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Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model

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Abstract

The flow near a wall suddenly set in motion for a viscoelastic fluid with the generalized Oldroyd-B model is studied. The fractional calculus approach is used in the constitutive relationship of fluid model. Exact analytical solutions of velocity and stress are obtained by using the discrete Laplace transform of the sequential fractional derivative and the Fox H-function. The obtained results indicate that some well known solutions for the Newtonian fluid, the generalized second grade fluid as well as the ordinary Oldroyd-B fluid, as limiting cases, are included in our solutions.

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Authors and Affiliations

  1. Department of Applied Mathematics and Statistics, Shandong University at Weihai, Weihai, 264209, China

    Haitao Qi

  2. School of Mathematics and System Science, Shandong University, Jinan, 250100, China

    Mingyu Xu

Authors
  1. Haitao Qi
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  2. Mingyu Xu
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Correspondence to Haitao Qi.

Additional information

The project supported by the National Natural Science Foundation of China (10272067), the Doctoral Program Foundation of the Education Ministry of China (20030422046), the Natural Science Foundation of Shandong Province, China (Y2006A14) and the Research Foundation of Shandong University at Weihai.

The English text was polished by Keren Wang.

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Qi, H., Xu, M. Stokes’ first problem for a viscoelastic fluid with the generalized Oldroyd-B model. Acta Mech Sin 23, 463–469 (2007). https://doi.org/10.1007/s10409-007-0093-2

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  • DOI: https://doi.org/10.1007/s10409-007-0093-2

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