## 1 Introduction  
The development of technology in the fields of mechanics, electronics, defense (e.g., in UAVs (unmanned aerial vehicles)) and biomedicine, among others, has been directed towards the miniaturization of their components, which are currently reaching micro- and nano-scales [1; 2; 3; 4]. Their robustness makes them fit to be used in harsh environments, such as to provide basic health care in developing countries and for military applications. Microfluidic devices, such as microchannel heat sinks, have been broadlyexplored for heat removal due to their reduced dimensions [5]. In addition, it should be emphasized that the scaling down from macro to micro leads to several relevant issues in thermal management in several applications, including in micro combustors, pushing the need for the optimization of their geometry [6; 7].Besides this miniaturization factor, the heat transfer coefficient in microchannels is comparatively very high because of the effect of the very small hydraulic diameter and the associated latent heat of evaporation. This coefficient is influenced directly by the thermophysical properties of the working fluid, the mass and heat fluxes, and the geometry of the microchannels (geometric configuration shape, internal hydraulic diameter, cross-section shape, area and aspect ratio). It should also be emphasized that it is paramount to avoid instability (malfunctioning of the flow) in micro channeled devices, which worsens the heat transfer performance and may cause troublesome vibration, thermal fatigue, and even surface burnout. The mains sources of instability in microchannels are flow maldistribution, pressure drops, wall temperature gradient and, in some cases, vapor flow reversal, resulting in re-entrant cavities, points of bubble nucleation, throttling points and working fluid superheating. The required number of micro components in a micro channeled device (pump, valve, mixer, reactor, manifold, among others) that is usually assembled in a microchip leads to a high degree of complexity [8], which in turn highlights the pressing need for the evaluation by numerical simulations of the microchannel heat sinks. Registering quantities such as pressure and velocity fields demands complex experimental set-ups and extensive measurement campaigns, the resultsof which should always validate the numerical models. Over the last few years, different methods and toolboxes have been studied to simulate the heat transfer phenomena that occur in microfluidic devices. [PERSON] et al. [8] developed a mathematical model using the commercial _COMSOL Multiphysics 5.6\({}^{\text{\tiny\textregistered}}\)_(Burlington, MA, USA) [9] software to optimize the fabrication of micro nanofluidic devices through photopolymerization. The model expressed the decomposition of the material that would occur due to the manufacture process. [PERSON] et al. [10] implemented a volume of fluid (VOF)-based model in the Open FOAM ComputationalFluid Dynamics (CFD) toolbox to compare the heat transfer in straight and finned microchannels. The presence of the fins improved the heat exchanges; however, the optimization of the geometry of the fins is still required. Since conventional heat transfer theories are not sufficient to describe the heat exchange through fluid-solid boundaries, some difficulties can arise when simulating a fluid flow in microchannels [1]. Macroflow regimes can be described by the classic Navier-Stokes equations. The Navier-Stokes method with the no-slip boundary condition is not adequate for describing microflow regimes. Those, in turn, can be described by the Boltzman kinetic model with the aid of numeric simulation methods, such as the Lattice Boltzmann Method (LBM), the Molecular Dynamics (MD) method, the Direct Simulation of Monte Carlo (DSMC) [11; 12] and the Computer Fluid Dynamics (CFD) method. The LBM method derives from the Boltzmann equation without the continuum assumption, and is a common tool used in numerical studies [13].