Generalized Stokes’ Problems for an Incompressible Couple Stress Fluid
In this paper, we investigate the generalized Stokes’ problems for an incompressible couple stress fluid. Analytical solution of the governing equations is obtained in Laplace transform domain for each problem. A standard numerical inversion technique is used to invert the Laplace transform of the velocity in each case. The effect of various material parameters on velocity is discussed and the results are presented through graphs. It is observed that, the results are in tune with the observation of V.K.Stokes in connection with the variation of velocity in the flow between two parallel plates when the top one is moving with constant velocity and the bottom one is at rest.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1090538Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2880
 V.K. Stokes, Couple stresses in fluids, 9(9) (1966), pp.1710-1715.
 V.K. Stokes, Theory of fluids with microstructure-An introduction, Springer Verlag, (1984).
 N.B. Naduvinamani, P.S. Hiremath, G. Gurubasavaraj, Squeeze film lubrication of a short porous journal bearing with Couple stress fluids, Tribology International, 34(11) (2001), pp. 739-747.
 N.B. Naduvinamani, P.S. Hiremath, G. Gurubasavaraj, Surface roughness effects in a short porous journal bearing with a Couple stress fluid, Fluid Dynamics Research, 31(5-6) (2002), pp. 333-354.
 N.B. Naduvinamani, P.S. Hiremath, G. Gurubasavaraj, Effects of surface roughness on the Couple stress squeeze film between a sphere and a flat Plate, Tribology International, 38(5) (2005), pp. 451-458.
 N.B. Naduvinamani, Syeda Tasneem Fathima, P.S. Hiremath, Hydrodynamic lubrication of rough slider bearings with Couple stress fluids, Tribology International, 36(12) (2003), pp. 949-959.
 N.B. Naduvinamani, Syeda Tasneem Fathima, P.S. Hiremath, Effect of surface roughness on characteristics of couplestress squeeze film between anisotropic porous rectangular plates, Fluid Dynamics Research, 32(5) (2003), pp. 217-231.
 Jaw-Ren Lin, Chi-Ren Hung, Combined effects of non-Newtonian couple stresses and fluid inertia on the squeeze film characteristics between a long cylinder and an infinite plate, Fluid Dynamics Research, 39(8) (2007), pp. 616-639.
 H. Schlichting, K. Gersten, Boundary Layer Theory, Springer, (2002).
 P.R. Gupta, K.L. Arora, Hydromagnetic flow between two parallel planes, one is oscillating and the other fixed, Pure. Appl. Geophy., 112(2) (1974), pp.498-505.
 I.A. Hassanien, M.A. Mansour, Unsteady magnetohydrodynamic flow through a porous medium between two infinite parallel plates, Astrophy. Spac. Scie., 163(2) (1990), pp.241-246.
 I.A. Hassanien, Unsteady hydromagnetic flow through a porous medium between two infinite parallel porous plates with time varying suction, Astrophy. Spac. Scie., 175(1) (1991), pp.135-147.
 T. Hayat, S. Asghar, A.M. Siddiqui, Some unsteady unidirectional flows of a non-Newtonian fluid, Int. J. Engg. Sci., 38(3) (2000), pp 337-346.
 M.E. Erdogan, On the unsteady unidirectional flows generated by impulsive motion of a boundary or sudden application of a pressure gradient, Int. J. Non-Linear Mech., 37(6) (2002), pp.1091-1106.
 T. Hayat, Masood Khan, A.M. Siddiqui, S. Asghar, Transient flows of a second grade fluid”, Int. J. Non-Linear Mech., 39(10) (2004), pp.1621-1633.
 M.E. Erdogan, C.E. Imrak, On unsteady unidirectional flows of a second grade fluid, Int. J. Non-Linear Mech., 40(10) (2005), pp.1238-1251.
 M.E. Erdogan, C.E. Imrak, On some unsteady flows of a non-Newtonian fluid, Appl. Math. Model., 31(2) (2007), pp.170-180.
 C. Fetecau, C. Fetecau, Starting solutions for some unsteady unidirectional flows of second grade fluid, Int. J. Engg. Sci., 43(10) (2005), pp.781-789.
 G. Honig, U. Hirdes, A method for the numerical inversion of Laplace Transforms, J. Comp. Appl. Math., 10(1) (1984)., pp.113-132.
 M. Devakar, T.K.V. Iyengar, Stokes’ problems for an incompressible couple stress fluid”. Non-Linear Anal. Mode. Contr., 13(2) (2008), pp.181-190.