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Acta Mechanica

, Volume 113, Issue 1–4, pp 233–239 | Cite as

Exact solutions for some simple flows of an Oldroyd-B fluid

  • K. R. Rajagopal
  • R. K. Bhatnagar
Note

Summary

We present two simple but elegant solutions for the flow of an Oldroyd-B fluid. First, we consider the flow past an infinite porous plate and find that the problem admits an asymptotically decaying solution in the case of suction at the plate, and that in the case of blowing it admits no such solution. Second, we study the longitudinal and torsional oscillations of an infinitely long rod of finite radius. The solutions are found in terms of Bessel functions.

Keywords

Dynamical System Exact Solution Fluid Dynamics Bessel Function Transport Phenomenon 
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.

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References

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    Schlichting, H.: Boundary layer theory. New York: McGraw-Hill 1960.Google Scholar
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    Stokes, G. G.: On the effect of the rotation of cylinders and spheres about their own axes in increasing the logarithmic decrement of the arc of vibration. (Mathematical and Philosophical Papers 5) Cambridge: Cambridge University Press 1886.Google Scholar
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    Casarella, M. J., Laura, P. A.: Drag on an oscillating rod with longitudinal and torsional motion. J. Hydronautics3, 180–183 (1969).Google Scholar
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    Rajagopal, K. R.: Longitudinal and torsional oscillations of a rod in a non-Newtonian fluid. Acta Mech.49, 281–285 (1983).Google Scholar
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    Oldroyd, J. G.: On the formulation of rheological equations of state. Proc. R. Soc. London Ser. A200, 523–541 (1950).Google Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • K. R. Rajagopal
    • 1
  • R. K. Bhatnagar
    • 2
  1. 1.Dept. of Mech. EngineeringUniversity of PittsburghPittsburghU.S.A.
  2. 2.Dept. of MathematicsUniversity of PittsburghGreensburgU.S.A.

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