Archive for Rational Mechanics and Analysis

, Volume 62, Issue 3, pp 237–294 | Cite as

Flow of a Newtonian fluid between eccentric rotating cylinders: Inertial effects

  • B. Y. Ballal
  • R. S. Rivlin
Article

Abstract

A detailed analysis is carried out of the flow of a Newtonian fluid in the annular region between two infinitely long circular cylinders with parallel axes, resulting from the uniform rotation of one, or both, of the cylinders about their axes. No restriction is placed on the geometry of the system and results are obtained both with the neglect of inertial effects and for the linearized inertial approximation. In both cases, the resultant of the forces exerted by the fluid on the cylinders and the distribution of their normal and tangential components over the cylinders are calculated, and the stream-line patterns are analyzed in some detail. A number of conditions, under which stagnation points, separation points and eddies can exist, are established.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. DiPrima, R. C., & J. T. Stuart, 1972 J. Lubr. Tech., Trans. A.S.M.E. 94, 266–274.Google Scholar
  2. Duffing, G., 1924 Z. angew. Math. Mech. (ZAMM) 4, 297–314.Google Scholar
  3. Jeffrey, G. B., 1922 Phil. Trans. R. Soc. Land. A101, 169–174.Google Scholar
  4. Kamal, M. M., 1966 J. Basic Engng., Trans. A.S.M.E. 88, 717–724.Google Scholar
  5. Kulinski, E., & S. Ostrach, 1967 J. Appl. Mech., Trans. A.S.M.E. 89, 16–22.Google Scholar
  6. Müller, W., 1942(a) Ing.-Arch. 13, 37–58.Google Scholar
  7. Müller, W.1942(b) Ann. Physik 41, 335–354.Google Scholar
  8. Müller, W.1942(c) Z. angew. Math. Mech. (ZAMM) 22, 177–189.Google Scholar
  9. Reissner, H., 1935 Z. angew. Math. Mech. (ZAMM) 15, 81–87.Google Scholar
  10. Reynolds, O., 1886 Phil. Trans. R. Soc. Lond. 177(I), 157–234.Google Scholar
  11. Sood, D. R., & H. G. Elrod, 1970 Report 17, Lubr. Res. Lab., Columbia U., N. Y., 1–44.Google Scholar
  12. Wannier, G., 1950 Q. Appl. Math. 8, 1–32.Google Scholar
  13. Yamada, Y, & K. Nakabayashi, 1968 Bull. Japan Soc. Mech. Engrs. 11, 455–462.Google Scholar
  14. Zhukowski, N. E., 1887 Comm. Math. Soc. Kharkov 17, 31–46.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • B. Y. Ballal
    • 1
  • R. S. Rivlin
    • 1
  1. 1.Center for the Application of MathematicsLehigh UniversityBethlehemPennsylvania

Personalised recommendations