The exact solutions for the motion of a Maxwell fluid due to longitudinal and torsional oscillations of an infinite circular cylinder are determined by means of the Laplace transform. These solutions are presented as sum of the steady-state and transient solutions and 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 required times to reach the steady-state are determined for sine, cosine and combined oscillations of the boundary.
Maxwell fluid Oscillating motion Starting solutions Mechanics of fluids
This is a preview of subscription content, log in to check access.
Stokes GG (1886) On the effect of the rotation of cylinders and spheres about their axes in increasing the logarithmic decrement of the arc of vibration. Cambridge University Press, Cambridge
Casarella MJ, Laura PA (1969) Drag on oscillating rod with longitudinal and torsional motion. J Hydronaut 3:180–183
Rajagopal KR (1983) Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid. Acta Mech 49:281–285
Fetecau C, Fetecau Corina (2005) Starting solutions for some unsteady unidirectional flows of a second grade fluid. Int J Eng Sci 43:781–789
Fetecau C, Fetecau Corina (2006) Starting solutions for the motion of a second grade fluid due to longitudinal and torsional oscillations of a circular cylinder. Int J Eng Sci 44(11–12):788–796
Dapra I, Scarpi G (2006) Pulsatile pipe flows of pseudoplastic fluids. Meccanica 41:501–508
Asghar S, Hanif K, Hayat T (2007) The effect of the slip condition on unsteady flow due to non-coaxial rotations of disk and a fluid at infinity. Meccanica 42(2):141–148
Böhme G (1981) Strömungsmechanik nicht-newtonscher fluide. Teubner, Stuttgart