Exact Solutions for an Unsteady Flow of Viscoelastic Fluid in Cylindrical Domains Using the Fractional Maxwell Model

Abstract

This paper deals with the unsteady flow of an incompressible fractional Maxwell fluid filled in the annular region between two infinite coaxial circular cylinders. The motion of the fluid is due to the inner cylinder that applies a time dependent torsional shear to the fluid and outer cylinder which is moving at a constant velocity. The velocity field and shear stress are determined by the Laplace and finite Hankel transforms. The obtained solutions are presented in terms of the generalized G and R functions. Solutions for Ordinary Maxwell fluid and Newtonian fluid are also obtained by imposing appropriate limits. Finally, the influence of different values of parameters, constants and fractional coefficient, as well as a comparison between the velocity field and shear stress are also analyzed using graphical illustration.