## 1 Introduction
[PERSON] and [PERSON] [24] modelled a microchannel cooled by Al\({}_{2}\)O\({}_{3}\) nanofluid, showing that single-phase and two-phase mixture models produced a maximum Nusselt number deviation of 11% and 3.2% compared to experiment, respectively. [PERSON] and [PERSON] [25] modelled the laminar forced convection of Al\({}_{2}\)O\({}_{3}\) nanofluids in a microchannel heat sink. The single-phase and mixture models predicted average Nusselt numbers 22.57% and 13.21% different than in experiment, respectively. The main alternatives to the mixture model for the two-phase approach are compared in [PERSON] and [PERSON] [26], where a steady, laminar microchannel flow simulation with Al\({}_{2}\)O\({}_{3}\) nanofluid uses the single-phase, VOF, mixture, and Eulerian methods. The two-phase model predictions are in closer agreement to experiment than the single-phase model predictions. [PERSON] and [PERSON] [27] reported the same finding using TiO\({}_{2}\) nanofluids in a minichannel heat sink and so did [PERSON] and [PERSON] [26] by way of applying Al\({}_{2}\)O\({}_{3}\) nanofluid in a liquid block. [PERSON], et al. [28] made use of the single-phase, Eulerian-Lagrangian, and mixture models to simulate nanofluid flow inside a minichannel and documented a consistent flow and heat transfer behavior among the three models. [PERSON], et al. [29] analyzed the 0.2% CuO nanofluid heat transfer inside a tube and found the average relative error between the experiment and single-phase and two-phase model predictions to be 16% and 8%, respectively, with the best performing two-phase model. [PERSON], et al. [30] studied the forced convection of a nanofluid in a horizontal tube using single-phase, mixture, and Eulerian two-phase models, showing that the mixture model is more accurate than the other two models. Whereas the reduced assumptions of the two-phase mixture model compared with the single-phase approach can provide higher fidelity predictions, some authors reported over-estimations of the heat transfer with the two-phase mixture model compared to the single-phase approach [31]. This generates lack of confidence in the application of the two-phase mixture simulations for modelling microchannel and minichannel heat sink flows. The main aim of this work is to review the implementation of the two-phase mixture model to microchannel and mini-channel heat exchangers and show that improved heat prediction performance with respect to a single-phase approach can be achieved when appropriate physical modelling assumptions are made. This provides a significant contribution to the scientific community by identifying how the two-phase mixture model can be used with confidence and exploit its greater fidelity to the physical flow. The main expected outcome is the wider adoption of this higher fidelity model, to provide significant energy savings, longevity, and cost reduction to microprocessor-aided technology, now ubiquitous across all industrial sectors. To reach this aim, this paper provides the following content: Section 2 Methodology states the two-phase mixture model formulation used in this work, which is essential in a paper aimed at providing an archival reference on how to implement such a model. Therein, Section 2.9 validates the implementation against experimental results recorded by [PERSON] and [PERSON] [25] in a minichannel cooled by Al\({}_{2}\)O\({}_{3}\) nanofluid. Section 3 shows a key aspect for obtaining physically consistent and reliable heat transfer model predictions from the minichannel two-phase mixture model, namely, to define two fluid phases, the first being water and the second being a suspension of Al\({}_{2}\)O\({}_{3}\) nanoparticles in water, modelled as a fluid of equivalent properties. Model limitations with respect to the nanoparticle volume fraction in the second phase and with respect to the size of the nanoparticles compared to that of the 'bubbles' of the second phase are documented. Section 3.4 explores another important aspect of minichannel heat sinks, from the second law of thermodynamics perspective.