Swirling flow of Bingham fluids above a rotating disk: An exact solution

An exact solution is found for swirling flow of Bingham fluids above a rotating disk. The similarity parameter, first introduced by von Karman for Newtonian fluids, is found to be applicable for Bingham fluids effectively reducing the governing PDEs into a set of coupled ODEs. The system of nonlinear ordinary differential equations so obtained is solved numerically. Numerical results are presented addressing the effect of a fluid's yield stress (as represented by the Bingham number) on the velocity profiles, wall shear stress distribution, and volumetric flow rate. Unlike the radial and axial velocity component, the tangential velocity is predicted to increase by an increase in the yield stress. On the other hand, the wall shear stress and the volumetric flow rate are both predicted to decrease when the fluid's yield stress is increased.