Study on the helicoidal flow through cylindrical annuli with prescribed shear stresses

Abstract

In this article, we presented an analysis of the helical flow, for evaluating the incompressible Maxwell fluid indwelling between the two circular regions created by infinitely long concentric circular cylinders. Time-depended longitudinal and torsional shear stresses are implemented around the periphery of the inner circular cylinder to set the fluid in motion, while keeping the outer one inert. Exact analytic solution of the mathematical model in form of partial differential equations(PDE) is obained by performing the integral transform. We also retrieved the analogous solution of fluid, encompassing same properties as of Newtonian fluid in form of our general solutions. To end up with, we presented different graphs, showing the sway of appropriate parameters affecting the shear stresses and velocity components. In addition, we also presented graphs for comparison of Newtonian and Maxwell fluids. To end up with, the significance of appropriate parameters on the components of shear stresses and velocities, as well as motion for Newtonian and Maxwell fluids are analyzed and discussed via graphs.