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Effects of Hall Current and Ion-Slip on MHD Flow Induced by Torsional Oscillations of a Disc in a Rotating Fluid

Published online by Cambridge University Press:  29 January 2013

N. Ghara ,
S. Das ,
S. L. Maji  and
R. N. Jana
N. Ghara
Affiliation:
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, West Bengal, India
S. Das*
Affiliation:
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, West Bengal, India
S. L. Maji
Affiliation:
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, West Bengal, India
R. N. Jana
Affiliation:
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, West Bengal, India
*
*Corresponding author (, [email protected])
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Abstract

The unsteady hydromagnetic flow due to torsional oscillations of a rotating disc in a viscous incompressible electrically conducting fluid which is also rotating is studied taking the effects of the Hall current and ion-slip into consideration. The governing equations are solved analytically. The results show that the inclusion of the Hall current and ion slip have important effects on the velocity distributions as well as shear stresses at the disc. The flow is characterized by two opposite circularly polarized waves, travelling with different velocities. It is found that there is a formation of two-deck boundary layers, thicknesses of which increase with increase in either Hall parameter or ion-slip parameter. The radial velocity increases with an increase in Hall parameter and the azimuthal velocity increases with an increase in either Hall parameter or ion-slip parameter. Further, it is found that the amplitude of the transverse shear stress at the disc decreases with an increase in either Hall parameter or ion-slip parameter.

Keywords

MHD flowHall currentIon-slip parameterFrequency parameter and torsional oscillations
Type
Articles
Information
Journal of Mechanics , Volume 29 , Issue 2 , June 2013 , pp. 337 - 344
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2013

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References

REFERENCES

1.Jana, R. N. and Datta, N., “Hall Effects on MHD Flow Induced by Torsional Oscillations of Disc in a Rotating System,” Journal of Mathematical Physics of Solids, 12, pp. 253–265 (1978).Google Scholar
2.Datta, S., “The Effects of Hall Current on the Torsional Oscillation of a Disc in a Conducting Fluid Subjected to a Uniform Axial Magnetic Field,” Mathematicki Vesnik, 23, p. 135 (1971).Google Scholar
3.Mittal, M. L. and Bhat, A. N., “Heat Transfer by a Developing MHD Flow with Hall and Ion-Slip Currents,” Proceeding of the 4th National Conference on Heat and Mass Transfer, Roorkee University, Roorkee, pp. 247–253 (1977).Google Scholar
4.Soundalgekar, V. M., Vighnesam, N. V. and Takhar, H. S., “Hall and Ion-Slip Effects in MHD Coutte Flow with Heat Transfer,” IEEE Transactions on Plasma Solids, 7, pp. 178–182 (1978).CrossRefGoogle Scholar
5.Abo-Eldahab, E. M. and Aziz, M. A. E., “Hall and Ion-Slip Effects on MHD Free Convective Heat Generating Flow Past a Semi-Infinite Vertical Flat Plate,” Physica Scripta, 61, pp. 344–348 (2000).CrossRefGoogle Scholar
6.Attia, H. A., “Transient Hartmann Flow with Heat Transfer Considering the Ion Slip,” Physica Scripta, 66, pp. 470–475 (2002).Google Scholar
7.Attia, H. A., “Unsteady Von-Karman Magnetic Flow and Heat Transfer Considering the Ion Slip,” International Communications Heat and Mass Transfer, 30, pp. 535–543 (2003).CrossRefGoogle Scholar
8.Attia, H. A., “Ion Slip Effect on the Flow Due to a Rotating Disk,” The Arabian Journal of Science Engineering, 29, pp. 165–172 (2004).Google Scholar
9.Attia, H. A., “On the Effectiveness of Ion Slip and Uniform Suction or Injection on Steady MHD Flow Due to a Roating Disk with Heat Transfer and Ohmic Heating,” Chemical Engineers Communications, 194, pp. 1396–1407 (2007).Google Scholar
10.Osalusi, E., Side, J., Harris, R. and Johnston, B., “On the Effectiveness of Viscous Dissipation and Joule Heating on Steady MHD and Slip Flow of a Bingham Fluid over a Porous Rotating Disk in the Presence of Hall and Ion-Slip Currents,” Romanian Reports in Physics, 61, pp. 71–93 (2009).Google Scholar
11.Osalusi, E., Side, J. and Harris, R., “The Effects of Ohmic Heating and Viscous Dissipation on Unsteady MHD and Slip Flow over a Porous Rotating Disk with Variable Properties in the Presence of Hall and Ion-Slip Currents,” International Communications Heat and Mass Transfer, 34, pp. 1017–1029 (2007).Google Scholar
12.Guria, M., Das, S. and Jana, R. N., “Hall Effects on Unsteady Flow of a Viscous Fluid Due to Non-Coaxial Rotation of a Porous Disk and a Fluid at Infinity,” International Journal of Non-Linear Mechanics, 42, pp. 1204–1209 (2007).Google Scholar
13.Guria, M., Kanch, A. K., Das, S. and Jana, R. N., “Effects of Hall Current and Slip Condition on Unsteady Flow of a Viscous Fluid Due to Non-Coaxial Rotation of a Porous Disk and a Fluid at Infinity,” Meccanica, 45, pp. 23–32 (2010).Google Scholar
14.Hayat, T., Ellahi, R. and Asghar, S., “Hall Effects on Unsteady Flow Due to Non-Coaxially Rotating Disk and a Fluid at Infinity,” Chemical Engineers Communications, 195, pp. 958–976 (2008).Google Scholar
15.Mayer, R. C., “On Reducing Aerodynamic Heat-Transfer Rates by Magnetohydrodynamic Techniques,” Journal of Aero/Space Sciences, 25, pp. 561–566 (1958).Google Scholar