AXIAL-COUETTE FLOW OF AN OLDROYD-B FLUID IN AN ANNULUS DUE TO A TIME-DEPENDENT SHEAR STRESS

Abstract

The velocity and the shear stress, corresponding to the unsteady flow of an Oldroyd-B fluid between two infinite circular cylinders, are established using the finite Hankel transform. The motion is produced by the inner cylinder, which after time is pulled with a time-dependent shear stress along its axis. The solutions for Maxwell, Second grade and Newtonian fluids, performing the same motion, are obtained as limiting cases of general solutions. Finally, the influence of the material parameters on the fluid motion is underlined by graphical illustrations.