A critical review of the most popular mathematical models for nanofluid thermal conductivity

The following article is a critical review of the most popular hypotheses that have been used in the past to model analytically or numerically the thermal conductivity enhancement of nanofluids (Λ). This analysis starts first with the Effective Medium Theories (EMT), which have been used in the past to calculate the macroscopic properties of solid composites. Secondly, the hypotheses of a Λ due to Brownian movement are evaluated. All estimations and characteristic dimensions point to a negligible Λ due to Brownian motion. In third place, the hypotheses based on the agglomeration of nanoparticles provide a convincing explanation for the experimental measurements of Λ. Furthermore, the complicated dynamics of agglomeration could be the source of disparity between the published measurements of Λ. Lastly, the possible effect of liquid layering is briefly discussed. All in all, agglomeration as the principal mechanism for Λ might prove to be sufficient to explain the thermal behavior of nanofluids.