Flow past a porous plate of non-Newtonian fluids with implicit shear stress shear rate relationships

One of the simplest problems in the classical Navier–Stokes theory that illustrates the development of boundary layers is the asymptotic suction problem (Schlichting (1960)). This problem has been studied within the context of many different non-Newtonian fluid models and in this note we consider it within the context of a new class of constitutive relations that has been put into place. Depending on the values of the parameters, this class of constitutive relations includes models for both shear thinning and shear thickening fluids, and truly implicit shear stress shear rate relationships. For any set of the material parameters we are able to find exact solutions to the governing equations, study their stability, show that suction has a stabilizing effect, and delineate the development of boundary layers.