a detailed analysis of the flow reversal at the crests. The ratio of the permeabilities (anisotropic ratio) is responsible for the flow separation near the crests of the wall where viscous forces are effective. For a flow configuration (say, low amplitude parameter) in which there is no separation if the porous media is isotropic, introducing anisotropy causes flow separation. On the other hand, interestingly, flow separation occurs even in the case of isotropic porous medium if the amplitude parameter a is large.