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Unsteady Flow between Two Orthogonally Moving Porous Disks

Published online by Cambridge University Press:  23 January 2015

M. Ghaffar
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
K. Ali
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
A. Yasmin
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
M. Ashraf*
Affiliation:
Centre for Advanced Studies in Pure and Applied Mathematics, Bahauddin Zakariya University, Multan, Pakistan
*
*Corresponding author ([email protected])
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Abstract

The unsteady laminar incompressible flow of a fluid between two orthogonally moving porous coaxial disks is considered numerically. A transformation is used to reduce the governing partial differential equations (PDEs) to a set of nonlinear coupled ordinary differential equations. The effects of physical parameters of interest such as the wall expansion ratio and the permeability Reynolds number on the velocity are discussed in detail.

Type
Research Article
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

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References

REFRENCES

1.Connor, J.J., Boyd, J. and Avallone, E.A., Standard Handbook of Lubrication Engineering, McGraw-Hill, New York, USA (1968).Google Scholar
2.Usha, R. and Ravindranthe, R., “Numerical Study of Film Cooling on Rotating Disk,International Journal of Nonlinear Mechanics, 36, pp. 147154 (2001).CrossRefGoogle Scholar
3.Banchok, N., Ishak, A. and Pop, I., “Flow and Heat Transfer over a Rotating Porous Disk in a Nanofluid,Physica B, 406, pp. 17671772 (2011).CrossRefGoogle Scholar
4.Elcrat, A.R., “On the Radial Flow of a Viscous Fluid between Porous Disks,Archive for Rational Mechanics and Analysis, 61, pp. 9196 (1976).CrossRefGoogle Scholar
5.Rasmussen, H., “Steady Viscous Flow Between Two Porous Disks,Zeitschrift fur Angewandte Mathematik und Physik, 21, pp. 187195 (1970).CrossRefGoogle Scholar
6.Turkyilmazoglu, M., “Three Dimensional MHD Stagnation Flow Due to a Stretchable Rotating Disk,International Journal of Heat and Mass Transfer, 55, pp. 69596965 (2012).CrossRefGoogle Scholar
7.Turkyilmazoglu, M. and Senel, P., “Heat and Mass Transfer of the Flow Due to a Rotating Rough and Porous Disk,International Journal of Thermal Sciences, 63, pp. 146158 (2013).CrossRefGoogle Scholar
8.Tiegang, F. and Zhang, J., “Flow Between Two Stretchable Disks — An Exact Solution of the Navier — Stokes Equations,International Communications in Heat and Mass Transfer, 35, pp. 892895 (2008).Google Scholar
9.Tiegang, F. and Hua, T., “Unsteady Viscous Flow over a Rotating Stretchable Disk with Deceleration,Communications in Nonlinear Science and Numerical Simulation, 17, pp. 50645072 (2012).Google Scholar
10.Kumar, N., Pant, A. and Kumar Singh, R., “Elastico-Viscous Flow Between Two Rotating Disks of Different Transcription for High Reynolds Numbers,IJE Transaction, 22, pp. 115122 (2009).Google Scholar
11.Ashraf, M. Zenkour, Mashat, Daoud S., “Analytical and Numerical Solutions for a Rotating Annular Disk of Variable Thickness,Applied Mathematics, 1, pp. 431438 (2010).Google Scholar
12.Uchida, S. and Aoki, H., “Unsteady Flows in a Semi-Infinite Contracting or Expanding Pipe,Journal of Fluid Mechanics, 82, pp. 371387 (1977).CrossRefGoogle Scholar
13.Dauenhauer, C.E. and Majdalani, J., “Exact Self-Similarity Solution of the Navier-Stokes Equations for a Porous Channel with Orthogonally Moving Walls,Physics of Fluids, 15, pp. 14851495 (2003).CrossRefGoogle Scholar
14.Majdalani, J., Zhou, C. and Dawson, C.A., “Two-Dimensional Viscous Flows Between Slowly Expanding or Contracting Walls with Weak Permeability,Journal of Biomechanics, 35, pp. 13991403 (2002).CrossRefGoogle ScholarPubMed
15.Majdalani, J. and Zhou, C., “Moderate-To-Large Injection and Suction Driven Channel Flows with Expanding or Contracting Walls,Zeitschrift fur Angewandte Mathematik, und Mechanik, 83, pp. 181196 (2003).CrossRefGoogle Scholar