Hybrid nanofluids (HNFs) are a promising type of nanofluid (NF) that combines two different nanoparticles to enhance their thermal and mechanical properties. They have gained significant attention in various engineering and scientific applications. This research focuses on studying the temperature‐dependent viscosity of a magnetohydrodynamic copper‐alumina‐water‐based HNF with thermal radiation, diffusions, and chemical reaction on a stretching sheet embedded in a porous medium. To achieve this, we transform the partial differential equations (PDEs) governing the system into a system of nonlinear ordinary differential equations (ODEs) using systematic similarity transformations. The resulting ODEs are solved using the shooting mechanism in combination with the Runge–Kutta–Fehlberg methodology. The results for the impact of the nanoparticle reactions on thermal, concentration, and velocity profiles, surface drag force, as well as mass and heat transfer rates are presented through graphs and tables. The key findings of this study demonstrate that the HNF accelerates velocity by 6.62%, but the magnetic field weakens it by 9.26%. Chemical reaction and Schmidt number affect nanoparticle concentration inversely. Radiation and heat source parameters increase the temperature by 14.89%, but the Prandtl number decreases it by 2.2%. Moreover, the Cu‐Al2O3/H2O HNF exhibits better thermal efficiency by 17.75% compared with the copper‐water NF. This research holds potential for applications in heat transduction, energy production, biomedical research, the manufacturing sector, aerospace technology, and more.