<p>This study presents a numerical analysis of conjugate convective heat transfer in a 3sD wavy microchannel heat sink (MCHS) using CuO–water nanofluid, with a focus on comparing the discrete phase model (DPM) and dense discrete phase model (DDPM) within an Eulerian–Lagrangian framework. The primary goal is to assess how nanoparticle concentration and Reynolds number influence thermal performance under laminar flow, using the field synergy principle (FSP) to evaluate flow–thermal interactions. Results demonstrate that DDPM predicts significantly higher enhancements in average Nusselt number—up to 11.21% compared to 4.36% in DPM—when increasing CuO concentration from 0.01 to 0.06 at Re = 400. As Reynolds number increases from 300 to 800, both models show substantial heat transfer improvement, with the DPM and DDPM yielding gains of 48.28% and 46.72%, respectively. Despite a slight reduction in relative convective heat transfer at higher concentrations, overall thermal performance improves by approximately 16% over the base fluid. These findings underscore the value of accurate multiphase modeling and flow-field optimization for the effective thermal design of advanced MCHSs.</p> Graphical abstract