Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

Unsteady flow of fractional Oldroyd-B fluids through rotating annulus AbstractIn this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Physics de Gruyter

Unsteady flow of fractional Oldroyd-B fluids through rotating annulus

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Publisher
De Gruyter Open
Copyright
© 2018 Madeeha Tahir et al.
ISSN
2391-5471
eISSN
2391-5471
D.O.I.
10.1515/phys-2018-0028
Publisher site
See Article on Publisher Site

Abstract

AbstractIn this paper exact solutions corresponding to the rotational flow of a fractional Oldroyd-B fluid, in an annulus, are determined by applying integral transforms. The fluid starts moving after t = 0+ when pipes start rotating about their axis. The final solutions are presented in the form of usual Bessel and hypergeometric functions, true for initial and boundary conditions. The limiting cases for the solutions for ordinary Oldroyd-B, fractional Maxwell and Maxwell and Newtonian fluids are obtained. Moreover, the solution is obtained for the fluid when one pipe is rotating and the other one is at rest. At the end of this paper some characteristics of fluid motion, the effect of the physical parameters on the flow and a correlation between different fluid models are discussed. Finally, graphical representations confirm the above affirmation.

Journal

Open Physicsde Gruyter

Published: Apr 18, 2018

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