Hybrid nanofluids outperform mono nanofluids in terms of heat transmission. They can be found in heat exchangers, the automobile industry, transformer cooling, and electronic cooling, in addition to solar collectors and military equipment. The primary goal of this study is to scrutinize the magnetohydrodynamic hybrids nanofluid (Copper-oxides and Titanium dioxide/water) [Formula: see text] and [Formula: see text] nanofluid flow in two parallel plates using walls suction/injection under the influence of a magnetic field and thermal radiation. Implementing the appropriate transformation, the governing partial differential equations are converted into equivalent ordinary differential equations. In MATLAB software, the built-in numerical technique bvp4c is used to evaluate the final system to generate the graphical results against velocity and temperature gradient for various parameters. The increasing evaluation of Reynolds number and magnetic parameter influenced velocity concentration. The response surface method is used to generate the sensitivity and contour graphs and tables. Skin friction and the Nusselt number have an outcome on flow characteristics as well. This type of research is critical in the coolant process, aviation engineering, and industrial cleaning processes, among other fields. In several cases, comparing current and historical findings reveals good agreement.