Abstract
Exact solutions are derived for a class of two dimensional couple stress flows. This class consists of flows for which the vorticity distribution is characterized by the Eq. (12). The solutions are obtained by introducing the functions Ψ, H and the canonical transformation. The effects of the parameters K, m, U, A, B, D, E, L, and M on velocity components u and v are discussed and streamlines for the various values of the parameters are also presented.
References
Stokes K. Couple stresses in fluids. Physics Fluids. 1966; 9: 1709-15. http://dx.doi.org/10.1063/1.1761925
Mindlin RD, Tierstea HF. Effect of couple stresses in linear elasticity. Arch Rat Mech Anal. 1962; 11: 415-48. http://dx.doi.org/10.1007/BF00253946
Ramanaiah G. Squeeze films between finite plates lubricated by fluid with couple stresss. Wear. 1979; 54: 315-20. http://dx.doi.org/10.1016/0043-1648(79)90123-6
Sinha P, Singh C. Couple stress in the lubrication of rolling contact bearings considering cavitations. Wear. 1981; 67: 85- 98.
http://dx.doi.org/10.1016/0043-1648(81)90077-6
Gupta RS. Sharma LG. Analysis of couple stresses lubricant in hydrostatics thrust bearing. Wear. 1988; 125: 257-69. http://dx.doi.org/10.1016/0043-1648(88)90117-2
Wang L. Zhu Q, Zhu W. On the performance of dynamically loaded journal bearings with couple stress fluids. Tribiology Int. 2002: 35(3): 185-91. http://dx.doi.org/10.1016/S0301-679X(01)00114-1
Naduvinamant NB, Hiremath PS, Girubasavaraj G. Squeeze film lubrication of a short porous journal bearing with couple stress fluids. Tribiology. 2001; 34: 739-47. http://dx.doi.org/10.1016/S0301-679X(01)00064-0
Naduvinamant NB, Hiremath PS, Girubasavaraj G. Surface roughness effects in a short porous journal bearing with a couple stress fluid. Fluid Dynamics Reseach. 2002; 31: 333- 54. http://dx.doi.org/10.1016/S0169-5983(02)00137-5
Naduvinamant NB, Hiremath PS, Girubasavaraj G. Effects of surface roughness on the couple stress squeeze film between a sphere and a flat plate. Tribiology Int. 2005; 38: 451-8. http://dx.doi.org/10.1016/j.triboint.2004.09.001
Islam S, Zhou CY. Exact solutions for two dimensional flows of couple stress fluids. ZAMP. 2007; 58: 1035-48. http://dx.doi.org/10.1007/s00033-007-5075-5
Devarkar M, Iyengar TKV. Stokes ’ Problems for an incompressible couple stress fluid. Non linear Analysis: Modelling and Control. 2008; 1: 181-90.
Devarkar M, Iyengar TKV. Run up flow of a Couple stress fluid between parallel plates. Nonlinear Analysis: Modelling and Control. 2010; 15: 29-37.
Naeem RK. Some New exact solutions to unsteady flow equations of incompressible couple stress fluid. International Journal of Applied Mathematics and Mechanics. 2010; 6: 1- 11.
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