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Viscous incompressible flow between concentric rotating spheres. Part 1. Basic flow

Published online by Cambridge University Press:  29 March 2006

B. R. Munson  and
D. D. Joseph
B. R. Munson
Affiliation:
Department of Mechanical Engineering, Duke University, Durham, North Carolina
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, Minnesota
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Abstract

The steady motion of a viscous fluid contained between two concentric spheres which rotate about a common axis with different angular velocities is considered. A high-order analytic perturbation solution, through terms of order Re7, is obtained for low Reynolds numbers. For larger Reynolds numbers an approximate Legendre polynomial series representation is used to reduce the governing system of equations to a non-linear ordinary differential equation boundary-value problem which is solved numerically. The resulting flow pattern and the torque required to rotate the spheres are presented for various cases considered.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 49 , Issue 2 , 29 September 1971 , pp. 289 - 303
Copyright
© 1971 Cambridge University Press

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