In this work, the entropy generation rate in a purely electroosmotic flow of a non-Newtonian fluid in a parallel flat plate microchannel is studied. The power-law model is used for the rheological constitutive equation of the fluid under consideration. The entropy generation rate is obtained as an asymptotic solution to the conjugate heat transfer problem between the fluid and the solid walls of the microchannel. The influence of the following dimensionless parameters on the entropy generation rate is predicted: the flow behavior index, n, the electrokinetic parameter, (kappa) over bar, the well-known Peclet number, Pe, the normalized power generation term, Lambda, the dimensionless temperature difference, Omega, the ratio of the microchannel thickness to the microchannel length, beta, the ratio of the microchannel wall thickness to the microchannel wall length, epsilon, and a conjugate heat transfer parameter, (alpha) over bar, which relates the competition between the conductive heat in the microchannel wall and the conductive heat in the laminar flow. This set of parameters directly determines the thermal performance of the microchannel model. We predict that the entropy generation is dominated by Joule heating. (C) 2013 Elsevier Ltd. All rights reserved.