Unsteady Helical Flow of a Generalized Oldroyd-B Fluid with Fractional Derivative

  IJMTT-book-cover
 
International Journal of Mathematical Trends and Technology (IJMTT)          
 
© 2014 by IJMTT Journal
Volume-5                          
Year of Publication : 2014
Authors : Yaqing Liu , Fenglei Zong , Jinbin Dai
  10.14445/22315373/IJMTT-V5P524

citation

Yaqing Liu , Fenglei Zong , Jinbin Dai Article:Unsteady Helical Flow of a Generalized Oldroyd-B Fluid with Fractional Derivative,International Journal of Mathematical Trends and Technology (IJMTT),V5:67-77: January 2014. Published by Seventh Sense Research Group.

Abstract
This paper considered some unsteady helical flows of a generalized Oldroyd-B fluid between two infinite concentrice cylinders and an infinite circular cylinder. The flow is due to the cylinders oscillate around their common axis and accelerating slide in the direction of the same axis with prescribed velocities. Exact solutions of some unsteady helical flows are obtained by using Laplace transform coupled with Hankel transform for fractional calculus. The corresponding solutions for generalized second grade fluid, Maxwell fluid, ordinary Oldroyd-B fluid or Newtonian fluid are obtained as limiting cases of general solutions. Finally, the influence of the fractional parameters and on the fluid motion is underlined by graphical illustrations.

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Keywords
Helical fluid, Oldroyd-B fluid, Laplace transform, Hankel transform.