Abstract
While two parallel disks are initially rotating with the same angular velocity about non-coincident axes, the axes are suddenly made coincident. The development of the flow is examined until the fluid rotates as a rigid body in the steady-state. The velocity field and the shear stress components on the disks are found exactly by a Fourier series solution. Furthermore, a series solution that converges rapidly at small times is obtained with the aid of the Laplace transform technique.
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References
Maxwell, B. and Chartoff, R.P., 'Studies of a polymer melt in an orthogonal rheometer', Trans. Soc. Rheol. 9 (1965) 41-52.
Rajagopal, K.R., 'Flow of viscoelastic fluids between rotating disks', Theoret. Comput. Fluid Dyn. 3 (1992) 185-206.
Ersoy, H.V., 'MHD flow of an Oldroyd-B fluid due to non-coaxial rotations of a porous disk and the fluid at infinity', Int. J. Engng Sci. 38 (2000) 1837-1850.
Rao, A.R. and Kasiviswanathan, S.R., 'On exact solutions of the unsteady Navier-Stokes equations — The vortex with instantaneous curvilinear axis', Int. J. Engng Sci. 25 (1987) 337-349.
Kasiviswanathan, S.R. and Rao, A.R., 'Exact solution for the unsteady flow and heat transfer between eccentrically rotating disks', Lett. Appl. Engng Sci. 27 (1989) 731-736.
Kasiviswanathan, S.R. and Rao, A.R., 'On exact solutions of unsteady MHD flow between eccentrically rotating disks', Arch. Mech. 39 (1987) 411-418.
Erdoğan, M.E., 'Unsteady viscous flow between eccentric rotating disks', Int. J. Non-Linear Mech. 30 (1995) 711-717.
Erdoğan, M.E., 'Flow due to parallel disks rotating about non-coincident axis with one of them oscillating in its plane', Int. J. Non-Linear Mech. 34 (1999) 1019-1030.
Erdoğan, M.E., 'Unsteady flow between two eccentric rotating disks executing non-torsional oscillations', Int. J. Non-Linear Mech. 35 (2000) 691-699.
Ersoy, H.V., 'Unsteady flow due to a sudden pull of eccentric rotating disks', Int. J. Engng Sci. 39 (2001) 343-354.
Abbott, T.N.G. and Walters, K., 'Rheometrical flow systems: Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations', J. Fluid Mech. 40 (1970) 205-213.
Carslaw, H.S. and Jaeger, J.C., Conduction of Heat in Solids, Oxford Univ. Press, Oxford, 1959, pp. 297-311.
Abramowitz, M. and Stegun, I.A., Handbook of Mathematical Functions, Dover Publications, New York, 1965, pp. 297-300.
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Volkan Ersoy, H. Unsteady Flow Due to Concentric Rotation of Eccentric Rotating Disks. Meccanica 38, 325–334 (2003). https://doi.org/10.1023/A:1023374214783
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DOI: https://doi.org/10.1023/A:1023374214783