The impulse back the sitting treatise is to study the properties of magnetohydrodynamic flow and heat transfer for Casson-Carreau hybrid nanofluid under the effects of heat sink/source, magnetic field, thermal radiation and slip conditions in a Darcy-Forchheimer porous medium with injection/suction effect. The examined hybrid nanofluid includes rheological action of non-Newtonian and pursues fluid paradigm of Casson-Carreau considering water as a base fluid, whereas Aluminium oxide and Copper as a hybrid nanoparticles. In this model, the formularization of the Casson-Carreau hybrid nanofluid has been used for expressing boundary layer problem. The obtained differential equations are switched by using non-similar transformations and then solved numerically. Some of the outcomes of the examination in both Casson-Carreau models influence the upsurging transfer of heat by thermal radiation and blowing/suction parameters. Moreover, skin friction coefficient display identical behaviour for thermal radiation, but the opposite behaviour is noticed in the state of the suction/injection parameter.