Impact of Hall current and buoyancy forces on heat transfer in blood-based Casson–Williamson tri-hybrid nanofluid flow through a vertical microchannel: An irreversibility analysis

Blood-based nanofluids provide a theoretical framework for investigating heat transfer and fluid motion in microscale systems relevant to biomedical transport. This study investigates the flow, heat transfer, and entropy generation of a blood-based Casson–Williamson trihybrid nanofluid containing silver, zirconium dioxide, and cobalt nanoparticles inside a vertical microchannel. The model incorporates magnetic-field effects, Hall current, buoyancy forces, nonlinear thermal radiation, wall slip, and convective heating. The governing equations are transformed into a dimensionless nonlinear boundary-value system and solved using the shooting technique combined with the fourth- and fifth-order Runge–Kutta–Fehlberg method. The results indicate that increasing the magnetic parameter reduces the primary velocity while enhancing the secondary velocity. The Reynolds number, pressure-gradient parameter, Hall parameter, Grashoff number, Casson parameter, and wall-slip parameter generally enhance fluid motion under the conditions investigated. The temperature increases with the Reynolds number, Grashoff number, heat-generation parameter, and Eckert number but decreases with the temperature-ratio parameter and Biot number. Entropy generation increases with the temperature-ratio, radiation, and Eckert parameters, while the magnetic field modifies its distribution across the channel. A normalized sensitivity analysis using a consistent five-percent perturbation around each baseline parameter is performed to evaluate the local influence of the governing parameters on entropy generation. The principal novelty is the integrated investigation of Hall-current effects, combined Casson–Williamson rheology, nonlinear thermal radiation, wall slip, and thermodynamic irreversibility in a blood-based trihybrid nanofluid flowing through a vertical microchannel. The findings clarify the interactions between magnetic forces, fluid motion, heat transfer, and irreversibility, providing theoretical insights into microscale thermal transport.