The unsteady incompressible viscous flow of a Generalised Maxwell fluid between two coaxial rotating infinite parallel circular disks is studied by using the method of integral transforms. The motion of the fluid is created by the rotation of the upper and lower circular disks with different angular velocities. A fractional calculus approach is utilized to determine the velocity profile in series form in terms of Mittag-Leffler function. The influence of the fractional as well as the material parameters on the velocity field is illustrated graphically.
This paper presents a study of visco-elastic flow of an
incompressible generalized Oldroyd-B fluid between two infinite parallel plates
in which the constitutive equation involves fractional order time derivative.
The solutions of field equations are being obtained for the motion of the said
fluid between two parallel plates where the lower plate starts to move with
steady velocity and the upper plate remains fixed in the first problem and the
upper plate oscillates with constant frequency and the other being at rest in
the second problem. The exact solutions for the velocity field are obtained by
using the Laplace transform and finite Fourier
Sine transform technique in terms of Mittag Leffler and generalised functions.
The analytical expression for the velocity fields are derived and the effect of
fractional parameters upon the velocity field is depicted graphically.