Analytical Analysis of Vorticity Transport in Magnetic Walters B' Fluid

Pardeep Kumar, Hari Mohan, Vivek Kumar


We consider the transport of vorticity in Walters B' viscoelastic fluid in the presence of suspended magnetic particles. The equations governing such a transport of vorticity problem in viscoelastic fluid are obtained from the equations of magnetic fluid flow proposed by Wagh and Jawandhia [1] in their study on the transport of vorticity in magnetic fluid. It follows from the analysis of these equations that the transport of solid vorticity  is coupled with the transport of fluid vorticity . Further, it is found that due to thermo-kinetic process, fluid vorticity may exist in the absence of solid vorticity but when fluid vorticity is zero, then solid vorticity is necessarily zero. A two-dimensional case is also studied.

Full Text:



D.K. Wagh and A. Jawandhia, “Transport of vorticity in magnetic fluid,” Indian J. Pure Appl. Phys., vol. 34, pp. 338-340, 1996.

P. Saffman “On the stability of a laminar flow of a dusty gas,” J. Fluid Mech., vol. 13, pp. 120-128, 1962.

D.K. Wagh, “A mathematical model of magnetic fluid considered as two-phase system,” Proc. Int. Symp. on Magnetic Fluids, held at REC Kurukshetra, India, during Sept. 21-23, 182, 1991.

Y. Yan and J. Koplik , “Transport and sedimentation of suspended particles in inertial pressure-driven flow,” Phys. Fluids, vol.21, 013301, 2009.

C.J. Wojcik and J.H. Buchholz, “Vorticity transport in the leading edge vortex on a rotating blade,” J. Fluid Mechanics, vol. 743, pp. 249-261, 2014.

J.E. Martin, “On the origin of vorticity in magnetic particle suspensions subjected to triaxial fields,” Soft Matter, vol. 12, pp. 5636-5644, 2016.

C.M. Vest and V.S. Arpaci , “Overstability of a viscoelastic fluid layer heated from below,” J. Fluid Mech., vol. 36, pp. 613-619, 1969.

P.K. Bhatia and J.M. Steiner, “Convective instability in a rotating viscoelastic fluid layer,” Z. Angew. Math. Mech., vol. 52, pp. 321-324, 1972.

R.C. Sharma and K.C. Sharma, “Thermal instability of a rotating Maxwell fluid through porous medium,” Metu J. Pure Appl. Sci., vol 10, pp. 223-229, 1977.

R.C. Sharma, “Thermal instability in a viscoelastic fluid in hydromagnetics,” Acta Physica Hungarica, vol. 38, pp. 293-298, 1975.

J.G. Oldroyd, “Non-Newtonian effects in steady motion of some idealized elastic-viscous liquids,” Proc. Royal Soc. London, vol A245, pp. 278-297, 1958.

K. Walters, “The motion of elastico-viscous liquid contained between coaxial cylinders,” J. Mech. Appl. Math., vol. 13, pp. 444-453, 1960.

K. Walters, “The solution of flow problems in case of materials with memory,” J. Mecanique, vol 1, pp. 469-479, 1962.

G. Chakraborty and P.R. Sengupta , “MHD flow of unsteady viscoelastic (Walters liquid B') conducting fluid between two concentric circular cylinders,” Proc. Nat. Acad. Sciences India, vol. 64, pp. 75-80, 1994.

R.C. Sharma and P. Kumar, “On the stability of two superposed Walters elastico-viscous liquid B',” Czech. J. Phys., vol 47, pp. 197204, 1997.

R.C. Sharma and P. Kumar, “Rayleigh-Taylor instability of two superposed Walters B' elastico-viscous fluids in hydromagneticsProc. Nat. Acad. Sciences India, vol. 68, pp. 151-161, 1998.

P. Kumar , “Effect of rotation on thermal instability in Walters B' elastico-viscous fluid,” Proc. Nat. Acad. Sciences India, vol 71, pp33-41, 2001.

P. Kumar , H. Mohan and G.J. Singh, “Stability of two superposed viscoelastic fluid- particle mixtures,” Z. Angew. Math. Mech., vol, 86, pp. 72-77, 2006.

R.E. Rosensweig, “Ferrohydrodynamics,” Dover Publications, Inc. Mineola, New York 1997.


  • There are currently no refbacks.

MAYFEB Journal of Mathematics 
Toronto, Ontario, Canada
ISSN 2371-6193