Starting solutions for oscillating motions of a generalized Burgers’ fluid in cylindrical domains
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- Tong, D. Acta Mech (2010) 214: 395. doi:10.1007/s00707-010-0288-7
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Exact solutions for the motions of a generalized Burgers’ fluid due to longitudinal and torsional oscillations of a circular cylinder are obtained using Hankel transform and Laplace transform. These solutions are expressed as sum of steady-state and transient solutions. They describe the motion of the fluid for some time after its initiation. After that time, when the transients disappear, the motion is described by the steady-state solution which is periodic in time and independent of the initial conditions. Finally, by means of graphical illustrations, the velocity field is determined for sine and cosine combined oscillations of the boundary.