<p>The utility of hybrid nanofluid has gained significant attention for enhancing thermal management systems because of the wide range of applications, i.e. electronic cooling, biomedical devices, etc. The heat transfer efficiency is improved due to the superior thermal conductivity properties of the hybrid nanofluid compared to the traditional fluids. The current study emphasizes the detailed analysis of the local Nusselt number for the free convection of hybrid nanofluid comprised of Al₂O₃ and Cu in the base liquid H₂O subjected to Marangoni convection over a permeable expanding surface. Additionally, several body forces such as the dissipative heat associated with Joule and Darcy, thermal radiation, and heat sources enrich the heat transport phenomenon. The conventional numerical technique, i.e. Runge–Kutta fourth-order shooting is utilized for the solution of the transformed model obtained with the help of similarity rules. The physical behaviour of certain characterizing factors is presented graphically with proper validation in comparison with earlier investigations. In a novel approach, central composite design (CCD) for the response surface methodology (RSM) is employed to analyse and optimize the heat transfer rate statistically. For the varying factors of magnetic parameter, porous parameter and thermal radiation the construction of a predictive model of Nusselt number response is obtained using CCD. The results demonstrate that the inclusion of Marangoni convection and thermal radiation significantly enhances the heat transport properties. Further, dissipative heat impact, i.e. enhanced Eckert number controls the heat transfer rate but thermal radiation favours in enhancing is significantly.</p>