## 1 Introduction
Nevertheless, the Navier-Stokes method with the first-order slip boundary condition can give results consistent with those obtained by numerical simulations based on the Boltzman model for fluids with a Knudsen number between 0.01 and 0.1. So, for this Knudsen number range, the Navier-Stokes method with a slip boundary condition is adequate to model nanofluids' regimes. Microflow regimes, on the other hand, can present important differences in pressure drop, flow pattern and transition from laminar to turbulence from their macro counterparts. Several studies have evaluated different geometrical configurations of heat sinks to optimize the flow and the heat transfer phenomena. [PERSON] et al. [14], using the commercial _COMSOL Multiphysics 5.6\({}^{\text{\tiny\textregistered}}\)_ software, analyzed a microchannel heat sink device for use as a cooler in a high-concentration photovoltaic system. The authors tested channels with and without triangular ribs on the inner side of the walls. The microchannels with ribs presented better heat transfer, increasing the Nusselt number1.7 times, on average. On the other hand, the simulation also showed that, for the same configuration, the average friction factor was 3.1 times higher. [PERSON] et al. [15] numerically compared the heat flux, pumping power, pressure drop and thermal resistance in microchannel heat sinks with different channel widths (Wc), heights (H), bases (tb) and wall thicknesses (Ww). Water and liquid metal Galinstan were used as working fluids. The authors reported that, regarding heat transfer performance, a deep and narrow channel would work better than a shallow and wide channel. [PERSON] et al. [16] used a conjugate heat transfer model to study the laminar convection heat transfer and fluid flow in an inclined slotted plate-fin minichannel heat sink. The impact of the height of the inclined slot, the angle of the slot and the position of the pin with respect to the slot's leading edge were investigated. An increase in the thermal and hydraulic performances was reported with the increase in the slot height and an inclination angle of 55 degrees. The addition of triangular pins further improved the performance, the optimal geometry being the one wherein the pins are placed far from the slot's leading edge. [PERSON] and [PERSON] [17] tested microchannel heat sinks with different materials and microchannel ratios, that is, the ratio between the microchannel's width and the microchannel's spacing. The materials used for the fabrication of the heat sinks were polymer-based (PDMS, Polytetrafluoroethylene-PTFE, PDMS/Multi-Walled Carbon Nanotubes-MWCNT) and metal-based (aluminum). Due to their low conductivity, the polymer-based materials tended to enhance the heat convection contribution and consequently improved the thermal performance of the heat sink. High values of microchannel ratio corresponded to a higher thermal contact area and a reduced fluid velocity in the microchannel, which improved the overall thermal performance. [PERSON] et al. [18] evaluated the performance of plate-fin heat sinks through a commercially available Computer Fluid Dymamicssoftware, ANSYS R 16.1 (Canonsburg, Pennsylvania, United States). The plate-fin heat sinks presented four different geometries: standard plate-fin; plate-fin with fillet profile; plate-fin with fillet profile and symmetrical half-round pins in a vertical arrangement; and plate-fin with fillet profile and corrugated half-round pins in a vertical arrangement. The two last designs manifested greater reduction in the base temperature and thermal resistance, and an increase in the Nusselt number, in comparison to the other two designs. [PERSON] and [PERSON] [19] also used a commercial CFD software, ANSYS-Fluent, to investigate the performance of micropin finned heat sinks with different relative positions and angles of the inlet and outlet.