JAMP  Vol.6 No.1 , January 2018
A Study of Flow through a Channel Bounded by a Brinkman Transition Porous Layer
Abstract: Flow through a channel bounded by a porous layer is considered when a transition layer exists between the channel and the medium. The variable permeability in the transition layer is chosen such that Brinkman’s equation governing the flow reduces to a generalized inhomogeneous Airy’s differential equation. Solution to the resulting generalized Airy’s equation is obtained in this work and solution to the flow through the transition layer, of the same configuration, reported in the literature, is recovered from the current solution.
Cite this paper: Zaytoon, M. , Alderson, T. and Hamdan, M. (2018) A Study of Flow through a Channel Bounded by a Brinkman Transition Porous Layer. Journal of Applied Mathematics and Physics, 6, 264-282. doi: 10.4236/jamp.2018.61025.

[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.

[2]   Nield, D.A. (1983) The Boundary Correction for the Rayleigh-Darcy Problem: Limitations of the Brinkman Equation. Journal of Fluid Mechanics, 128, 37-46.

[3]   Goyeau, B., Lhuillier, D. and Velarde, M.G. (2003) Momentum Transport at a Fluid-Porous Interface. International Journal of Heat and Mass Transfer, 46, 4071-4081.

[4]   Goharzadeh, A., Khalili, A. and Jorgensen, B.B. (2005) Transition Layer Thickness at a Fluid-Porous Interface. Physics of Fluids, 17, 057102.

[5]   Parvazinia, M., Nassehi, V., Wakeman, R.J. and Ghoreishy, M.H.R. (2006) Finite Element Modelling of Flow through a Porous Medium between Two Parallel Plates Using the Brinkman Equation. Transport in Porous Media, 63, 71-90.

[6]   Chandesris, M. and Jamet, D. (2007) Boundary Conditions at a Fluid-Porous Interface: An a priori Estimation of the Stress Jump Boundary Conditions. International Journal of Heat and Mass Transfer, 50, 3422-3436.

[7]   Hill, A.A. and Straughan, B. (2008) Poiseuille Flow in a Fluid Overlying a Porous Medium. Journal of Fluid Mechanics, 603, 137-149.

[8]   Duman, T. and Shavit, U. (2010) A Solution of the Laminar Flow for a Gradual Transition between Porous and Fluid Domains. Water Resources Research, 46, 09517.

[9]   Tao, J., Yao, J. and Huang, Z. (2013) Analysis of the Laminar Flow in a Transition Layer with Variable Permeability between a Free-Fluid and a Porous Medium. Acta Mechanica, 224, 1943-1955.

[10]   Hamdan, M.H. and Kamel, M.T. (2011) On the Ni(x) Integral Function and Its Application to the Airy’s Non-Homogeneous Equation. Applied Mathematics and Computation, 217, 7349-7360.

[11]   Nield, D.A. and Bejan, A. (2006) Convection in Porous Media. 3rd Edition, Springer.

[12]   Nield, D.A. (2009) The Beavers Joseph Condition and Related Matters: A Historical and Critical Note. Transport in Porous Media, 78, 537-540.

[13]   Swanson, C.A. and Headley, V.B. (1967) An Extension of Airy’s Equation. SIAM Journal on Applied Mathematics, 15, 1400-1412.