Unsteady Rotational Flow of a Second Grade Fluid with Non-Integer Caputo Time Fractional Derivative

Abstract

This article presents some starting solutions corresponding to unsteady rotational flow of a second grade fluid with the non-integer Caputo time fractional derivatives through an infinite long cylinder. The fluid in the infinitely long cylinder is initially at rest and at t = 0+, the fluid starts to rotate due to applied shear stress. By using modified Bessel equation and Laplace transformation, solutions for velocity field and shear stress are obtained. The solutions are presented in transformed domain in terms of modified Bessel functions I0(·) and I1(·) and satisfy all imposed initial and boundary conditions. In this paper, inverse Laplace transformation has been calculated numerically by using Stehfest’s algorithm. The hybrid technique presented in this paper has less computational effort and time cost as compared to other schemes in literature. Finally, the behavior of different parameters is graphically examined.