Hostname: page-component-7479d7b7d-767nl Total loading time: 0 Render date: 2024-07-10T19:46:04.199Z Has data issue: false hasContentIssue false

Coaxial-disk flow and flow about a rotating disk of a Maxwellian fluid

Published online by Cambridge University Press:  20 April 2006

N. Phan-Thien
Affiliation:
Department of Mechanical Engineering, University of Sydney, N.S.W. 2006. Australia Present address: Department of Chemical Engineering, Caltech, Pasadena, CA 91125.

Abstract

The flows of a Maxwellian fluid between two rotating coaxial disks and about a rotating disk are discussed. Asymptotic solutions are derived and numerical solutions are reported for a Weissenberg number up to 10 and a Reynolds number of up to 50. The solutions show transverse wave propagation. Also, at low Weissenberg number the moment coefficient for a rotating disk wetted on both sides is inversely proportional to the square root of the angular velocity of the disk. At high Weissenberg number it is inversely proportional to the angular velocity of the disk. The transition occurs at a Weissenberg number of unity.

Type
Research Article
Copyright
© 1983 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Batchelor, G. K. 1951 Q. J. Mech. Appl. Math. 4, 29.
Benton, E. R. 1966 J. Fluid Mech. 24, 781.
Bhatnagar, R. K. & Zago, J. V. 1978 Rheol. Acta 17, 557.
Bhatnagar, R. K. & Perera, M. G. N. 1982 J. Rheol. 26, 19.
Bird, R. B., Armstrong, R. C. & Hassager, O. 1977 Dynamics of Polymeric Liquids, vol. I. Wiley.
Boger, D. V. 1977/78 J. Non-Newt. Fluid Mech. 3, 87.
Cochran, W. G. 1934 Proc. Camb. Phil. Soc. 30, 365.
Griffiths, D. F., Jones, D. T. & Walters, K. 1969 J. Fluid Mech. 36, 161.
Good, P. A., Schwartz, A. J. & Macosko, C. W. 1974 A.I.Ch.E. J. 20, 67.
Holodniok, M., KUBÍĈEK, K. & HLAVÁĈEK, V. 1977 J. Fluid Mech. 81, 689.
Joseph, D. D. 1977 Arch. Rat. Mech. Anal. 66, 311.
Kármán, T. Von 1921 Z. angew. Math. Mech. 15, 191.
Pearson, J. R. A. 1982 Computer Methods in Chemical Engineering. Applied Science Publishers.
Phan-Thien, N. & Tanner, R. I. 1983 J. Fluid Mech. 129, 265.
Phan-Thien, N. 1982 Rheol. Acta (in press).
Rathna, S. L. 1962 Z. angew. Math. Mech. 42, 231.
Stewartson, K. 1953 Proc. Camb. Phil. Soc. 49, 333.
TANNER, R. I. 1962 Z. angew. Math. Phys. 13, 573.
Walters, K. 1975 Rheometry. Chapman & Hall.
Williams, E. W. 1976 J. Non-Newt. Fluid Mech. 1, 51.