<p>This study explores the unconventional yet impactful flow of Reiner–Rivlin nanofluid flow over an upper horizontal paraboloid of revolution (UHSPR). This geometry finds applications in aerodynamic designs like car bonnets and aircraft noses. The said nanofluid flow is generated at the free stream owing to interlayer stretching surfaces and the surface's chemical reaction. The novelty of the anticipated model is enhanced, considering the effects of magnetohydrodynamics, viscous dissipation, temperature-dependent thermal conductivity, and activation energy. Through numerical and graphical analysis, we reveal how chemical reactions, thermal radiation, and free stream stretching interact with the fluid’s non-Newtonian behavior, offering insights for high-performance cooling and propulsion systems. Governing partial differential equations are nondimensionalized via appropriate similarity transformations, and the resulting boundary value problem is solved numerically using the bvp4c algorithm implemented in MATLAB. To analyze the effects of key parameters, graphical representations of temperature, velocity, and concentration fields are provided. The variations in Nusselt number, skin friction, and Sherwood number are summarized in tabular form. The results show that velocity increases with higher Reiner–Rivlin parameter values, which physically correspond to a decrease in viscous resistance. The augmentation in the activation energy parameter initially decreases temperature profiles, but as chemical reactions intensify, nanoparticle motion increases, leading to an escalation in temperature. Conversely, the heat of reaction parameter causes an elevation in temperature due to the exothermic reaction of the surface. Additionally, the mass transfer rate reduces as the reaction rate coefficient increases. The validation of the model is a part of this exploration.</p>