This study addresses the growing demand for efficient thermal management in microscale systems through advanced modeling of trihybrid nanofluid behavior under magnetic effects. It presents a detailed analysis of entropy generation and heat transfer in the flow of a Carreau trihybrid nanofluid- \(Cu, CuO,\) and \(C71500\) nanoparticles suspended in \({H}_{2}O\) injected to a vertically oriented microchannel with a Hall current. To meet the need for energy-efficient devices, the model includes convective slip conditions, nonlinear thermal radiation, and internal heat generation. A novel hypergeometric wavelet technique is utilized to solve the governing equations efficiently and obtain solutions for velocity, temperature, entropy, Bejan number, Nusselt number, and skin friction. The study shows that with the increase in Hall parameter from 0.1 to 1, there is a moderate 4.44% increase in axial velocity and an enormous 80.45% increase in transverse velocity, which suggests an improved flow rotation because of magnetic influence. On the other hand, thermal efficiency decreases by 31.75% when the Biot number increases from 1 to 2.5, which points towards the reduction in conductive heat transfer at the boundary. The Hartmann number is majorly responsible for thermodynamic improvement through reducing the generation of entropy by 21.24% and, accordingly, proposing lowered irreversibility within the system. The Bejan number increases by 6.8% at larger values of Hartmann numbers, advocating increased dominance by heat transfer against viscous dissipation within the entropy profile. The outcomes are highly beneficial for optimum heat and energy control in compact heat exchangers, microreactors, and next-generation refrigeration apparatus.
