Abstract This manuscript is aimed at investigating the thermohydraulic characteristics of Al2O3 − Cu/water hybrid nanofluid in a micro pin-fin heat sink by implementing a multiphase Lagrangian–Eulerian approach. In modelling the nanofluid the influence of slip mechanisms i.e. Saffman lift and drag force, Brownian motion, gravity, virtual mass, thermophoresis and pressure gradient-induced force is included. In addition, the fin efficiency of the nanofluid cooled sharp and streamlined fin configurations is probed by analysing diamond, circular and elliptical fins arranged in the staggered assembly. Spherical shaped hybrid nanoparticles of 15 nm are studied for the particle volume fraction of 1%. The performance of heat sinks is evaluated by analysing the quantitative parameters including log mean temperature difference, average (Nuavg) and surface (Nus) Nusselt number. Besides, the flow streamlines, thermal and vorticity contours represent the qualitative depiction of flow and thermal distributions. Results demonstrate that utilising nanofluid optimises Nuavg enhancement to maximum values of 25.14%, 19.65% and 24% for diamond, circular and elliptical fins, respectively. The thermal efficiency of nanofluid is highest across the upstream fins and it diminishes towards the downstream fins. At the highest pressure drop, the fin efficiency of the studied fin configurations is in the order of circular, elliptical and diamond fins.