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Zeitschrift für angewandte Mathematik und Physik

, Volume 60, Issue 5, pp 921–933 | Cite as

The Rayleigh–Stokes problem for an edge in a generalized Oldroyd-B fluid

  • Corina Fetecau
  • Muhammad Jamil
  • Constantin Fetecau
  • Dumitru Vieru
Article

Abstract.

The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids. For β → 1, this last solution reduces to a previous solution obtained by a different technique.

Keywords.

Rayleigh–Stokes problem generalized Oldroyd-B fluid velocity field 

Mathematics Subject Classification (2000).

76A05 

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Copyright information

© Birkhäuser Verlag, Basel 2008

Authors and Affiliations

  • Corina Fetecau
    • 1
  • Muhammad Jamil
    • 2
  • Constantin Fetecau
    • 1
  • Dumitru Vieru
    • 1
  1. 1.Department of Theoretical MechanicsTechnical University of IaşiIaşiRomania
  2. 2.Abdus Salam School of Mathematical SciencesGC UniversityLahorePakistan

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