Advertisement

Non-torsional oscillations of a disc in rotating second order fluid

  • P. D. Verma
  • N. C. Sacheti
Article
  • 10 Downloads

Abstract

This paper deals with the non-torsional oscillations of a disc in rotating second-order fluid. The disc and the fluid are initially in a state of rigid rotation and the non-torsional oscillations in its own plane are then imposed on the disc. The depth of penetration of the oscillations is increased due to the presence of the coefficient of visco-elasticity. It tends to infinity when the frequency of the oscillations is twice the angular velocity of rotation, meaning thereby that no equilibrium boundary layer exist. An initial value problem for two cases—(i) one disc bounding a semi-infinite mass of the fluid, (ii) two discs containing the fluid in between them is discussed. The classical Rayleigh layer for second-order fluid is derived as a particualr case and it is also found that steady Ekman layer is reached for large time.

Keywords

Angular Velocity Rigid Rotation Oscillatory Solution Resonant Case Order Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Proudman, J...Proc. Roy. Soc., 1916,92 A, 408.Google Scholar
  2. 2.
    Taylor, G. I...Ibid., 1917,93 A, 99.Google Scholar
  3. 3.
    —..Proc. Cambridge Phil. Soc., 1921,20, 326.Google Scholar
  4. 4.
    —..Proc. Roy. Soc., 1922,100 A, 114.Google Scholar
  5. 5.
    —..Ibid., 1922,102 A, 180.Google Scholar
  6. 6,.
    —..Ibid., 1923,104 A. 213,Google Scholar
  7. 7.
    Grace, S. F...Proc. Roy. Soc., 1922,102 A, 89.Google Scholar
  8. 8.
    —..Ibid., 1923,104 A, 278.Google Scholar
  9. 9.
    —..Ibid., 1924,105 A, 532.Google Scholar
  10. 10.
    —..Ibid., 1926,113 A, 46.Google Scholar
  11. 11.
    Morgan, G. W...Ibid., 1951,206 A, 108.Google Scholar
  12. 12.
    Stewartson, K...Proc. Cambridge Phil. Soc., 1952,48, 168.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    —..Quart. J. Mech. Appl. Math., 1958,11, 39.MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Fraenkel, L. E...Proc. Roy. Soc., 1956,233 A. 506.MathSciNetGoogle Scholar
  15. 15.
    Childress, S...J. Fluid Mech., 1964,20, 305.CrossRefMathSciNetGoogle Scholar
  16. 16.
    Kaplun, S. and Lagerstrom, P. A.J. Math. Mech., 1957,6, 585.MATHMathSciNetGoogle Scholar
  17. 17.
    Davis, P. K...Physics of Fluids, 1965,8, 560.MATHCrossRefGoogle Scholar
  18. 18.
    Thornley, C...Quart. J. Mech. Appl. Math., 1968,21, 451.MATHCrossRefGoogle Scholar
  19. 19.
    Bhatnagar, P. L...Proc. Ind. Acad. Sci., 1961,53 A, 95.MathSciNetGoogle Scholar
  20. 20.
    Carslaw, H. S. and Jaegar, J. C.Operational Methods in Applied Mathematics, Oxford University Press, 1941, p. 75.Google Scholar
  21. 21.
    Rosenhead, L. (Editor)..Laminar Boundary Layers, Clarendon Press, Oxford, 1963, p. 136.MATHGoogle Scholar

Copyright information

© Indian Academy of Sciences 1972

Authors and Affiliations

  • P. D. Verma
    • 1
  • N. C. Sacheti
    • 1
  1. 1.Department of MathematicsUniversity of RajasthanJaipur-4

Personalised recommendations