Some New Exact Solutions for Prescribed Vorticity Distribution of Couple Stress Fluids in the Presence of Unknown Body Force
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Keywords

 Exact solutions, Couple stress fluid, Flows for prescribed vorticity distribution.

How to Cite

Rana Khalid Naeem. (2021). Some New Exact Solutions for Prescribed Vorticity Distribution of Couple Stress Fluids in the Presence of Unknown Body Force. Journal of Basic & Applied Sciences, 8(2), 485–490. https://doi.org/10.6000/1927-5129.2012.08.02.39

Abstract

In the present paper, we indicate some new exact solutions of equations of motion for plane steady incompressible couple stress fluids flows in the presence of unknown body force for which vorticity distribution is defined by Eq. (12). All solutions involve arbitrary real constants and arbitrary real constants depending on the parameter èindicating that a large number of streamfunctions and expressions for body force can be constructed. Some streamfunctions ø are constructed for some values of parameters. The streamlines patterns of these streamfunctions are presented and discussed.

https://doi.org/10.6000/1927-5129.2012.08.02.39
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References

Shehawey EFE, Mekheimer KS. Couple-Stresses in peristaltic transport of fluids. D Appl J Phys 1994; 27: 1163-70.

Ramanaiah G. Squeeze films between finite plates lubricated by fluid with couple stresses. Wear 1979; 54: 315-20. http://dx.doi.org/10.1016/0043-1648(79)90123-6

Stokes K. Couple stresses in fluids. Phys Fluids 1966; 9(9): 1709-15. http://dx.doi.org/10.1063/1.1761925

Srivastava LMS, Peristaltic Transport of a couple –stress fluid. Rheol Acta 1986; 25: 638-41. http://dx.doi.org/10.1007/BF01358172

Wang L, Zhu Q, Zhu W. On the performance of dynamically loaded journal bearings with fluids, couple stress. Tribiology -191 Int 2002; 35(3): 185-91.

Devarkar M, Iyengar TKV. Stokes’ Problems for an incompressible couple stress fluid. Non linear Analysis: Modelling and Control 2008; 1( 2): 181-90.

Devarkar M, Iyengar TKV. Run up flow of a Couple stress fluid between parallel plates, Nonlinear Analysis: Modelling and Control 2010; 15(1): 29-37.

Naduvinamant NB, Hiremath PS, Girubasavaraj G, Squeeze film lubrication of a short porous journal bearing with couple stress fluids. Tribiology 2001; 34(11): 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 Res 2002; 31(5-6): 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 2002; 38(5): 451-58. http://dx.doi.org/10.1016/j.triboint.2004.09.001

Sinha P, Singh C. Couple stress in the lubrication of rolling contact bearings considering cavitations. Wear 1981; 67(1): 85-98. http://dx.doi.org/10.1016/0043-1648(81)90077-6

Mindlin RD, Tierstea HF. Effect of couple stresses in linear elasticity. Arch Rat Mech Anal 1962; 11(1): 415-48. http://dx.doi.org/10.1007/BF00253946

Gupta RS, Sharma LG. Analysis of couple stresses lubricant in hydrostatics thrust bearing. Wear 1988; 125(3): 257-69. http://dx.doi.org/10.1016/0043-1648(88)90117-2

Naeem RK. Some New exact solutions to unsteady flow equations of incompressible couple stress fluid. Int J Appl Mathe Mechan 2010; 6(15): 1-11.

Islam S, Zhou CY. Exact solutions for two dimensional flows of couple stress fluids. ZAMP 2007b; 58(6): 1035-48. http://dx.doi.org/10.1007/s00033-007-5075-5

Islam S, Zhou CY. Exact solutions for different vorticity functions of couple stress fluids. J Zhejang Univ Sci A 2008; 5: 672-80.