Unsteady helical flows of a generalized Oldroyd-B fluid

Helical flows for Oldroyd-B fluid are studied in concentric cylinders and a circular cylinder. The fractional calculus approach in the constitutive relationship model Oldroyd-B fluid is introduced and a generalized Jeffreys model with the fractional calculus has been built. Exact solutions of some unsteady helical flows of Oldroyd-B fluid in an annular pipe are obtained by using Hankel transform and Laplace transform for fractional calculus. For α=β=1α=β=1, λ1=0λ1=0, λ2=0λ2=0 or λ1=λ2=0λ1=λ2=0 they reduce to the similar solutions for a Maxwell fluid, a second grade or Newtonian fluid, respectively. Numerical results for helical flow in pipe are presented.