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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Taylor, G. T.: On the decay of vortices in a viscous fluid. Phil. Mag.46, 671–674 (1923).
Kovasnay, L. I. G.: Laminar flow behind a two-dimensional grid. Proc. Cambridge Phil. Soc.44, 58–62 (1948).
Wang, C. Y.: On a class of exact solutions of the Navier-Stokes equations. J. Appl. Mech.33, 696–698 (1966).
Lin, S. P., Tobak, M.: Reversed flow above a plate with suction. AIAA J.24, 334–335 (1986).
Hui, W. H.: Exact solutions of the unsteady two-dimensional Navier-Stokes equation. ZAMP38, 689–102 (1987).
Rivlin, R. S., Ericksen, J. L.: Stress deformation relations for isotropic materials. J. Rat. Mech. Anal.4, 323–425 (1955).
Coleman, B. D., Noll, W.: An approximation theorem for functionals with application in continuum mechanics. Arch. Rat. Mech. Anal.6, 355–370 (1960).
Rajagopal, K. R.: On the decay of vortices in a second grade fluid. Meccanica,9, 185–188 (1980).
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).
Kaloni, P. N., Huschilt, K.: Semi-inverse solutions of non-Newtonian fluid. Int. J. Non-Linear Mech.19, 373–381 (1984).
Siddiqui, A. M., Kaloni, P. N.: Certain-inverse solutions of a non-Newtonian fluid. Int. J. Non-Linear Mech.21, 459–473 (1986).
Siddiqui, A. M.: Some more inverse solutions of a non-Newtonian fluid. Mech. Res. Comm.17, 157–163 (1990).
Markovitz, H., Coleman, B. D.: Incompressible second order fluids. Adv. Appl. Mech.8, 69–101 (1964).
Ting, T. W.: Certain non-steady flows of second order fluids. Arch. Rat. Mech. Anal.14, 1–26 (1963).
Rajagopal, K. R.: A note on unsteady unidirectional flows of a non-Newtonian fluid. Int. J. Non-Linear Mech.17, 369–373 (1982).
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).
Fosdick, R. L., Rajagopal, K. R.: Anomalous features in the model of second-order fluids. Arch. Rat. Mech. Anal.70, 145–152 (1979).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Benharbit, A.M., Siddiqui, A.M. Certain solutions of the equations of the planar motion of a second grade fluid for steady and unsteady cases. Acta Mechanica 94, 85–96 (1992). https://doi.org/10.1007/BF01177007
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01177007