Unsteady rotating shear flow of power law fluids

Abstract

We have investigated unsteady circular Couette flow for non-Newtonian fluids of power law behavior. We considered two specific problems: 1. A solid cylinder rotating in a power law fluid of infinite extent and 2. A power law fluid filling the gap between two concentric rotating cylinders. Due to the nonlinearity of non-Newtonian constitutive equations, velocity disturbances from a rotating cylinder propagate through the the fluid with finite speed. The existence of this moving velocity disturbance front was observed in the analytic similarity solutions and numerical solutions. For the problem with one cylinder two numerical methods were used to determine the velocity and shear stress distributions: 1. The Method of Lines combined with the Shooting Method, and 2. A front fixing transformation was employed and the resulting problem solved via various implicit (including Crank-Nicolson) finite diference schemes. For the two cylinder problem the velocity distribution was obtained via the Method of Lines together with a variable step-size finite difference method. For both problems the temperature distribution was obtained numerically via an implicit finite difference method. The interaction effect between the angular velocity and the thermal field was addressed.