Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders
A. Mahmood1,S. Parveen2,N.A. Khan3
1. Department of Mathematics, COMSATS Institute of Information Technology, Lahore, Pakistan 2. Abdus Salam School of Mathematical Sciences, Lahore, Pakistan 3. Department of Mathematics, University of Karachi, Karachi-75270, Pakistan
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 $\omega_1$ and $\omega_2$. 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.
Corresponding Authors:
A. Mahmood
E-mail: amir4smsgc@gmail.com
Cite this article:
A. -Mahmood,S. -Parveen,N.A. -Khan. Exact solutions for the flow of second grade fluid in annulus between torsionally oscillating cylinders[J]. Acta Mechanica Sinica, 2011, 27(2): 222-227.
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