Exact Solution for Some Rotational Motions of Fractional Oldroyd-B Fluids Between Circular Cylinders

In this analysis motion of an incompressible fractional Oldroyd-B fluid [IFOBF] in an annulus is studied. The movement in fluid is created by the motion of the both cylinders. At (t = 0(+)), the inner cylinder exerts rotational shear which is time dependent and outer cylinder moves with time depended linear velocity. The analysis of velocity field and shear stress are made with the help of integral transform techniques. For simplicity and better perception, generalized R and G functions are used to represent the obtained results. These solutions are satisfied all the imposed conditions. By imposing favourable limits, general solution is reduced to ordinary Oldroyd-B, Maxwell, second grade and Newtonian fluids for the same motion. From the final expressions of velocity fields and shear stress, we recover the previously obtained results by choosing some limits. Finally, the effect of parameters and their comparison are explained graphically.