  We use a generic and general numerical method to obtain solutions for the
flow of generalized Newtonian fluids through circular pipes and plane slits.
The method, which is simple and robust can produce highly accurate solutions
which virtually match any analytical solutions. The method is based on
employing the stress, as a function of the pipe radius or slit thickness
dimension, combined with the rate of strain function as represented by the
fluid rheological constitutive relation that correlates the rate of strain to
stress. Nine types of generalized Newtonian fluids are tested in this
investigation and the solutions obtained from the generic method are compared
to the analytical solutions which are obtained from the
Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was
obtained in all the investigated cases. All the required quantities of the flow
which include local viscosity, rate of strain, flow velocity profile and
volumetric flow rate, as well as shear stress, can be obtained from the generic
method. This is an advantage as compared to some traditional methods which only
produce some of these quantities. The method is also superior to the numerical
meshing techniques which may be used for resolving the flow in these systems.
The method is particularly useful when analytical solutions are not available
or when the available analytical solutions do not yield all the flow
parameters.
