Iterative calculation of non-Newtonian flows in pipes of annular cross section

The present paper is concerned with the numerical solution of the equation of motion for the axial flow of an incompressible, non-Newtonian fluid in a long cylindrical annulus. It is only supposed that the material law of the fluid is Lipschitzian and monotone. Under these conditions the nonlinear flow problem can be solved numerically by means of a projection-iteration method. The initial value problem as well as the steady-state problem are considered for constant and periodic pressure gradient. Numerical calculations are performed to find the velocity profiles, velocity gradients and volume rates of flow for pseudoplastic fluids of Williamson-type and power law-type.