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# The Characteristics of Fluid Flow Through Multilayer Porous Media

[+] Author and Article Information
F. M. Allan, M. A. Hajji, M. N. Anwar

Department of Mathematical Sciences, United Arab Emirates University, P. O. Box 17551, Al Ain, United Arab Emirates

J. Appl. Mech 76(1), 014501 (Oct 23, 2008) (7 pages) doi:10.1115/1.2998483 History: Received March 08, 2007; Revised March 25, 2008; Published October 23, 2008

## Abstract

The characteristics of fluid flow through three porous layers are investigated. The two outer porous layers are considered to be of infinite width, while the middle porous layer is assumed to be of finite width. The mathematical model of the fluid flow in the middle region can be described as laminar fully developed flow and is assumed to be governed by Brinkman equations. The flow through the upper and lower porous media is governed by Forchheimer equations. At the two interface regions between the middle finite width porous layer and the outer infinite porous layers, the continuity of the velocity and of the shear stress are imposed. Under these matching conditions, the exact solutions for the set of equations describing the flow velocity are obtained. It is found that the flow velocity is affected by two parameters, namely, Reynolds number and Darcy’s number. The effects of these parameters on the flow velocity profiles through the flow regions are investigated and presented.

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## Figures

Figure 1

A schematic of the flow configuration through three porous layers

Figure 2

Velocity profile for Configuration 1 with Da1=1, Da2=Da3=10. and Re=0.5,1,2,5

Figure 3

Velocity profile for Configuration 1 with Da2=Da3=10, Re=10, and Da1=0.001,0.01,0.5,1

Figure 4

Velocity profile for Configuration 1 with Re=10, Da1=10, Da2=10, and Da3=1,10,100,1000

Figure 5

A plot of (ui3/ui2) versus (Da3/Da2) for Configuration 1 with Re=10, Da1=10, Da2=10, and Da3=10i, i=1,2,…,100

Figure 6

Velocity profile for Configuration 2 with Da2=Da3=10, and Re=0.5,1,2,5

Figure 7

Velocity profile for Configuration 2 with Re=10, Da2=10, and Da3=1,10,100,1000

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