Geodesic
Vorticity transport in a viscoelastic fluid in the presence of suspended particles through porous media
Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 341-349 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider the transport of vorticity in an Oldroydian viscoelastic fluid in the presence of suspended magnetic particles through porous media. We obtain the equations governing such a transport of vorticity from the equations of magnetic fluid flow. It follows from these equations that the transport of solid vorticity is coupled to the transport of fluid vorticity in a porous medium. Further, we find that because of a thermokinetic process, fluid vorticity can exist in the absence of solid vorticity in a porous medium, but when fluid vorticity is zero, then solid vorticity is necessarily zero. We also study a two-dimensional case.
Keywords: Oldroydian viscoelastic fluid, suspended magnetic particle, vorticity, porous media. 
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P. Kumar; G. J. Singh. Vorticity transport in a viscoelastic fluid in the presence of suspended particles through porous media. Teoretičeskaâ i matematičeskaâ fizika, Tome 165 (2010) no. 2, pp. 341-349. http://geodesic.mathdoc.fr/item/TMF_2010_165_2_a10/

[1] P. G. Saffman, J. Fluid Mech., 13 (1962), 120–128 | DOI | MR | Zbl

[2] D. K. Wagh, “A Mathematical model of magnetic fluid considered as two-phase system”, Proc. Int. Symp. on Magnetic Fluids (REC Kurukshetra, India, September 21–23, 1991), 182

[3] D. K. Wagh, A. Jawandhia, Indian J. Pure Appl. Phys., 34:5 (1996), 338–340

[4] Y. Yan, J. Koplik, Phys. Fluids, 21:1 (2009), 013301, 9 pp. | DOI | Zbl

[5] C. M. Vest, V. S. Arpaci, J. Fluid Mech., 36 (1969), 613–623 | DOI | Zbl

[6] P. K. Bhatia, J. M. Steiner, Z. Angew. Math. Mech., 52:6 (1972), 321–327 | DOI | Zbl

[7] B. A. Toms, D. J. Strawbridge, Trans. Faraday Soc., 49 (1953), 1225–1232 | DOI

[8] J. G. Oldroyd, Proc. Roy. Soc. A, 245:1241 (1958), 278–297 | DOI | MR | Zbl

[9] R. C. Sharma, Acta Physica Hung., 40:1 (1976), 11–17 | DOI

[10] I. A. Eltayeb, Z. Angew. Math. Mech., 55:10 (1975), 599–604 | DOI | Zbl

[11] O. M. Phillips, Flow and Reactions in Permeable Rocks, Cambridge Univ. Press, Cambridge, 1991

[12] D. B. Ingham, I. Pop (eds.), Transport Phenomena in Porous Media, Pergamon Press, Oxford, 1998 | MR | Zbl

[13] D. A. Nield, A. Bejan, Convection in Porous Medium, Springer, New York, 1999 | MR | Zbl

[14] E. R. Lapwood, Proc. Cambridge Philos. Soc., 44:4 (1948), 508–521 | DOI | MR | Zbl

[15] R. A. Wooding, J. Fluid Mech., 9 (1960), 183–192 | DOI | MR | Zbl

[16] R. C. Sharma, P. Kumar, Indian J. Pure Appl. Math., 24:9 (1993), 563–569 | Zbl

[17] R. C. Sharma, P. Kumar, Engrg. Trans., 44:1 (1996), 99–111 | MR

[18] P. Kumar, Z. Naturforsch., 51a (1996), 17–22

[19] P. Kumar, H. Mohan, G. J. Singh, Transp. Porous Media, 56:2 (2004), 199–208 | DOI | MR

[20] R. E. Rosensweig, Ferrohydrodynamics, Dover, New York, 1997