Thermodynamic analysis and hybrid surrogate-assisted multi-criteria optimization of heat transfer in mini-pipes

This study experimentally investigates the thermohydraulic performance of mini-pipes ( D = 2.26 and 2.74 mm) under forced convection (8070 ≤ Re ≤ 13678) to optimize the trade-off between heat transfer enhancement and thermodynamic irreversibilities. Analysis reveals that the 2.74-mm pipe exhibits superior performance. While the designs remain energy-efficient (PEC > 1), second law analysis confirms that frictional effects are the dominant source of irreversibility (Be < 0.002). To explore the entire design space using limited experimental data, a high-fidelity Kriging surrogate model ( R 2 > 0.96) was developed, which demonstrated superior predictive accuracy across all thermohydraulic parameters compared to support vector regression (SVR). A Surrogate-assisted high-resolution Grid Search approach, evaluating over 10,000 virtual points, was applied to find the exact Pareto optimal frontier, which was subsequently analyzed via Shannon Entropy-weighted TOPSIS. Shannon Entropy analysis identified S’gen,total as the most critical performance determinant (84.95% mass), followed by Nu (8.34%) and f (6.71%). Consequently, the global optimum operating point was identified at Re = 8070.0 and D = 2.74 mm. At this point, total entropy generation is minimized to 0.0161 W K −1 , with a corresponding Nu of 88.68 and f of 0.0485. These results demonstrate that despite thermal gains at higher velocities, minimizing friction-induced thermodynamic inefficiencies at lower Reynolds numbers yields the most efficient operation in mini-channels.