Numerical modeling of electro-osmotic flow in heterogeneous micro-channels using two different models is presented in this article. For the through modeling of such flows, the coupled equations of Navier-Stokes, Nernst-Planck and the Poisson-Boltzmann are solved for the flow field, electric charges transport and electric field, respectively. Numerical solution of these equations for the heterogeneous micro-channels is complicated and difficult. Therefore, simple and approximate models such as Helmholtz-Smoluchowski have been proposed in which the solution of Poisson-Boltzmann, Nernst-Planck are neglected and the effect of the electric field on the flow field is applied through a prescribed slip boundary condition at the walls of micro-channel. The electro-osmotic flow fields within the heterogeneous micro-channels are usually complex and contain the vortex region that is ideal for mixing purpose. Hence, in this paper, the micro-channels designed so that they are capable to serve as micro-mixers in the mixing applications. For the micro-channels proposed here, the flow fields are obtained both with approximate modeling and the full simulation of electro-osmotic flows so that a comparison can be made to discuss the accuracy of the approximate model. The results of this study can be used to model the electro-osmotic flow field within heterogeneous micro-channels.