Abstract
In this paper, we have determined the exact starting solutions of velocity field and associated shear and normal stresses corresponding to the unsteady flow of a Maxwell fluid, due to torsional oscillations of two infinite coaxial circular cylinders by means of Laplace and Hankel transforms. The fluid is situated at rest in an annular region between the cylinders. Suddenly both cylinders start torsional sine oscillations around their common axis, with different angular frequencies of their oscillations. The starting solutions that have been obtained satisfy the governing equation of motion and all imposed initial and boundary conditions. Furthermore, these solutions, presented as a sum of steady-state and transient solutions, reduce to the similar solutions for Newtonian fluid as the limiting case. They describe the motion of the fluid for some time after its initiation. After that time, when the transients disappear, the unsteady solutions tend to the steady-state solutions which are periodic in time and independent of initial conditions. Finally, numerical results and concluding remarks are given.
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