<p>This study presents a comprehensive numerical analysis of hybrid nanofluid (Al₂O₃-Cu/H₂O) flow over an exponentially stretching sheet, incorporating the Cattaneo–Christov heat flux model and radiative heat transfer effects. The results reveal that hybrid nanofluids significantly enhance heat transfer performance. The local Nusselt number increases by up to 28.5% compared to conventional fluids, with the overall heat transfer coefficient (OHTC) rising by 4–47.5% depending on nanoparticle concentration and flow conditions.&#xa0;An increase in the stretching parameter <i>λ</i> and velocity slip parameter <i>A</i> leads to a higher local Nusselt number and skin friction coefficient in the first (stable) solution, while momentum slip reduces skin friction but raises heat transfer. The thermal relaxation time (α) notably thickens the thermal boundary layer and raises fluid temperature, while higher suction (<i>S</i>) enhances both velocity and heat transfer. Multiple solutions are observed for <i>λ</i> exceeding a critical value (<i>λc</i>), with only the first solution being stable. Additionally, increases in the heat generation parameter (<i>Q</i>) and hybridization of nanoparticles further improve temperature profiles and heat transfer efficiency. These findings underscore the superior thermal performance of hybrid nanofluids under the Cattaneo–Christov framework, making them promising for advanced thermal management applications.</p>