## 1 Introduction  
The performance growth and size reduction of micro-electronic devices, such as computer cores, are currently limited by the ability to dissipate the heat produced by the supplied electrical power, through a conventional air-cooled heat sink. There is therefore a sustained research interest in water-based liquid coolants for mini/microchannels cooling systems, owing to the higher specific heat capacity of water compared to air. Water-based suspensions of nanoparticles, referred to as nanofluids, have an even better cooling potential. Compared to the base fluid (water), the nanofluids can extract more heat for the same volume flow rate. Many studies have investigated nanofluids by way of experiment and/or simulation. As the tracking of individual nanoparticles by a Eulerian-Lagrangian approach remains computationally expensive, nanofluid numerical computations use either a single-phase or a two-phase approach. In the single-phase approach, the suspension of nanoparticles in a base fluid is assumed to be homogeneous and the nanoparticles are assumed to be in thermal equilibrium with the base fluid [1]. The nanofluid is replaced by a single fluid of equivalent thermophysical properties to the ones of the suspension, determined from experiment or by a physical model. The accuracy to which the thermophysical properties of the single fluid are estimated is very important for this type of flow simulation. [PERSON], et al. [2], [PERSON] and [PERSON] [3], and [PERSON] and [PERSON] [4] used this single-phase approach, which is relatively computationally inexpensive and has been shown to reproduce flow predictions close to experimental measurements. The single-phase approach is popular for modelling the nanofluid flow for electronic core heat sinks. For example, [PERSON], et al. [5] examined the laminar forced convective heat transfer of Al\({}_{2}\)O\({}_{3}\) nanofluid in a microchannel heat sink of a rectangular cross-section and found the addition of nanoparticles to be more beneficial to cooling at a lower Reynolds number. [PERSON] and [PERSON] [6] and [PERSON], et al. [7,8] modelled Al\({}_{2}\)O\({}_{3}\) nanofluid in a microchannel heat sink and showed that the nanofluids can increase the Nusselt number and reduce the heat sink contact surface temperature compared to water, at an acceptable through-flow pressure drop penalty. In the two-phase approach, nanoparticles and their base flow are split in two separate phases. These phases move and interact according to a volume of fluid model (VOF) [9], a mixture model [10], an Eulerian model [11], or a Discrete Phase model [12]. Each model is distinct in the way it manages the mass, momentum, and energy conservation of each phase. The mixture model solves one momentum and one energy equation for the mixture, one volume fraction equation, and individual continuity equations for each phase. The phase velocities are then obtained by empirical correlations [13,14]. By this, a greater insight into the role of each phase on heat transfer is obtained compared to a single-phase approach [15]. Mixture models of microchannel flows have shown heat transfer enhancement with increasing nanoparticle concentration, in [PERSON], et al. [16], in line with previous findings by [PERSON], et al. [17], secondary flow generated by helical inserts, in [PERSON], et al. [18], and nanoparticle size effect on heat transport, in [PERSON] and [PERSON] [19] and in [PERSON] and [PERSON] [20]. Comparisons between single-phase and two-phase mixture model predictions are shown in [PERSON], et al. [21], who report the two-phase model in good agreement in Nusselt number with a CuO nanofluid experiment, and in [PERSON], et al. [22], where the laminar and turbulent forced convection by the two-phase model was in closer agreement with experiments by [PERSON] and [PERSON] [23].