'Lab-on-a-chip'-based analytic micro-systems commonly handle complex fluids for which standard models of Newtonian fluids are an inadequate representation. Moreover, the different confining boundaries of flow conduits in these devices are often fabricated from different materials which result in different physicochemical characterization of the surfaces. Thus, as a first step towards an advanced modeling paradigm geared towards predictive designing, the present work delineates the transport characteristics of non- Newtonian fluids through nano-scale fluidic confinements, with asymmetric wall zeta- potentials. The non-Newtonian fluids are assumed to follow constitutive relations in the form of power-laws. Under such circumstances, the influences of the underlying electrokinetic phenomenon, as primarily manifested through the induced streaming potential, on the cross-sectional flow velocity, and volumetric flow rate are detailed by adopting a semi-analytical approach. The alterations in the flow dynamics, due to variations in the streaming field induced 'back flow', triggered by increasing strength of wall zeta-potential asymmetry are nicely captured for fluids having different constitutive relations, by considering finite-size effect or steric effect of ions. It is further shown that exclusion of the steric factor from the electrokinetic analysis framework results in erroneous estimation of the involved electrokinetic effect, culminating in aphysical description of the flow characteristics. Moreover, the intrinsic role of the Stern-layer conductivity, as reflected by the Dukhin number, in estimating even more accurate electrokinetic flow characteristics is also highlighted upon. © 2015 Nova Science Publishers, Inc.