Hybrid nanofluids have been regarded as among the supreme and sophisticated nanofluids, just as demonstrated through their heat transfer characteristics as well as emerging advantages which support the determination to accelerate the rate of heat transfer. Discussion of the dual effects of heat generation/absorption in addition to thermal radiation over hybrid nanofluid is the main goal of the current paper. Using water (H2O) as the base fluid, metal (Cu) in addition to metal oxide (Al2O3) nanoparticles are combined. The purpose of heat generation and absorption is to improve the efficiency of the heat transport sensation. The necessary controlling partial differential equations are converted into dimensionless forms of ordinary differential equations using the appropriate similarity modifications. The transformed differential equations are solved using the fourth order Runge-Kutta in addition to shooting technique to find solutions to the problem. For the effect of different shape factors on the solution profiles of momentum, temperature and Nusselt quantity, the numerical results are presented as tabulated data and graphical system. The results revealed that momentum is a decreasing function with Radiation Parameter Rd, Temperature is also a decreasing functions with Eckert number Ec and Radiation Parameter Rd, likewise Nusselt number is also decreasing with Prandtl number Pr and Suction/ injection Parameter S. momentum profile fluctuates in case of Heat generation/ absorption parameter, Suction/ injection Parameter, as well as Radiation and Heat generation/ absorption parameters simultaneously.