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In the presented article I developed a formulation and mathematical model of elektrokinetic fluid motion and nanofluid motion and temperature distribution in rectangular and circular microchannels. I have developed the formulations for pressure driven flow, flow under electromagnetic forces with slip conditions. The transport properties for nanofluids I have calculated on the basis of statistical mechanics. Friction, thermal and electromagnetic irreversibilities have significance in energy efficiency of microfluid systems. The results indicate that influence of volume fraction of nanoparticles have the big influence on velocity and sensitive influence on temperature distribution in microchannels.