Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders |
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Authors: | Amir Mahmood Saima Parveen Najeeb Alam Khan |
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Institution: | Amir Mahmood · Saima Parveen · Najeeb Alam Khan Department of Mathematics,COMSATS Institute of Information Technology,Lahore,Pakistan Abdus Salam School of Mathematical Sciences,Pakistan Department of Mathematics,University of Karachi,Karachi-75270,Pakistan |
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Abstract: | The velocity field and the associated shear stress corresponding to the torsional oscillatory flow of a second grade fluid,
between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time t = 0, the fluid and both the cylinders are at rest and at t = 0+, cylinders suddenly begin to oscillate around their common axis in a simple harmonic way having angular frequencies ω1 and ω2. The obtained solutions satisfy the governing differential equation and all imposed initial and boundary conditions. The
solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore,
the corresponding solutions for Newtonian fluid are also obtained as limiting cases of our general solutions. |
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Keywords: | Second grade fluid · Velocity field · Shear stress · Longitudinal oscillatory flow · Laplace and Hankel transforms |
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