This paper aims to contribute to the analysis of a heat sink designed for the active cooling of small flat surfaces. The heat transfer device investigated here consists of a flat square substrate and a cover, separated by parallel channels with a rectangular cross-section. The cold air flowing in the channels is sucked from the environment, and the bottom of the substrate adheres closely to the hot surface of the device to be cooled. The thermal problem is tackled by considering two different conditions: the first one assuming one long side of the channel is heated and the three other sides are adiabatic (version 1L) and the second one assuming high conductivity of the walls (version 4), in both the H1 and H2 boundary conditions. Moreover, to investigate the effect of the number of channels on the performance of the heat sink, the number of channels is changed between 1 and 20. The results, presented in terms of the f Re product, Nusselt number, maximum surface temperature, and thermal resistance, reveal that both the thermal boundary conditions and the number of channels significantly affect the performance of the investigated heat transfer device.