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Transport in Porous Media

, Volume 84, Issue 1, pp 219–227 | Cite as

Darcy–Brinkman Flow over a Grooved Surface

  • C. Y. WangEmail author
Article

Abstract

Uniform Darcy–Brinkman flow over a surface with periodic rectangular grooves is studied by domain decomposition and matching. It is found that the effect of corrugations is equivalent to replacing the rough surface with a smooth surface with an apparent slip for the bulk flow. Such equivalence would greatly simplify the boundary conditions for porous flow bounded by a rough surface. The slip velocity is larger along the grooves than transverse to the grooves, and is increased by the porous media parameter k.

Keywords

Porous medium Grooves Apparent slip 

List of Symbols

a

Normalized half width of groove

an

Constants defined by Eq. 7

An

Coefficients

b

Normalized depth of groove

Bn

Coefficients

Cn

Coefficients

Dn

Coefficients

En

Coefficients

Fn

Functions of y

Gn

Coefficients

H

Number of terms

i

Integer

j

Integer

k

\({L\sqrt{\mu /\mu_{\rm e} K}}\)

K

Permeability (m2)

L

Half period of grooves (m)

M

Number of terms

N

Number of terms

Ri

Functions of y, Eq. 17

S

Normalized apparent slip velocity

T

Function of x, Eq. 17

\({\vec{u}}\)

Normalized velocity vector

U

Uniform velocity at infinity (m/s)

w

Normalized velocity in the z direction

x, y, z

Normalized Cartesian coordinates

αn

n π

\({\tilde {\alpha}_n}\)

\({\sqrt{\alpha_n^2 +k^{2}}}\)

βn

(n − 0.5)π/a

\({\tilde {\beta }_n}\)

\({\sqrt{\beta_n^2 +k^{2}}}\)

μ

Fluid viscosity (Ns/m2)

μe

Effective viscosity of matrix (Ns/m2)

ψ

Stream function

Dimensional quantity

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References

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Departments of Mathematics and Mechanical EngineeringMichigan State UniversityEast LansingUSA

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