Helical flows of second grade fluid due to constantly accelerated shear stresses

The helical flows of second grade fluid between two infinite coaxial circular cylinders is considered The motion is produced by the inner cylinder that at the initial moment applies torsional and longitudinal constantly accelerated shear stresses to the fluid The exact ana lytic solutions obtained by employing the Laplace and finite Hankel transforms and pre sented in series form in term of usual Bessel functions of first and second kind satisfy both the governing equations and all imposed initial and boundary conditions In the limiting case when alpha -> 0 the solutions for Newtonian fluid are obtained for the same motion The large-time solutions and transient solutions for second grade fluid are also obtained and effect of material parameter a and kinematic viscosity v is discussed In the last the effects of various parameters of Interest on fluid motion as well as the comparison between second grade and Newtonian fluids are analyzed by graphical illustrations (C) 2010 Elsevier B V All rights reserved