Heat transfer characteristics of thermally and hydrodynamically developing flows in multi-layer mini-channel heat sinks

•A new type of air-cooled multi-layer mini-channel heat sink is proposed.•The thermally/hydrodynamically developing flow inside the heat sink channels is studied.•Correlations are proposed to cover both developing and developed flows.•An analytical solution is proposed to calculate the average base temperature.•The heat sink operates with lower entropy generation than plate-fin heat sinks.