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In this paper, a three-dimensional numerical model is developed to analyze flow characteristics of pressure driven, electroosmotic and combined pressure driven-electroosmotic flows through micro-channels. The governing system of equations consists of the electric-field and flow-field equations. The solution procedure involves three steps. The net charge distribution on the cross section of the micro-channel is computed by solving two-dimensional Poisson-Boltzmann equation using the finite element method. Then, using the computed fluid’s charge distribution, the magnitude of the resulting body force due to interaction of an external electric field with the charged fluid is calculated along the micro-channel. Finally, three dimensional Navier-Stokes equations are solved by considering the presence of the electro-kinetic body forces in the flow system for electroosmotic and combined pressure driven electroosmotic flow cases. The results reveal that the flow patterns for combined PD-EO cases are significantly different from the parabolic velocity profile of the laminar pressure-driven flow. The effect of the liquid bulk ionic concentration and the external electric field strength on flow patterns through the square-shaped micro-channels is also investigated over a wide range of external electric field strengths and bulk ionic concentration.