Advertisement

Acta Mechanica

, Volume 94, Issue 1–2, pp 85–96 | Cite as

Certain solutions of the equations of the planar motion of a second grade fluid for steady and unsteady cases

  • A. M. Benharbit
  • A. M. Siddiqui
Contributed Papers

Summary

Solutions for the equations of motion of an incompressible second grade fluid are derived by assuming certain conditions on the stream function. Exact solutions are obtained for a planar motion for both steady and unsteady cases.

Keywords

Dynamical System Exact Solution Fluid Dynamics Transport Phenomenon Stream Function 
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]
    Taylor, G. T.: On the decay of vortices in a viscous fluid. Phil. Mag.46, 671–674 (1923).Google Scholar
  2. [2]
    Kovasnay, L. I. G.: Laminar flow behind a two-dimensional grid. Proc. Cambridge Phil. Soc.44, 58–62 (1948).Google Scholar
  3. [3]
    Wang, C. Y.: On a class of exact solutions of the Navier-Stokes equations. J. Appl. Mech.33, 696–698 (1966).Google Scholar
  4. [4]
    Lin, S. P., Tobak, M.: Reversed flow above a plate with suction. AIAA J.24, 334–335 (1986).Google Scholar
  5. [5]
    Hui, W. H.: Exact solutions of the unsteady two-dimensional Navier-Stokes equation. ZAMP38, 689–102 (1987).Google Scholar
  6. [6]
    Rivlin, R. S., Ericksen, J. L.: Stress deformation relations for isotropic materials. J. Rat. Mech. Anal.4, 323–425 (1955).Google Scholar
  7. [7]
    Coleman, B. D., Noll, W.: An approximation theorem for functionals with application in continuum mechanics. Arch. Rat. Mech. Anal.6, 355–370 (1960).Google Scholar
  8. [8]
    Rajagopal, K. R.: On the decay of vortices in a second grade fluid. Meccanica,9, 185–188 (1980).Google Scholar
  9. [9]
    Rajagopal, K. R., Gupta, A. S.: On a class of exact solutions to the equations of motion of a second grade fluid. Int. J. Engng. Sci.19, 1009–1014 (1981).Google Scholar
  10. [10]
    Kaloni, P. N., Huschilt, K.: Semi-inverse solutions of non-Newtonian fluid. Int. J. Non-Linear Mech.19, 373–381 (1984).Google Scholar
  11. [11]
    Siddiqui, A. M., Kaloni, P. N.: Certain-inverse solutions of a non-Newtonian fluid. Int. J. Non-Linear Mech.21, 459–473 (1986).Google Scholar
  12. [12]
    Siddiqui, A. M.: Some more inverse solutions of a non-Newtonian fluid. Mech. Res. Comm.17, 157–163 (1990).Google Scholar
  13. [13]
    Markovitz, H., Coleman, B. D.: Incompressible second order fluids. Adv. Appl. Mech.8, 69–101 (1964).Google Scholar
  14. [14]
    Ting, T. W.: Certain non-steady flows of second order fluids. Arch. Rat. Mech. Anal.14, 1–26 (1963).Google Scholar
  15. [15]
    Rajagopal, K. R.: A note on unsteady unidirectional flows of a non-Newtonian fluid. Int. J. Non-Linear Mech.17, 369–373 (1982).Google Scholar
  16. [16]
    Dunn, J. E., Fosdick, R. L.: Thermodynamics, stability and boundedness of fluids of complexity 2 and fluids of second grade. Arch. Rat. Mech. Anal.3, 191–252 (1974).Google Scholar
  17. [17]
    Fosdick, R. L., Rajagopal, K. R.: Anomalous features in the model of second-order fluids. Arch. Rat. Mech. Anal.70, 145–152 (1979).Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • A. M. Benharbit
    • 1
  • A. M. Siddiqui
    • 1
  1. 1.Pennsylvania State UniversityYorkUSA

Personalised recommendations