Back
 JAMP  Vol.4 No.1 , January 2016
Flow over a Darcy Porous Layer of Variable Permeability
Abstract: In this work we consider coupled-parallel flow through a finite channel bounded below by a porous layer that is either finite or infinite in depth. The porous layer is one in which Darcy’s equation is valid under the assumption of variable permeability. A suitable permeability stratification function is derived in this work and the resulting variable velocity profile is analyzed. It will be shown that when an infinite porous layer is implemented, Darcy’s equation must be used with a constant permeability.
Cite this paper: Zaytoon, M. , Alderson, T. and Hamdan, M. (2016) Flow over a Darcy Porous Layer of Variable Permeability. Journal of Applied Mathematics and Physics, 4, 86-99. doi: 10.4236/jamp.2016.41013.
References

[1]   Nield, D.A. and Kuznetsov, A.V. (2009) The Effect of a Transition Layer between a Fluid and a Porous Medium: Shear Flow in a Channel. Transport in Porous Media, 78, 477-487.
http://dx.doi.org/10.1007/s11242-009-9342-0

[2]   Parvazinia, M., Nassehi, V., Wakeman, R.J. and Ghoreishy, M.H.R. (2006) Finite Element Modeling of Flow through a Porous Medium between Two Parallel Plates Using the Brinkman Equation. Transport in Porous Media, 63, 71-90.
http://dx.doi.org/10.1007/s11242-005-2721-2

[3]   Rudraiah, N. (1986) Flow past Porous Layers and Their Stability. In: Cheremisinoff, N.P., Ed., Encyclopedia of Fluid Mechanics: Slurry Flow Technology, Gulf Publishing, Houston, 567-647.

[4]   Vafai, K. and Thiyagaraja, R. (1987) Analysis of Flow and Heat Transfer at the Interface Region of a Porous Medium. International Journal of Heat and Mass Transfer, 30, 1391-1405.
http://dx.doi.org/10.1016/0017-9310(87)90171-2

[5]   Alazmi, B. and Vafai, K. (2000) Analysis of Variants within the Porous Media Transport Models. Journal of Heat Transfer, 122, 303-326.
http://dx.doi.org/10.1115/1.521468

[6]   Beavers, G.S. and Joseph, D.D. (1967) Boundary Conditions at a Naturally Permeable Wall. Journal of Fluid Mechanics, 30, 197-207.
http://dx.doi.org/10.1017/S0022112067001375

[7]   Ochoa-Tapia, J.A. and Whitaker, S. (1981) Momentum Jump Condition at the Boundary between a Porous Medium and a Homogeneous Fluid: Inertial Effects. Journal of Porous Media, 1, 201-217.

[8]   Neale, G. and Nader, W. (1974) Practical Significance of Brinkman’s Extension of Darcy’s Law: Coupled Parallel Flows within a Channel and a Bounding Porous Medium. The Canadian Journal of Chemical Engineering, 52, 475-478.
http://dx.doi.org/10.1002/cjce.5450520407

[9]   Ehrhardt, M. (2010) An Introduction to Fluid-Porous Interface Coupling. Weierstrass Institute for Applied Analysis and Stochastics, Berlin.

[10]   Tao, L.N. and Joseph, D.D. (1962) Fluid Flow between Porous Rollers. Journal of Applied Mechanics, 29, 429-423.
http://dx.doi.org/10.1115/1.3640566

[11]   Saffman, P.G. (1971) On the Boundary Condition at the Surface of a Porous Medium. Studies in Applied Mathematics, 50, 93-101.
http://dx.doi.org/10.1002/sapm197150293

[12]   Chandesris, M. and Jamet, D. (2007) Boundary Conditions at a Fluid-Porous Interface: An a priori Estimation of the Stress Jump Coefficients. International Journal of Heat and Mass Transfer, 50, 3422-3436.
http://dx.doi.org/10.1016/j.ijheatmasstransfer.2007.01.053

[13]   Kaviany, M. (1985) Laminar Flow through a Porous Channel Bounded by Isothermal Parallel Plates. International Journal of Heat and Mass Transfer, 28, 851-858.
http://dx.doi.org/10.1016/0017-9310(85)90234-0

[14]   Chandrasekhara, B.C., Rajani, K. and Rudraiah, N. (1978) Effect of Slip on Porous-Walled Squeeze Films in the Presence of a Transverse Magnetic Field. Applied Scientific Research, 34, 393-411.
http://dx.doi.org/10.1007/BF00383973

[15]   Sahraoui, M. and Kaviany, M. (1992) Slip and No-Slip Velocity Boundary Conditions at Interface of Porous, Plain Media. International Journal of Heat and Mass Transfer, 35, 927-943.
http://dx.doi.org/10.1016/0017-9310(92)90258-T

[16]   Cheng, A.H.-D. (1984) Darcy’s Flow with Variable Permeability: A Boundary Integral Solution. Water Resources Research, 20, 980-984.
http://dx.doi.org/10.1029/WR020i007p00980

[17]   Mahmoud, M.S. and Deresiewicz, H. (1980) Settlement of Inhomogeneous Consolidating Soils—I: The Single-Drained Layer under Confined Compression. International Journal for Numerical and Analytical Methods in Geomechanics, 4, 57-72.
http://dx.doi.org/10.1002/nag.1610040105

[18]   Hamdan, M.H. and Kamel, M.T. (2011) Flow through Variable Permeability Porous Layers. Advances in Theoretical and Applied Mechanics, 4, 135-145.

 
 
Top