Hydrothermal and entropy generation analysis of mixed convection heat transfer in Couette–Poiseuille flow of a trihybrid nanofluid over a backward-facing step

This study introduces and systematically investigates a novel Couette–Poiseuille backward-facing step configuration, in which the conventional stationary upper wall is replaced by a uniformly moving belt. The flow domain is filled with a trihybrid nanofluid composed of (${\text{Al}}_2{O}_3-\text{Cu}-\text{MWCNT}$) nanoparticles, enabling the interplay of pressure-driven and shear-driven forces within a sudden-expansion geometry with $\text{ER}=2$. Numerical analysis explores the effects of varying Reynolds numbers ($100\le R{e}_H\le 500$), Rayleigh numbers ($6.99\times {10}^5\le R{a}_H\le 1.75\times {10}^7$), Grashof numbers ($1.0\times {10}^4\le {\text{Gr}}_H\le 2.5\times {10}^5$), and top wall terminal velocity ratios ($-3\le U_{belt,r}\le +3$) on flow behavior, heat transfer, and entropy generation, with the constant Prandtl number ($\mathrm{Pr}$) of $69.93$. At low $R{e}_H$, aiding wall motion stabilizes the flow and minimizes entropy generation, while opposing wall motion induces strong recirculation, vortex shedding, and Kelvin–Helmholtz instabilities at higher $R{e}_H$. Thermal field analysis reveals that counter-flow enhances convective mixing and thermal dispersion, whereas co-flow confines heated fluid near the lower wall. The moving wall improves heat transfer performance by up to $14\%$ in optimal opposing-flow conditions and reduces the Irreversibility-to-Heat Transfer Index ($\text{IHTI}$) by over $90\%$ at low $R{e}_H$, where values remain below $5\times {10}^{-7}$, indicating high thermodynamic efficiency. However, at high $R{e}_H=500$, entropy generation increases by more than $10$ times compared to $R{e}_H=100$, and $\text{IHTI}$ rises sharply, peaking at $4.2\times {10}^{-6}$, highlighting the cost of intensified shear and recirculation. Entropy generation analysis, including Bejan number ($\text{Be}$) and $\text{IHTI}$, identifies transitions from thermal to frictional irreversibility as $R{e}_H$ increases and wall motion intensifies. The study defines four distinct hydrothermal regimes based on the Cumulative Heat Transfer Enhancement Ratio ($\text{CHTER}$) and Thermo-Hydraulic Performance Factor ($\text{THPF}$), highlighting trade-offs between enhanced mixing and viscous dissipation. Three thermodynamic regimes, Diffusion-Dominated, Transitional Coupled, and Inertia-Dominated, are characterized by evolving entropy profiles and thermodynamic efficiency. The results offer new insights into optimizing mixed convection flows using wall-driven mechanisms and advanced trihybrid nanofluids for superior heat transfer and energy performance in compact thermal systems.