Influence of non-integer-order derivatives on unsteady unidirectional motions of an Oldroyd-B fluid with generalized boundary conditions

  • A. A. Zafar
  • M. B. Riaz
  • N. A. Shah
  • M. A. Imran
Regular Article
  • 17 Downloads
Part of the following topical collections:
  1. Focus Point on Modelling Complex Real-World Problems with Fractal and New Trends of Fractional Differentiation

Abstract.

The objective of this article is to study some unsteady Couette flows of an Oldroyd-B fluid with non-integer derivatives. The fluid fills an annular region of two infinite co-axial circular cylinders. Flows are due to the motion of the outer cylinder, that rotates about its axis with an arbitrary time-dependent velocity while the inner cylinder is held fixed. Closed form solutions of dimensionless velocity field and tangential tension are obtained by means of the finite Hankel transform and the theory of Laplace transform for fractional calculus. Several results in the literature including the rotational flows through an infinite cylinder can be obtained as limiting cases of our general solutions. Finally, the control of the fractional framework on the dynamics of fluid is analyzed by numerical simulations and graphical illustrations.

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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • A. A. Zafar
    • 1
  • M. B. Riaz
    • 2
  • N. A. Shah
    • 3
  • M. A. Imran
    • 2
  1. 1.Department of MathematicsGC UniversityLahorePakistan
  2. 2.Department of MathematicsUniversity of Management and TechnologyLahorePakistan
  3. 3.Abdus Salam School of Mathematical SciencesGC UniversityLahorePakistan

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