Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 60, Issue 5, Pages 921-933Publisher
SPRINGER BASEL AG
DOI: 10.1007/s00033-008-8055-5
Keywords
Rayleigh-Stokes problem; generalized Oldroyd-B fluid; velocity field
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Funding
- Ministry of Education and Research, CNCSIS, through PN II-Ideas [26/28-09-2007, Cod CNCSIS ID_593]
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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 beta -> 1, this last solution reduces to a previous solution obtained by a different technique.
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