Entropy optimization of magnetohydrodynamic Casson hybrid nanofluid flow over a rotating disk with Cattaneo Christov heat flux.

This study investigates unsteady rotating-disk transport of a water-based Casson nanofluid (Cu/H[Formula: see text]O) and a Casson hybrid nanofluid (Cu+Fe[Formula: see text]O[Formula: see text])/H[Formula: see text]O in a porous medium under magnetic forcing, suction, heat source/sink, and thermal radiation, while accounting for thermal relaxation to model non-Fourier heat conduction. Using similarity transformations, the governing multi-physics equations are reduced to a coupled nonlinear system for the radial and tangential velocities and temperature. To obtain reproducible semi-analytical benchmark solutions, the Homotopy Analysis Method (HAM) is employed with convergence-control parameters selected via [Formula: see text]-curves and residual-error minimization. A central contribution is a controlled comparison between Cu/H[Formula: see text]O and (Cu+Fe[Formula: see text]O[Formula: see text])/H[Formula: see text]O under identical parameter sets, focusing on velocity and temperature characteristics. The results show that Cu/H[Formula: see text]O yields higher velocity levels, whereas the hybrid nanofluid sustains higher temperatures within the thermal boundary layer, revealing a thermal-hydraulic trade-off for aqueous rotating systems. The magnetic parameter M physically quantifies Lorentz-force damping, leading to reduced velocities and modified thermal fields, while the thermal relaxation parameter [Formula: see text] delays the heat-flux response and tends to suppress temperature diffusion, thereby lowering the temperature profile. For the hybrid nanofluid, the skin-friction and Nusselt-number trends obtained from the plots are in good agreement with the tabulated values, confirming the consistency of the solution. Physically, increasing M enhances the skin-friction coefficient because stronger Lorentz braking demands greater wall shear to maintain the flow, while increasing Nr elevates the Nusselt number by strengthening radiative heat transport and steepening the wall temperature gradient. In addition, the thermodynamic irreversibility of the system is characterized through entropy generation and the Bejan number. Physically, increasing Br intensifies entropy generation because stronger viscous dissipation converts more mechanical energy into irreversible thermal energy, whereas increasing [Formula: see text] increases the Bejan number by making thermal irreversibility more dominant relative to frictional irreversibility under stronger non-Fourier heat-flux effects. The findings are relevant to rotating-disk cooling, porous heat-exchanger components, and nano-assisted aqueous lubrication/thermal management in compact and micro-scale rotating devices.