Unsteady Flow of a Dusty Visco-Elastic Fluid Through an Incliend Channel

ABSTRACT

The present discussion deals with the study of an unsteady flow of a dusty fluid through an inclined channel under the influence of pulsatile pressure gradient along with the effect of a uniform magnetic field. The analytical solutions of the problem are obtained using variable separable and Fourier transform techniques. The graphs drawn for the velocity fields of both fluid and dust phase under the effect of Reynolds number. The velocity profiles for the liquid and the dust particles decreases at different values of time t increases. As the visco-elastic parameter λ increases the velocity of the liquid and the dust particles deceases. When relaxation time parameter σ increases, the velocity of the liquid and dust particles decreases.

The present discussion deals with the study of an unsteady flow of a dusty fluid through an inclined channel under the influence of pulsatile pressure gradient along with the effect of a uniform magnetic field. The analytical solutions of the problem are obtained using variable separable and Fourier transform techniques. The graphs drawn for the velocity fields of both fluid and dust phase under the effect of Reynolds number. The velocity profiles for the liquid and the dust particles decreases at different values of time t increases. As the visco-elastic parameter λ increases the velocity of the liquid and the dust particles deceases. When relaxation time parameter σ increases, the velocity of the liquid and dust particles decreases.

KEYWORDS

Dusty Fluid, Pulsatile Pressure Gradient, Velocities of Dust and Fluid Phase, Inclined Channel, Reynolds Number

Dusty Fluid, Pulsatile Pressure Gradient, Velocities of Dust and Fluid Phase, Inclined Channel, Reynolds Number

Cite this paper

G. Alle, A. Roy, S. Kalyane and R. Sonth, "Unsteady Flow of a Dusty Visco-Elastic Fluid Through an Incliend Channel,"*Advances in Pure Mathematics*, Vol. 1 No. 4, 2011, pp. 187-192. doi: 10.4236/apm.2011.14033.

G. Alle, A. Roy, S. Kalyane and R. Sonth, "Unsteady Flow of a Dusty Visco-Elastic Fluid Through an Incliend Channel,"

References

[1] D. H. Michael, “Kelvin-Helmholtz Instability of A Dusty Gas,” Proceeding Cambridge Philosophical Sciety, Vol. 61, No. 2, 1965, pp. 569-571. HHHUUUdoi:10.1017/S030500410000414XUUU

[2] D. H. Michael and D. A. Millar, “Plane Parallel Flow of a Dusty Gas,” Mathematika, Vol. 13, No. 1, 1966, pp. 97- 109. HHHUUUdoi:10.1112/S0025579300004289UUU

[3] P. G. Saffman, “(jr.) On stability of a Laminar Flow of a Dusty Gas,” Journal of Fluid Mechanics, Vol. 13, No. 1, 1962, pp. 120-128. HHHUUUdoi:10.1017/S0022112062000555UUU

[4] C. B. Singh and P. C Ram, “Unsteady Flow of an Electrically Conducting Dusty Viscous Liquid Through a Channel,” Indian Journal of Pure and Applied Mathematics, Vol. 8, No. 9, 1977, pp. 1022-1028.

[5] G. C. Sharma, “Unsteady Flow of an Electri-cally Conducting Dusty Viscous Liquid between Two Parallel Plates,” International Journal of Pure & Applied Mathematical, Vol. 18, No. 12, 1987, p.1131.

[6] K. K Singh, “Unsteady Flow of Conducting Dusty Viscous Liquid in an Annulas,” Acta Ciecia Indica, Vol. 3, No. 3, 1977, p. 264.

[7] O. P Varshney, “Flow of a Dusty Rivlin-Ericksen Fluid through a Channel. Ph.D Thesis,” Agra University, Agra, 1983.

[8] M. L. Sharma, “MHD Flow of a Conducting Dusty Viscous Liquid through a Long Elliptic Duct with Pressure Gradient as Func-tion of a Time,” Ph.D Thesis Agra University, Agra, 1980.

[1] D. H. Michael, “Kelvin-Helmholtz Instability of A Dusty Gas,” Proceeding Cambridge Philosophical Sciety, Vol. 61, No. 2, 1965, pp. 569-571. HHHUUUdoi:10.1017/S030500410000414XUUU

[2] D. H. Michael and D. A. Millar, “Plane Parallel Flow of a Dusty Gas,” Mathematika, Vol. 13, No. 1, 1966, pp. 97- 109. HHHUUUdoi:10.1112/S0025579300004289UUU

[3] P. G. Saffman, “(jr.) On stability of a Laminar Flow of a Dusty Gas,” Journal of Fluid Mechanics, Vol. 13, No. 1, 1962, pp. 120-128. HHHUUUdoi:10.1017/S0022112062000555UUU

[4] C. B. Singh and P. C Ram, “Unsteady Flow of an Electrically Conducting Dusty Viscous Liquid Through a Channel,” Indian Journal of Pure and Applied Mathematics, Vol. 8, No. 9, 1977, pp. 1022-1028.

[5] G. C. Sharma, “Unsteady Flow of an Electri-cally Conducting Dusty Viscous Liquid between Two Parallel Plates,” International Journal of Pure & Applied Mathematical, Vol. 18, No. 12, 1987, p.1131.

[6] K. K Singh, “Unsteady Flow of Conducting Dusty Viscous Liquid in an Annulas,” Acta Ciecia Indica, Vol. 3, No. 3, 1977, p. 264.

[7] O. P Varshney, “Flow of a Dusty Rivlin-Ericksen Fluid through a Channel. Ph.D Thesis,” Agra University, Agra, 1983.

[8] M. L. Sharma, “MHD Flow of a Conducting Dusty Viscous Liquid through a Long Elliptic Duct with Pressure Gradient as Func-tion of a Time,” Ph.D Thesis Agra University, Agra, 1980.