Exact solutions of starting flows for a fractional Burgers’ fluid between coaxial cylinders

Abstract

This paper deals with the unsteady flows of a viscoelastic fluid between two infinitely long concentric circular cylinders. The fractional calculus approach in the constitutive relationship model of a Burgers’ fluid is introduced. With the help of integral transforms (the Laplace transform and the Weber transform), exact solutions are constructed for the following two problems: (i) when the outer cylinder makes a simple harmonic oscillation; and (ii) when the outer cylinder suddenly begins rotating while the inner cylinder remains stationary. Some previous and classical results can be recovered from the presented results, such as starting solutions for second grade, Maxwell, Oldroyd-B, and Burgers’ fluids.