In this book, a numerical investigation has been carried out to discuss the steady, two-dimensional flow and heat transfer on micropolar nanofluid over a stretching/shrinking sheet with variable suction or injection in the presence of magnetic field and Newtonian heating. Copper (Cu), alumina (Al2O3) and titanium (TiO2) in water ¿ based micropolar nanofluid has been considered for the present investigation. The solutions of the transformed nonlinear equations have been obtained by using Runge-Kutta-Gill procedure together with the shooting method. The results are presented graphically and discussed for various resulting parameters. Dual solutions are found to exist in a certain range of the governing parameters. The thickness of thermal boundary layer for Cu nanofluid is the more than that of other nanofluids in the cases of shrinking and stretching sheets. Newtonian heating effect significantly increases the thermal boundary layer thickness for both sheets under investigation.