This study explores the effects of a first-order slip boundary condition on the magnetohydrodynamic flow and heat transfer in a Casson-based hybrid nanofluid containing copper oxide (CuO) and graphite oxide (GO) nanoparticles in methanol \((\text {CH}_3{\text {OH}})\) . To address the critical need in advanced cooling and thermal management, the research delves into the complexities of thermal radiation, viscous dissipation, and Joule heating. To ensure comprehensive validation and robustness of the findings, we employed both the bvp4c and Keller–Box numerical methods, each chosen for its strengths in different aspects of the model problem. This dual-method approach, detailed in our comparative analysis section, enhances the scientific rigor of our results. Using an effective similarity transformation, complex governing equations are transformed into a manageable set of ordinary differential equations, which are then numerically solved. Our findings reveal that hybrid nanofluids offer enhanced thermal properties and flow adjustability compared to single-nanoparticle fluids, with significant impacts of radiation and magnetic field on the thermal boundary layer. These insights not only advance theoretical knowledge but also have substantial practical applications in fields such as medical sciences, opto- electronics, and energy systems, establishing a new benchmark in fluid dynamics and materials science for thermal management technologies.
