Hostname: page-component-848d4c4894-p2v8j Total loading time: 0.001 Render date: 2024-05-16T02:47:32.523Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Berman, A. S., “Laminar Flow in Channels with Porous Walls,” Journal of Applied Physics, 24, pp. 1232–1235 (1953).CrossRefGoogle Scholar
2.Sellars, J. R., “Laminar Flow in Channels with Porous Walls at High Suction Reynolds Numbers,” Journal of Applied Physics, 26, pp. 489–490 (1955).CrossRefGoogle Scholar
3.Terrill, R. M., “Laminar Flow in a Uniformly Porous Channel with Large Injection,” The Aeronautical Quarterly, 16, pp. 323–332 (1965).Google Scholar
4.Taylor, C. L., Banks, W. H. H., Zaturska, M. B. and Drazin, P. G., “Three-dimensional Flow in a Porous Channel,” Quarterly Journal of Mechanics and Applied Mathematics, 44, pp. 105–133 (1991).Google Scholar
5.Cox, S. M., “Two-dimensional Flow of a Viscous Fluid in a Channel with Porous Walls,” Journal of Fluid Mechanics, 227, pp. 1–33 (1991).Google Scholar
6.Majdalani, J., “Modeling of the Oscillatory Flow field Between Two Parallel Plates with Sidewall Injection,” 29th AIAA Fluid Dynamics Conference, Albuquerque, New Mexico, AIAA-98-2977 (1998).Google Scholar
7.Jankowski, T. A. and Majdalani, J., “Acoustical and Vortical Interactions Inside a Channel with Wall Suction,” 6th AIAA/CEAS Aeroacoustics Conference, Maui, Hawaii, AIAA-2000-1988 (2000).Google Scholar
8.Jankowski, T. A. and Majdalani, J., “The Oscillatory Channel Flow with Large Wall Injection,” Proceedings of the Royal Society of London, A 456, pp. 1625–1657 (2000).Google Scholar
9.Majdalani, J., “The Oscillatory Channel Flow with Arbitrary Wall Injection,” Zeitschrift für angewandte Mathematik und Physik, 52, pp. 33–61 (2001).Google Scholar
10.Majdalani, J. and Roh, T. S., “The Oscillatory Channel Flow with Hard Blowing,” Proc. ASME Fluids Engineering Division Summer Meeting, New Orleans, Los Angeles, ASME-FEDSM2001-18096 (2001).Google Scholar
11.Jankowski, T. A. and Majdalani, J., “Oscillatory Viscous Flow in a Porous Channel with Arbitrary Wall Suction,” 32nd AIAA Fluid Dynamics Conference, St Louis, Missouri, AIAA-2002-2855 (2002).Google Scholar
12.Lee, W. and Jerry, F., Applied Bio-fluid Mechanics, McGraw-Hill Company, USA (2007).Google Scholar
13.Vafai, K., Handbook of Porous Media, 2nd Edition, Taylor and Francis Group, NY (2005).CrossRefGoogle Scholar
14.Nield, D. A. and Bejan, A., Convection in Porous Media, Third Edition, Springer Science + Business Media, Inc. Digital, New York, NY (2006).Google Scholar
15.Ingham, D. B. and Pop, I., Transport Phenomenon in Porous Media, Vol. 1. Pergamon, Oxford (1998).Google Scholar
16.Muntz, S., “Fluid Structure Interaction for Fluid Flow Normal to Deformable Porous Media,” Ph. D Dissertation, Department of Mathematics, Technical University Kaiserslautern, Germany (2008).Google Scholar
17.Vafai, K. and Tien, C. L., “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” International Journal of Heat Mass Transfer, 24, pp. 195–203.Google Scholar
18.Duck, P. W., “Oscillatory Flow Inside a Square Cavity,” Journal of Mechanics, 122, pp. 215–234 (1982).Google Scholar
19.Hsiao, S. C. and Liu, L. F. P., “Oscillatory Flows Over a Permeable Wavy Boundary,” Journal of Mechanics, 19, pp. 279–297 (2003).CrossRefGoogle Scholar
20.Deng, C. and Martinez, D. M., “Viscous Flow in a Channel Partially Filled with a Porous Medium and with Wall Suction,” Chemical Engineering Science, 60, pp. 329–336 (2005).Google Scholar
21.Khan, M., Fetecau, C. and Hayat, T., “MHD Transient Flows in a Channel of Rectangular Cross-Section with Porous Medium,” Physics Letters A, 309, pp. 44–54 (2007).CrossRefGoogle Scholar
22.Shahzad, F. and Asghar, S., “A Note on Oscillatory Flow of a Third Grade Fluid in a Porous Medium,” Journal of Porous Media, 5, pp. 467–473 (2008).Google Scholar
23.Yurusoy, M., Pakdemirli, M. and Yylbap, B. S., “Perturbation Solution for a Third Grade Fluid Flowing Between Parallel Plates,” Proceedings of the Institution of Mechanical Engineers, Part C, Journal of Mechanical Engineering Science, 222, pp. 653–656 (2008).Google Scholar
24.Pantokratoras, A. and Fang, T., “Flow of a Weakly Conducting Fluid in a Channel filled with a Porous Medium,” Transport in Porous Media, 83, pp. 667–676 (2010).CrossRefGoogle Scholar
25.Chan, H. C., Zhang, Y., Leu, J. M. and Chen, Y. S., “Numerical Calculation of Turbulent Channel Flow with Porous Ribs,” Journal of Mechanics, 26, pp. 15–28 (2010).Google Scholar
26.Liu, I. C., Wang, H. H., and Umavathi, J. C., “Poiseuille-Couette Flow and Heat Transfer in an Inclined Composite Porous Medium,” Journal of Mechanics, 28, pp. 171–178 (2012).Google Scholar
27.Jankowski, T. A. and Majdalani, J., “Symmetric Solutions for the Oscillatory Channel Flow with Arbitrary Suction,” Journal of Sound and Vibration, 294, pp. 880–893 (2006).Google Scholar
28.Stokes, G. G., “On the Dynamical Theory of Diffraction,” Mathematical and Physical Papers, 2, pp. 243–328 (1883).Google Scholar
29.Carrier, B. T. and Carlson, F. D., “On the Propagation of Small Disturbances in a Moving Compressible Fluid,” Quarterly Applied Mathematics, 4, pp. 1–12 (1946).Google Scholar
30.Chu, B. T. and Kovasznay, L. S. G., “Non-Linear Interactions in a Viscous Heat-Conducting Compressible Gas,” Journal of Fluid Mechanics, 3, pp. 494–514 (1957).CrossRefGoogle Scholar
31.Flandro, G. A., “Effects of Vorticity on Rocket Combustion Stability,” Journal of Propulsion and Power, 11, pp. 607–625 (1995).Google Scholar
32.Majdalani, J. and Van Moorhem, W. K., “A Multiple-Scale Solution to the Acoustic Boundary Layer in Solid Rocket Motors,” Journal of Propulsion and Power, 13, pp. 186–193 (1997).Google Scholar