Unsteady flow of viscoelastic fluid between two cylinders using fractional Maxwell model

The unsteady flow of an incompressible fractional Maxwell fluid between two infinite coaxial cylinders is studied by means of integral transforms. The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid. The exact solutions for velocity and shear stress are presented in series form in terms of some generalized functions. They can easily be particularized to give similar solutions for Maxwell and Newtonian fluids. Finally, the influence of pertinent parameters on the fluid motion, as well as a comparison between models, is highlighted by graphical illustrations.