<p>A sensitivity-based optimization for heat transfer (HT) in hydromagnetic flow of carbon nanotubes (CNTs) based hybrid nanofluids (HNFs) is conducted. The effects of nonlinear radiation, slip, and catalysis are also considered. The leading PDEs are transmuted into their non-dimensional forms and then tackled numerically. The impacts of the radiation, magnetic field, slip, viscous dissipation, and nanoparticle volume fraction on the flow and thermal dynamics are assessed. To show the reliability of the chosen numerical method, a comparison in a limiting case with available data in the literature is made, and an error estimation of less than 10⁻⁴ is achieved. The sensitivity analysis shows that the magnetic parameter lowers the Nusselt number by over 65%. The HT is raised approximately 48% by the radiation parameter. A moderate positive contribution of 32% is made by the slip parameter, whereas the smaller impacts of 21% and 12% are respectively made by the heat source/sink parameter and volume fraction of single-walled CNT. An elevated temperature within the thermal boundary layer (BL) is predicted by the Hamilton-Crosser (HC) model as compared to the Yamada–Ota (YO) model. From these findings, it is observed that the magnetic damping and radiative transport are of utmost importance for the HT mechanism. Also, the slip and customization of nanoparticles provide other means of controlling the HT. Finally, this research study gives thorough guidance for improving the HNF-based energy and thermal management systems.</p>