Exact solutions for the rotational flow of a generalized Maxwell fluid between two circular cylinders

Unsteady flow of an incompressible generalized Maxwell fluid between two coaxial circular cylinders is studied by means of the Laplace and finite Hankel transforms. The motion of the fluid is produced by the rotation of cylinders around their common axis. The solutions that have been obtained, written in integral and series form in terms of the generalized Ga,b,c(·, t)-functions, are presented as a sum of the Newtonian solutions and the corresponding non-Newtonian contributions. They satisfy all imposed initial and boundary conditions and for λ → 0 reduce to the solutions corresponding to the Newtonian fluids performing the same solution. Furthermore, the corresponding solutions for ordinary Maxwell fluids are also obtained for β = 1. Finally, in order to reveal some relevant physical aspects of the obtained results, the diagrams of the velocity field ω(r, t) have been depicted against r and t for different values of the material and fractional parameters.

Research highlights
► Exact solutions are obtained for the generalized Maxwell fluid flow between two coaxial circular cylinders.
► The motion of the fluid is produced by the rotation of the cylinders around their common axis.
► The solutions are obtained by means of the Laplace and finite Hankel transforms.
► Obtained solutions are presented in integral and series form.
► Graphical illustrations are given to highlight dependence of physical parameters on flow.