In the paper, a unified treatment by a new technique (known as Stodola-Vianello method) is applied to power law non-Newtonian fluids of the pseudo-plastic type (index N > 1), and the shear-thickening ones (N < 1). Fluid flow is fully developed laminar; physical properties of fluids are temperature-independent. Both parallel channel and round pipe flow are considered. First three eigenvalues are calculated and Nusselt numbers based on bulk temperature are determined. It is seen that shear-thickening fluids approach a fully Newtonian behavior asymptotically as N → 1.0 from below, while pseudo-plastic fluids approach Newtonian flow from above, as N → 1.0. Slug flow results then, formally, when N → ∞ in both flow geometries considered. Simplicity of the method used allowed a coverage of two important geometries and of a large spectrum of physical parameters in a unified fashion, with a very reasonable accuracy.