Pulsating Flow of an Incompressible Couple Stress Fluid Between Permeable Beds
The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.
[1] D.N.Ku, D.P.Giddens, C.K. Zairns, S. Glagov, Pulsatile flow and
atherosclerosis in human carotid bifurcation: positive correlation between
plaque location and low and oscillating shear stress, Arteriosclerosis 5
(1985) 293-302.
[2] R.M.Nerem, M.J.Levesque, Hemodynamics and the arterial wall, Vasc.
Disc. (1987) 295-317.
[3] F.Fedele, D.Hitt, R.D.Prabhu, Revisiting the stability of pulsatile pipe
flow, European J. of Mech. ÔÇö B/Fluids 24 (2005) 237-254.
[4] Y.C. Wang, Pulsatile flow in a porous channel, J. Appl. Mech. 38 (1971)
553-555.
[5] K. Vajravelu, K. Ramesh, S. Sreenadh, P.V. Arunachalam, Pulsatile flow
between permeable beds, Int. J. Non-Linear Mech. 38 (2003) 999-1005
[6] G.S. Beavers, D.D.Joseph : Boundary conditions at a naturally permeable
wall. J. Fluid Mech., Vol 30, (1967) 197-207.
[7] V.K.Stokes, Couple Stresses in Fluids, Phys. Fluids., Vol 9,(1966) 1709-
1715.
[8] V.K.Stokes, Theories of Fluids with Microstructure, Springer-Verlag,
Berlin 1984.
[9] S.K.Lakshmana Rao and T.K.V.Iyengar, Analytical and computational
studies in couple stress fluid flows, U.G.C. Research project C-8-4/82
SR III, (1985)
[10] L.M.Srivastava,Flow of couple stresss fluid through stenotic blood
vessels, J.Bio Mech., Vol 18, 479-485 (1985)
[11] L.M.Srivastava, Perstaltic transport of a couple stresss fluid, Rheo.Acta,
Vol 25, 638-641 (1986).
[12] N.B.Naduvinamani, P.S.Hiremath and G.Gurubasavaraj : Squeeze film
lubrication of a short porous journal bearing with couple stress fluids,
Tribo.Inter.,Vol 34, 739-747 (2001).
[13] N.B.Naduvinamani, P.S.Hiremath and G.Gurubasavaraj : Surface roughness
effects in a short porous journal bearing with couple stress fluid,
Fluid Dyn. Res.,Vol 31, 333-354 (2002).
[14] N.B.Naduvinamani,Syeda Taseem Fathima and P.S.Hiremath: Effects of
surface roughness on characteristics of couple stress squeeze film between
anisotropic porous rectangular plates, Fluid Dyn. Res., Vol 32, 217-231
(2003).
[15] M.Devakar and T.K.V.Iyengar, Stoke-s problems for an incompressible
couple stress fluid, Nonlinear Analysis: Modeling and Control, Vol 1,
181-190 (2008).
[16] M.Devakar and T.K.V.Iyengar, Runup flow a couple stress fluid between
parallel plates , Nonlinear Analysis: Modeling and Control, Vol 15, 29-37
(2010).
[17] T.S.L.Radhika and T.K.V.Iyengar, Stokes flow of an incompressible couple
stress fluid past a porous spherical shell, Proceedings of International
Multi conference of Engineers and Computer Scientists, Vol 3, 1634-1639
(2010)
[1] D.N.Ku, D.P.Giddens, C.K. Zairns, S. Glagov, Pulsatile flow and
atherosclerosis in human carotid bifurcation: positive correlation between
plaque location and low and oscillating shear stress, Arteriosclerosis 5
(1985) 293-302.
[2] R.M.Nerem, M.J.Levesque, Hemodynamics and the arterial wall, Vasc.
Disc. (1987) 295-317.
[3] F.Fedele, D.Hitt, R.D.Prabhu, Revisiting the stability of pulsatile pipe
flow, European J. of Mech. ÔÇö B/Fluids 24 (2005) 237-254.
[4] Y.C. Wang, Pulsatile flow in a porous channel, J. Appl. Mech. 38 (1971)
553-555.
[5] K. Vajravelu, K. Ramesh, S. Sreenadh, P.V. Arunachalam, Pulsatile flow
between permeable beds, Int. J. Non-Linear Mech. 38 (2003) 999-1005
[6] G.S. Beavers, D.D.Joseph : Boundary conditions at a naturally permeable
wall. J. Fluid Mech., Vol 30, (1967) 197-207.
[7] V.K.Stokes, Couple Stresses in Fluids, Phys. Fluids., Vol 9,(1966) 1709-
1715.
[8] V.K.Stokes, Theories of Fluids with Microstructure, Springer-Verlag,
Berlin 1984.
[9] S.K.Lakshmana Rao and T.K.V.Iyengar, Analytical and computational
studies in couple stress fluid flows, U.G.C. Research project C-8-4/82
SR III, (1985)
[10] L.M.Srivastava,Flow of couple stresss fluid through stenotic blood
vessels, J.Bio Mech., Vol 18, 479-485 (1985)
[11] L.M.Srivastava, Perstaltic transport of a couple stresss fluid, Rheo.Acta,
Vol 25, 638-641 (1986).
[12] N.B.Naduvinamani, P.S.Hiremath and G.Gurubasavaraj : Squeeze film
lubrication of a short porous journal bearing with couple stress fluids,
Tribo.Inter.,Vol 34, 739-747 (2001).
[13] N.B.Naduvinamani, P.S.Hiremath and G.Gurubasavaraj : Surface roughness
effects in a short porous journal bearing with couple stress fluid,
Fluid Dyn. Res.,Vol 31, 333-354 (2002).
[14] N.B.Naduvinamani,Syeda Taseem Fathima and P.S.Hiremath: Effects of
surface roughness on characteristics of couple stress squeeze film between
anisotropic porous rectangular plates, Fluid Dyn. Res., Vol 32, 217-231
(2003).
[15] M.Devakar and T.K.V.Iyengar, Stoke-s problems for an incompressible
couple stress fluid, Nonlinear Analysis: Modeling and Control, Vol 1,
181-190 (2008).
[16] M.Devakar and T.K.V.Iyengar, Runup flow a couple stress fluid between
parallel plates , Nonlinear Analysis: Modeling and Control, Vol 15, 29-37
(2010).
[17] T.S.L.Radhika and T.K.V.Iyengar, Stokes flow of an incompressible couple
stress fluid past a porous spherical shell, Proceedings of International
Multi conference of Engineers and Computer Scientists, Vol 3, 1634-1639
(2010)
@article{"International Journal of Engineering, Mathematical and Physical Sciences:51022", author = "T. K. V. Iyengar and Punnamchandar Bitla", title = "Pulsating Flow of an Incompressible Couple Stress Fluid Between Permeable Beds", abstract = "The paper deals with the pulsating flow of an incompressible couple stress fluid between permeable beds. The couple stress fluid is injected into the channel from the lower permeable bed with a certain velocity and is sucked into the upper permeable bed with the same velocity. The flow between the permeable beds is assumed to be governed by couple stress fluid flow equations of V. K. Stokes and that in the permeable regions by Darcy-s law. The equations are solved analytically and the expressions for velocity and volume flux are obtained. The effects of the material parameters are studied numerically and the results are presented through graphs.
", keywords = "Pulsating flow, couple stress fluid, permeable beds, mass flux, shear stress.", volume = "5", number = "8", pages = "1135-11", }
