An emerging concept of hybrid nanofluid with a new improved model of its thermophysical properties are introduced in the present work. Hybrid nanofluid is an advanced type of conventional heat transfer fluids, which has been employed for the enhancement of heat transfer rate. Two distinct fluids, namely hybrid nanofluid $({\rm{Cu - A}}{{\rm{l}}_{\rm{2}}}{{\rm{O}}_{\rm{3}}}{\rm{/water}})$ and nanofluid (Cu/water) are used to investigate the parametric features of the flow and heat transfer phenomena over a permeable stretching sheet in the presence of magnetic field. The effects of various physical parameters and effecting physical quantities of interest are analyzed. From this study it is observed that the heat transfer rate of hybrid nanofluid $({\rm{Cu - A}}{{\rm{l}}_{\rm{2}}}{{\rm{O}}_{\rm{3}}}{\rm{/water}})$ is higher than that of Nanofluid (Cu/water) under magnetic field environment. More combinations of different nanocomposites can be tried so that the desired heat transfer rate can be achieved.