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Oscillatory Flow in a Porous Channel with Porous Medium and Small Suction

Published online by Cambridge University Press:  13 March 2014

A. Ali  and
S. Asghar
A. Ali*
Affiliation:
Department of Mathematics, COMSATS Institute of Information Technology, Park Road Chak Shahzad, Islamabad 44000, Pakistan
S. Asghar
Affiliation:
Department of Mathematics, COMSATS Institute of Information Technology, Park Road Chak Shahzad, Islamabad 44000, Pakistan Department of Mathematics, King Abdulaziz University, Jeddah 21432, Saudi Arabia
*
Aamir.ALI@unice.fr, aamir_ali@comsats.edu.pk
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Abstract

This paper deals with an analytical solution of an oscillatory flow in a channel filled with a porous medium saturated with a viscous fluid. The consideration of porosity in the channel is the basic idea of the paper. The oscillatory waves in the channel with porous medium are produced due to self-excited pressure disturbances caused by inevitable fluctuation in a suction rate at the porous walls. The ensuing steady axial velocity and the time dependent oscillatory axial velocity are found analytically using perturbation method and WKB approximation. The important physical quantities like the velocity profile, amplitude of the oscillation and penetration depth of the oscillatory velocity have been given special emphasis in this analysis. The effects of porosity of the medium on these quantities are calculated analytically and examined graphically. We find that the amplitude of oscillatory velocity and the penetration depth of the oscillatory axial velocity decrease with increasing values of inverse Darcy parameter. The oscillations in the fluid can be minimized by decreasing the permeability of the medium.

Keywords

Oscillatory channel flowCompressible flowLaminar flowNavier-StokesPartial differential equationsPorous mediaViscous flowsWKBPerturbation method
Type
Research Article
Information
Journal of Mechanics , Volume 30 , Issue 2 , April 2014 , pp. 153 - 159
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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