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Unsteady Plane Couette Flow of an Incompressible Couple Stress Fluid with Slip Boundary Conditions

Hikmat S. Saad, E. A. Ashmawy

Hikmat S. Saad 1 ,

E. A. Ashmawy 1 
  1. Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, Lebanon 1

Pages: 85-92

DOI: 10.18488/journal.9/2016.3.7/9.7.85.92

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Abstract:

In this work, the unsteady flow of an incompressible couple stress fluid between two parallel plates is studied. Slip boundary conditions are applied on the two plates and vanishing couple stress condition at the boundaries is assumed. The upper plate is suddenly moved with time dependent velocity while the other plate is fixed. The problem is solved analytically in the Laplace domain through the use of Laplace transform technique. The inverse transform of the fluid velocity is obtained numerically. The velocity profiles for different times and different physical parameters are plotted and the numerical results are discussed.

Contribution/ Originality
This paper contributes to the field of couple stress fluids by applying the more realistic slip condition to Couette flow of an incompressible couple stress fluid. It is found that the time, the couple stress coefficient and the slip parameters have significant effect on the flow field.

Keywords:

Couple stresses fluids, Incompressible, Couette flow, Unsteady flow, Slip boundary condition, Laplace transform.

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Reference:

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Funding:

This study received no specific financial support.

Competing Interests:

The authors declare that they have no competing interests.

Acknowledgement:

All authors contributed equally to the conception and design of the study.

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