Analytical Solution of Transient Flow of Fractional Oldroyd-B Fluid between Oscillating Cylinders

Abstract

This paper investigates the fractional Oldroyd-B fluid flow across two interminable coaxial cylinders, where the fluid’s motion is generated by the oscillatory movement of cylinders and the oscillating pressure gradient. The profile of velocity and shear stress of the flow is derived with the assistance of Caputo fractional derivative utilizing an analytical technique, finite Hankel transform and Laplace transforms. The semi-analytical solution is then displayed as generalized functions of G and R satisfying fundamental constitutive equations and all initial and boundary conditions. To validate the results, some limitations have been imposed on the determined equations and the results have been contrasted against previous results. Moreover, the influence of various parameters on the flow of fractionalized Oldroyd-B fluid is investigated and depicted graphically.