Some exact solutions for the rotational flow of a generalized second grade fluid between two circular cylinders

TL;DR

This paper derives exact solutions for the rotational flow of a generalized second grade fluid between two cylinders, analyzing the effects of fractional coefficients and comparing with Newtonian and second grade fluids.

Contribution

It provides new analytical solutions for the flow of a generalized second grade fluid between cylinders, including effects of fractional derivatives and initial conditions.

Findings

Solutions satisfy all governing equations and conditions.

Fractional coefficient significantly influences fluid velocity.

Results include special cases for Newtonian and second grade fluids.

Abstract

The velocity field and the associated tangential stress corresponding to flow of a generalized second grade fluid between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. At time $t=0$ the fluid is at rest and at $t=0^+$ cylinders suddenly begin to rotate about their common axis with a constant angular acceleration. The solutions that have been obtained satisfy the governing differential equations and all imposed initial and boundary conditions. The similar solutions for a second grade fluid and Newtonian fluid are recovered from our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.