In this paper, a mathematical model has been developed to analyze the combined electroosmotic and pressure driven flow of power law fluids in a micro channel in the presence of Joule heating effects. The effects of Navier slip boundary condition and thermal radiation is examined for effective heat transfer in a hydrophobic microchannel. The analytical treatment has been performed for fluid flow and heat transfer effects in terms of flow governing parameters. This study highlights the effect of channel height to the electric double layer thickness and observed the flow variation due to heat transfer effect with the available scientific data. For a pure EOF, velocity slip have more significant role to get a maximum flow rate as expected. For both pseudo-plastic and dilatent fluids Nusselt number is decreased with the increment of the hydrophobic parameter and dimensionless pressure gradient where as increment in Joule heating effect enhance the heat transfer rate.

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