A similar flow between two rotating disks
Authors:
E. A. Hamza and D. A. MacDonald
Journal:
Quart. Appl. Math. 41 (1984), 495-511
MSC:
Primary 76U05
DOI:
https://doi.org/10.1090/qam/724059
Correction:
Quart. Appl. Math. 42 (1984), 255.
MathSciNet review:
724059
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Abstract: When viscous incompressible fluid is contained between two parallel disks which, at time $t$, are spaced a distance $H\sqrt {1 - \alpha t}$ apart and are rotating with angular velocities proportional to ${\Omega _1}{(1 - \alpha t)^{ - 1}}$ the governing Navier-Stokes equations reduce to a set of ordinary differential equations. We present approximate solutions to these equations for a range of values of the three linearly independent parameters which influence the fluid motion. Special attention is given to the normal forces and the torques which the fluid exerts on the rotating surfaces.
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- M. Holodniok, M. Kubíček, and V. Hlaváček, Computation of the flow between two rotating coaxial disks, J. Fluid Mech. 81 (1977), no. 4, 689–699. MR 455886, DOI 10.1017/S0022112077002298
Th. v. Kármán, Z. Angew. Math. Mech. 1 (1921), 244
G. K. Batchelor, Quart. J. Mech. Appl. Math. 4 (1951), 29
K. Stewartson, Proc. Camb. Phil. Soc. 49 (1953), 333
M. Holodniok, M. Kubiček and V. Hlaváček, J. Fluid Mech. 108 (1981), 227
C. E. Pearson, J. Fluid Mech. 21 (1965), 623
S. Ishizawa, Bull. J.S.M.E. 9 (1966), 533
C. Y. Wang, J. Apl. Mech., Trans. A.S.M.E., 43 (1976), 579
W. G. Cochran, Proc. Camb. Phil. Soc. 30 (1934), 365
G. N. Lance and M. H. Rogers, Proc. Roy. Soc. (A) 266 (1962), 109
M. Holodniok, M. Kubiček and V. Hlaváček, J. Fluid Mech. 81 (1977), 689
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© Copyright 1984
American Mathematical Society
