Some Exact Solutions for Helical Flows of Maxwell Fluid in an Annular Pipe due to Accelerated Shear Stresses

Abstract

Some exact solutions corresponding to helical flows of Maxwell fluid between two infinite coaxial circular cylinders are determined by means of finite Hankel transform, presented in series form, satisfied all imposed initial and boundary conditions. The motion is produced by the inner cylinder that applies the torsional and longitudinal time-dependent accelerated shear stresses to the fluid. The corresponding solutions for Newtonian fluid and large-time solutions are also obtained as limiting cases and effect of material parameters on the large-time solutions are discussed. Finally, the influence of pertinent parameters as well as a comparison between Maxwell and Newtonian fluids on the velocity components and shear stresses profiles is also examined by graphical illustrations.