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The decision to write this monograph on nano uids was courageous but also had its problems. As most of the studies on nanofluids are experimental. Theoretical work on nanofluids is not much. However such studies for experimentalists are of great benefits to compare their data.Therefore,in this work nanofluids are studied inside a vertical channel containing different shapes and sizes of nanopartilces. Five different types of nanoparticles with five different shapes (platelets, blades, cylinders, bricks and spherical) are used in ethylene glycol (EG) chosen as a conventional base fluid. The problem is solved using perturbation method by taking into account three different models namely Maxwell, Hamilton and Crosser, and Koo and Kleinstieur. A comparison of different particles with different shapes is analyzed. Moreover, ethylene glycol (EG) and water are chosen as conventional base fluids.Solutions for velocity and temperature are obtained and discussed graphically in various plots.