Physically Consistent Implementation of the Mixture Model for Modelling Nanofluid Conjugate Heat Transfer in Minichannel Heat Sinks

Abstract

As much as two-phase mixture models resolve more physics than single-phase homogeneous models, their inconsistent heat transfer predictions have limited their use in modelling nanofluid cooled minichannel heat sinks. This work investigates, addresses, and solves this key shortcoming, enabling reliable physically sound predictions of minichannel nanoflows, using the two-phase mixture model. It does so by applying the single-phase and the two-phase mixture model to a nine-passages rectangular minichannel, 3 mm deep and 1 mm wide, cooled by a 1% by volume suspension of Al2O3 nanoparticles in water, over the Reynolds number range 92 to 455. By varying the volume fraction αnf of the second phase between 2% and 50%, under a constant heat flux of 16.67 W/cm2 and 30 Celsius coolant inflow, it is shown that the two-phase mixture model predicts heat transfer coefficient, pressure loss, friction factor, exergy destruction rate, exergy expenditure rate, and second law efficiency values converging to the single-phase model ones at increasing αnf. A two-phase mixture model defined with 1% second phase volume fraction and 100% nanoparticles volume fraction in the second phase breaks the Newtonian fluid assumption within the model and produces outlier predictions. By avoiding this unphysical regime, the two-phase mixture model matched experimental measurements of average heat transfer coefficient to within 1.76%. This has opened the way for using the two-phase mixture model with confidence to assess and resolve uneven nanoparticle dispersion effects and increase the thermal and mass transport performance of minichannels.