Exploring multi-physical behaviours in unsteady Casson hybrid nanofluid flow across a semi-infinite moving flat surface

• The magnetic fields give rise to an electromagnetic drag that suppresses the motion of the fluid, while hybrid nanofluids display superior thermal performance in relation to mono nanofluids. • The volume fractions of GO significantly enhance thermal conductivity and convective heat removal rates. • The in-depth parametric study incorporating the combination of the inclusion of the porous media, the slip conditions, the temperature radiation, and the action of thermophoresis provides essential information useful in hybrid nanofluid formulation optimisation. • The verification based on available literature confirms the justification of the numerical technique. These findings contribute towards the development of thermal management systems in electronics cooling, in biomedical therapy, as well as in practices in the industry where superior convective heat removal performance is needed. • The innovation is based on the simultaneous evaluation of various physical actions for non-Newtonian hybrid nanofluids, providing bases for future references in superior nanofluid applications. This work analyses the unsteady MHD flow with heat and mass transfer of a Casson-type hybrid nanofluid (GO-TiO 2 /SCMC) over a semi-infinite moving plate, considering porosity, electromagnetic drag, velocity and thermal slip, thermal radiation, Joule heating, Brownian diffusion and thermophoresis. The focus is to investigate the multi-physical effects on transport phenomena and to make a comparison between the hybrid nanofluid and its mono counterpart. The similarity transformations reduce the governing equations into nonlinear ODEs, which are solved using the BVP4C algorithm. The magnetic parameter ( 0 ≤ M ≤ 1.5 ) introduces Lorentz-induced resistance, which reduces skin friction and suppresses the Nusselt number. The rise in porosity ( 0.2 ≤ K 1 ≤ 1.5 ) decreases the fluid velocity and thickens the thermal boundary layer. Accordingly, hybrid nanofluid heat-transfer performance exhibits improvement compared with the mono nanofluid. Thermal radiation 0.1 ≤ R d ≤ 0.5 enhances the temperature level and, thus, weakens heat-transfer rates, while the presence of Joule heating adds internal energy and further reduces thermal efficiency. The accretion parameter π / 6 ≤ α ≤ π / 2 augments convection and increases the rate of heat and mass transport. These results guarantee, in principle, the feasibility of GO-TiO 2 /SCMC hybrid nanofluids in advanced cooling, heat-exchange and biomedical systems.