Flow of Fractional Maxwell Fluid in Oscillating Pipe-Like Domains

Abstract

This paper presents an analysis for oscillating flows of fractional Maxwell fluid in the annular region between two infinite concentric circular cylinders. The fluid motion is created as both cylinders begin to oscillate around their common axis. The exact solutions are established using the sequential fractional derivatives Laplace transform and finite Hankel transform in terms of generalized G and R functions. Also, we obtain the solutions for ordinary Maxwell fluid and Newtonian fluid as special cases of the generalized solutions. Moreover, the effects of various parameters on the velocity field and shear stress are analyzed by graphical illustration. Finally, a comparison is drawn between motions of fractional Maxwell fluid, ordinary Maxwell fluid and Newtonian fluid.