Unsteady flow of a maxwell fluid with fractional derivatives in a circular cylinder moving with a nonlinear velocity

Abstract

In this paper we determine the velocity field and the shear stress corresponding to the unsteady flow of a Maxwell fluid with fractional derivatives driven by an infinite circular cylinder that slides along its axes with a velocity Ata. The general solutions, obtained by means of integral transforms, satisfy all imposed initial and boundary conditions. They can be easily particularized to give the similar solutions for ordinary Maxwell and Newtonian fluids. Finally, the influence of the parameters a and on the fluid motion as well as a comparison between models is underlined by graphical illustrations.

Keywords: Maxwell fluid with fractional derivatives, velocity field, shear stress, exact solutions

Quaestiones Mathematicae 37(2014), 139–156