ANALYTIC AND SEMI ANALYTIC SOLUTION FOR MOTION OF FRACTIONAL SECOND GRADE FLUID IN A CIRCULAR CYLINDER

Unsteady flow of fractional second grade fluid subject to a time dependent shear stress through a circular cylinder is considered. The motion is produced by the boundary of the cylinder which is subject to the longitudinal time dependent shear stress. The governing equation corresponding to second grade fluid given by a new definition of fractional derivatives without singular kernel is used, given by Caputo and Fabrizio. The flow is studied analytically by using finite Hankel and Laplace transforms. The corresponding solutions for ordinary second grade and Newtonian fluids are obtained as limiting cases of our general solutions, where as Stehfest's algorithm is used to developed the numerical solution of our problem. The numerically obtained solutions are in terms of the modified Bessel's equations of first and second kind, satisfying all imposed conditions. A good comparison between existing analytical solution and our solutions are made. Finally, the effect of different parameters and their comparison are explained graphically.