Exact analytical solutions for a longitudinal flow of a fractional Maxwell fluid between two coaxial cylinders

Abstract

In this paper the velocity field and the adequate shear stress corresponding to the longitudinal flow of a fractional Maxwell fluid, between two infinite coaxial circular cylinders, are determined by applying the Laplace and finite Hankel transforms. Initially both cylinders are at rest and at time t = 0+ both cylinders begin to translate along their common axis with different constant accelerations. The solutions that have been obtained are presented in terms of generalized G functions. The expressions for the velocity field and the shear stress are in the most simplified form, and the point worth mentioning is that these expressions are free from integral of the generalized G functions, in contrast with [20], in which the expression for the velocity field involves integral of the generalized G functions. Moreover, these solutions satisfy both the governing differential equation and all imposed initial and boundary conditions. The corresponding solutions for ordinary Maxwell and Newtonian fluids are obtained as limiting case of general solutions. Furthermore, the solutions for the motion between the cylinders, when one of them is at rest, can also be obtained from our results.