Entropy Optimization and Transport Analysis of Ag–Al ₂ O ₃ /Water Hybrid Nanofluid Flow Over a Rotating Porous Disk in the Presence of Hall Current

The transport behavior of hybrid nanofluids over rotating porous disks is important for improving thermal management and mass-transfer performance in advanced engineering systems. This study aims to investigate the effects of Hall current, exponential heat source, chemical reaction, and other governing parameters on the flow, heat, mass transfer, and entropy generation characteristics of Ag–Al ₂ O ₃ /H ₂ O hybrid nanofluid over a rotating porous disk. The governing partial differential equations are transformed into a system of ordinary differential equations using scaling group transformations and then solved numerically by the Cash–Carp method. The results show that the radial velocity increases with increasing magnetic, Casson, and Hall parameters, while temperature rises with thermophoresis effects and concentration decreases under the same influence. Further-more, entropy generation increases with the thermophoresis and Brownian motion parameters, but decreases with larger activation energy, magnetic, and Hall parameters, demonstrating the strong coupled influence of these parameters on the thermal and transport behavior of the hybrid nanofluid system.