The thermal conductivity of alumina-water nanofluids from the viewpoint of micromechanics

The thermal conductivity of alumina-water nanofluids is analysed from the viewpoint of micromechanics. Wiener and Hashin-Shtrikman bounds are recalled, and it is shown how these model-independent bounds can be used to check experimental results and literature data. Further, it is shown that in the infinite-phase-contrast case (i.e. for superconducting particles), a useful approximation is obtained for the lower Hashin-Shtrikman bound (= Maxwell model = Hamilton-Crosser model for spherical particles). It is also shown that the second-order approximation of this infinite-phase-contrast relation is identical to the Choy-Torquato cluster expansion for impenetrable spheres with a "well-separated" distribution, whose dilute limit approximation is identical to that of other popular models, such as the self-consistent and differential scheme approximation. It is found that a considerable amount of published data violates the Hashin-Shtrikman lower bound, i.e. lies below the Maxwell model; the possible reasons are discussed. On the other hand, it is shown that the strong temperature dependence reported for the thermal conductivity of nanofluids cannot be explained within the framework of micromechanics and, if confirmed by future measurement where macroscopic convection can safely be excluded, indeed requires other mechanisms of heat transfer, such as forced nano- or micro-convection caused by Brownian motion of nanoparticles.