A novel formulation is presented applicable to flows of inelastic, shear-thinning and shear-thickening fluids between parallel plates. The solution is documented by comphrensive contour maps allowing flow: descriptions to be reconstructed for the Ostwald-deWaele and the Cross/Carreaau fluid model fluids within an exhaustive range of rheological and flow parameters, 0 < n less than or equal to 2 and 0 less than or equal to q less than or equal to 2. The description of pseudoplastic behavior is extended to values approaching zero, numerical stability permitting (0.01 less than or equal to n < I). The paper highlights the dilatant behavior; 1 less than or equal to n less than or equal to 2, reported previously to arise in certain heterogeneous systems, and shown to affect significantly other types of non-Newtonian flows. Ir is suggested that in thermally and compositionally developing flows, typical of reactive processing, where dilatancy may arise, the present formulation can facilitate solutions to the coupled rheological and heat/mass transfer problems encountered The newly generated data on dilarant liquids suggest a dramatic increase in energy dissipation with the increasing degree of dilatancy.