Exact solutions for the longitudinal flow of a generalized Maxwell fluid in a circular cylinder

Abstract

This paper deals with the longitudinal flow of a generalized Maxwell fluid in an infinite circular cylinder, due to the longitudinal variable time-dependent shear stress that is prescribed on the boundary of the cylinder. The fractional calculus approach in the constitutive relationship model of a Maxwell fluid is introduced. The velocity field and the resulting shear stress are obtained by means of the Laplace and finite Hankel transforms and satisfy all the imposed initial and boundary conditions. The solutions corresponding to ordinary Maxwell fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. Finally, the influence of the fractional coefficient on the velocity and shear stress of the fluid is analyzed by graphical illustrations.