MHD Pulsatile Flow of a Conducting Fluid Sandwiched Between Viscous Fluids Inside Permeable Beds

Year 2018, Volume: 6 Issue: 1, 63 - 75, 15.04.2018

Deepak Kumar Manju Agarwal

Abstract

In the present paper the problem of MHD pulsatile flow of a viscous conducting fluid in porous medium sandwiched between viscous fluids is investigated inside permeable beds. The flow in porous region is modelled using Brinkman equation and in the permeable beds by Darcy's law. The Beavers Joseph slip boundary condition is used at the interfaces of permeable beds. The governing partial differential equations of flow are transformed in to ordinary differential equations by separating steady and oscillatory terms. The differential equations are solved analytically and the expressions for velocity, mass flux and shear stress are obtained. The analytical solutions are evaluated numerically and depicted graphically to show the effects of physical governing parameters on velocity and shear stress.

Keywords

Beavers-Joseph slip boundary condition, Brinkman equation, Immiscible fluids, Permeable beds, Pulsatile flow

References

• [1] Beavers, G. and D. Joseph, Boundary conditions at naturally permeable wall, J. Fluid Mech Vol:30,No.1(1967), 197-207.
• [2] Bhattacharyya, P., Unsteady laminar flow in a channel with porous bed, J.Indian Inst. Sci Vol:62(B)(1980), 89-99.
• [3] Carpinlioglu, M. O., An overview on pulsatile flow dynamics, Journal of Thermal Engineering,Vol:1,No.3(2015), 496-504.
• [4] D.A.Nield, Modelling fluid flow and heat transfer in a saturated porous medium, Journal of applied mathematics and decision sciences Vol:4,No.2(2000), 165-173.
• [5] Iyengar, T.K.V. and P. Bitla, Pulsating flow of an incompressible couple stress fluid between permeable beds. International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering Vol:5,No.8(2011), 1241-1251.
• [6] Jogie, D. and B. Bhatt, Flow of immiscible fluids in a naturally permeable channel, International Journal of Pure and Applied Mathematics Vol:78,No.3(2012), 435-449.
• [7] Khan, A. and G. Zaman, Unsteady magnetohydrodynamic flow of second grade fluid due to uniform accelerating plate, Journal of Applied Fluid Mechanics Vol:9,No.6(2016), 3127-3133.
• [8] Ku, D., D. Giddens, C. Zairns, and S. Glagov, Pulsatile flow and atherosclerosis in human carotid bifurcation, Arterioscler Thromb. Vasc. Biol. Vol:5,No.3(1985), 293-302.
• [9] Panda, S., S. C. Martha, and A. Chakrabarti, Three layer fluid flow over a small obstruction on the bottom of a channel, The Anziam journal Vol:56,No.3(2015), 248-274.
• [10] Prasad, B. and A. Kumar, Flow of a hydromagnetic fluid through porous media between permeable beds under exponentially decaying pressure gradient, Computational methods in science and technology Vol:17,No.1(2011), 63-74.
• [11] Shit, G. C. and M. Roy, Hydromagnetic pulsating flow of blood in a constricted porous channel: A theoretical study, In Proceedings of the World Congress on Engineering, London, U.K. Vol:1(2012).
• [12] Siddiqui, A. M., N. Z. Khan, M. A. Rana, and T. Haroon, Flow of a second grade fluid through constricted tube using integral method, Journal of Applied Fluid Mechanics Vol:9,No.6(2016), 2803-2812.
• [13] Sreenadh, S., A. Parandhama, and R. Hemadrireddy, Unsteady flow of couple stress fluid in contact with a newtonian fluid between permeable beds, International J. of Math. Sci. and Engg. Appls. (IJMSEA) Vol:6,No.IV(2012), 241–258.
• [14] Srinivas, J. and J. V. R. Murthy, Flow of two immiscible couple stress fluids between two permeable beds Journal of Applied Fluid Mechanics Vol:9,No.1(2016), 501-507.
• [15] Sulochana, P., Unsteady MHD pulsatile flow of couple stress fluid under the influence of periodic body acceleration between two parallel plates, Advances in Applied Science Research Vol:5,No.4(2014), 136-143.
• [16] Umavathi, J., A. J. Chamakha, A. Mateem, and A. Al-Mudhaf, Unsteady oscillatory flow and heat transfer in a horizontal composite porous medium channel, Non-linear Analysis:Modelling and Control Vol:14,No.3(2009), 397-415.
• [17] Umavathi, J. C., I. Leu, J. P. Kumar, and D. S. Meera, Unsteady flow and heat transfer of porous media sandwiched between viscous fluids, Appl. Math. and Mech. - Engl. Ed. Vol;31,No.12(2010), 1497-1516.
• [18] Venugopal, R. and D. Bathaiah, Magnetohydrodynamic flow past a permeable bed, Def Sci J. Vol:33,No.1(1983), 69-90.
• [19] Yamamoto, K. and Z. Yoshida, Flow through a porous wall with convective acceleration, Journal of Physical Society of Japan Vol.37,No.3 (1974), 774-779.
• [20] Zamir, M.,The Physics of Pulsatile Flow, Springer-Verlag, (2000).