Optimization of co-flow micro-heat-exchanger performance using Response Surface Methodology: energy transfer rate and thermodynamic irreversibility

This paper investigates the optimization of energy transfer rates and minimization of thermodynamic irreversibility in a co-flow microchannel heat exchanger using Response Surface Methodology (RSM) coupled with a Box-Behnken Design of Experiments. A surrogate model is developed to correlate critical input parameters-including Reynolds number (Re), Knudsen number (Kn), volume fraction (Vf), and particle diameter (Dp)-with the system responses: average Nusselt number (Nu_avg) and entropy generation (S_gen). The study explicitly addresses the effects of inlet flow conditions on thermal performance by analyzing shear-driven forced convection mechanisms. As highlighted in the boundary conditions, velocity gradients at the inlet create a mixing-dominated environment, where the Reynolds number (Re) governs fluid dynamics and heat transfer. This shear-enhanced mixing significantly improves thermal transport, while temperature gradients at the inlet contribute to localized heat exchange between the channel's bottom and top surfaces. The impacts of input parameters are evaluated through velocity profiles, slip velocity, temperature jump, heat transfer rates, and entropy generation. The interplay between these factors reveals that higher Re (linked to increased inlet velocities) intensifies convective heat transfer but also elevates viscous dissipation, presenting a trade-off between Nu_avg and S_gen. RSM optimization identifies Pareto-optimal conditions that maximize heat transfer while minimizing irreversibility. Analysis of Variance (ANOVA) validates the significance of each parameter, yielding regression equations for Nu_avg and S_gen. The results demonstrate RSM's efficacy in balancing competing objectives, offering actionable insights for designing high-efficiency microchannel heat exchangers in applications demanding precise thermal management with minimal energy losses. This work underscores the critical role of inlet flow conditions in dictating microchannel performance, bridging the gap between idealized models and practical operational constraints.