A pressure driven electroosmotic flow (EOF) is numerically studied in a slit micro-channel with alternating hydrodynamic slip patches. The coupled Poisson-Boltzman-Navier Stokes equations dealt with external electric potential are solved for the flow enhancement of non-Newtonian fluids in microfluidic domain, which is a big challenge in the transportation and mixing of fluids in BioMEMS devices as the drag effect is very strong along the walls. This effect can be minimized with the use of slip boundary conditions by the coupling effects of liquid-liquid or gas-liquid interface positioning. In the present article, the fluid is considered to be a power-law fluids which is driven due to the coupling effects of two superimposed electric fields: the externally imposed electric field and the induced potential. An additional pressure gradient is created by the electrokinetic pumping to generate a higher velocity gradient in the presence of viscous dissipation and Joule heating effects. The analytical quantification of the electroosmotic flow velocity and temperature distribution is made and compared with the numerical results due to the staggered grid based finite volume method. The results are presented in terms of flow enhancement factor (Ef) (provides maximum species transport) and the average entropy generation due to fluid friction, viscous dissipation and Joule heating effect. The advantages and disadvantages of utilizing slip conditions are discussed which has large scale applications on drug delivery, DNA analysis and sequencing and especially biomedical applications, since cell damage due to pumping will be minimized compared to the micro pumps with moving valves, blades and pistons.