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 JEMAA  Vol.3 No.9 , September 2011
Revolving Ferrofluid Flow under the Influence of MFD Viscosity and Porosity with Rotating Disk
Abstract: In the present case, we have studied the effect of magnetic field-dependent viscosity (MFD) along with porosity on the revolving Axi-symmetric steady ferrofluid flow with rotating disk by solving the boundary layer equations using Neuringer-Rosensweig (NR) model. Here, we have calculated the velocity components and pressure for different values of MFD viscosity (k) and porosity (ε) with the variation of Karman’s dimensionless parameter α. Also, we have calculated the displacement thickness of the boundary layer and total volume flowing outward the z-axis. The numerical results which are obtained for various flow characteristics are shown graphically.
Cite this paper: nullP. Ram and K. Sharma, "Revolving Ferrofluid Flow under the Influence of MFD Viscosity and Porosity with Rotating Disk," Journal of Electromagnetic Analysis and Applications, Vol. 3 No. 9, 2011, pp. 378-386. doi: 10.4236/jemaa.2011.39060.
References

[1]   R. P. Feynman, R. B. Leighton and M. Sands, “Lecturers on Physics,” Addison-Wesley, Reading, 1963.

[2]   M. I. Shliomis, “Ferrofluids as Thermal Ratchets,” Physical Review Letters, Vol. 92, No. 18, 2004, Article ID: 188901. doi:10.1103/PhysRevLett.92.188901

[3]   J. L. Neuringer and R. E. Rosensweig, “Magnetic Fluids,” Physics of Fluids, Vol. 7, No. 12, 1964, pp. 1927-1937. doi:10.1063/1.1711103

[4]   P. D. S. Verma and M. Singh, “Magnetic Fluid Flow through Porous Annulus,” International Journal of Non-linear Mechanics, Vol. 16, No. 3-4, 1981, pp. 371-378. doi:10.1016/0020-7462(81)90049-4

[5]   P. D. S. Verma and M. J. Vedan, “Steady Rotation of a Sphere in a Paramagnetic Fluid,” Wear, Vol. 52, No. 2, 1979, pp. 201-218. doi:10.1016/0043-1648(79)90063-2

[6]   P. D. S. Verma and M. J. Vedan, “Helical Flow of Ferrofluid with Heat Conduction,” Journal of Mathematical Physics, Vol. 12, No. 4, 1978, pp. 377-389.

[7]   R. E. Rosensweig, “Ferrohydrodynamics,” Cambridge University Press, Cambridge, 1985.

[8]   H. Schlichting, “Boundary Layer Theory,” McGraw-Hill Book Company, New York, 1960.

[9]   V. Karman, “Uber Laminare and Turbulente Reibung,” Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 1, No. 4, 1921, pp. 232-252.

[10]   W. G. Cochran, “The Flow Due to a Rotating Disk,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 30, No. 3, 1934, pp. 365-375. doi:10.1017/S0305004100012561

[11]   E. R. Benton, “On the Flow Due to a Rotating Disk,” Journal of Fluid Mechanics, Vol. 24, No. 4, 1966, pp. 781-800. doi:10.1017/S0022112066001009

[12]   H. A. Attia, “Unsteady MHD Flow near a Rotating Porous Disk with Uniform Suction or Injection,” Journal of Fluid Dynamics Research, Vol. 23, No. 5, 1998, pp. 283-290. doi:10.1016/S0169-5983(98)80011-7

[13]   K. G. Mithal, “On the Effects of Uniform High Suction on the Steady Flow of a Non-newtonian Liquid Due to a Rotating Disk,” The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 14, No. 4, 1961, pp. 403-410. doi:10.1093/qjmam/14.4.403

[14]   H. A. Attia and A. L. Aboul-Hassan, “On Hydromagnetic Flow Due to a Rotating Disk,” Applied Mathematical Modelling, Vol. 28, No. 12, 2004, pp. 1007-1014. doi:10.1016/j.apm.2004.03.004

[15]   H. Attia, “Steady Flow over a Rotating Disk in Porous Medium with Heat Transfer,” Nonlinear Analysis: Modelling and Control, Vol. 14, No. 1, 2009, pp. 21-26.

[16]   F. Frusteri and E. Osalusi, “On MHD and Slip Flow over a Rotating Porous Disk with Variable Properties,” International Communications in Heat and Mass Transfer, Vol. 34, No. 4, 2007, pp. 492-501. doi:10.1016/j.icheatmasstransfer.2007.01.004

[17]   S. Venkatasubramanian and P. N. Kaloni, “Effect of Rotation on the Thermo-Convective Instability of a Horizontal Layer of Ferrofluids,” International Journal of Engineering Sciences, Vol. 32, No. 2, 1994, pp. 237-256. doi:10.1016/0020-7225(94)90004-3

[18]   A. V. Belyaev and B. L. Simorodin, “Convection of a Ferrofluid in an Alternating Magnetic Field,” Journal of Applied Mechanics and Technical Physics, Vol. 50, No. 4, 2009, pp. 558-565. doi:10.1007/s10808-009-0075-1

[19]   R. Sekar, G. Vaidyanathan and A. Ramanathan, “The Ferroconvection in Fluid Saturating a Rotating Densely Packed Porous Medium,” International Journal of Engineering Sciences, Vol. 31, No. 2, 1993, pp. 241-250. doi:10.1016/0020-7225(93)90037-U

[20]   P. Ram, A. Bhandari and K. Sharma, “Axi-Symmetric Ferrofluid Flow with Rotating Disk in a Porous Medium,” International Journal of Fluid Mechanics, Vol. 2, No. 2, 2010, pp. 151-161.

[21]   S. Odenbach, “Magneto Viscous Effects in Ferrofluids,” Springer-Verlag, Berlin, 2002.

[22]   Sunil, Divya and R.C. Sharma, “The Effect of Magnetic Field Dependent Viscosity on Thermosolutal Convection in a Ferromagnetic Fluid Saturating a Porous Medium,” Transport in Porous Media, Vol. 60, No. 3, 2005, pp. 251-274. doi:10.1007/s11242-004-5739-y

[23]   Sunil, A. Sharma, R. G. Shandil and U. Gupta, “Effect of Magnetic Field Dependent Viscosity and Rotation on Ferroconvection Saturating a Porous Medium in the Presence of Dust Particles,” International Communication in Heat and Mass Transfer, Vol. 32, No. 10, 2005, pp. 1387-1399. doi:10.1016/j.icheatmasstransfer.2005.07.001

[24]   Sunil, P. K. Bharti, D. Sharma and R. C. Sharma, “The Effect of a Magnetic Field Dependent Viscosity on the Thermal Convection in a Ferromagnetic Fluid in a Porous Medium,” Zeitschrift fur Naturforschung, Vol. 59a, 2004, pp. 397-406.

[25]   C. E. Nanjundappa, I. S. Shivakumara and R. Arunkumar, “Benard-Marangoni Ferroconvection with Magnetic Field Dependent Viscosity,” Journal of Magnetism and Magnetic Materials, Vol. 322, No. 15, 2010, pp. 2256-2263. doi:10.1016/j.jmmm.2010.02.021

[26]   P. Ram, A. Bhandari and K. Sharma, “Effect of Magnetic Field-Dependent Viscosity on Revolving Ferrofluid,” Journal of Magnetism and Magnetic Materials, Vol. 322, No. 21, 2010, pp. 3476-3480. doi:10.1016/j.jmmm.2010.06.048

[27]   P. Ram, K. Sharma and A. Bhandari, “Effect of Porosity on Ferrofluid Flow with Rotating Disk,” International Journal of Applied Mathematics and Mechanics, Vol. 6, No. 16, 2010, pp. 67-76. doi:Y2010V6N16P67C95255679

[28]   M. Turkyilmazoglu, “The MHD Boundary Layer Flow Due to a Rough Rotating Disk,” Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 90, No. 1, 2010, pp. 72-82. doi:10.1002/zamm.200900259

 
 
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