Using effective medium theory the authors demonstrate that the thermal conductivity of nanofluids can be significantly enhanced by the aggregation of nanoparticles into clusters. Predictions of the effective medium theory are in excellent agreement with detailed numerical calculation on model nanofluids involving fractal clusters and show the importance of cluster morphology on thermal conductivity enhancements.

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We use a kinetic theory based analysis of heat flow in fluid suspensions of solid nanoparticles (nanofluids) to demonstrate that the hydrodynamics effects associated with Brownian motion have only a minor effect on the thermal conductivity of the nanofluid. This analysis is supported by the results of molecular dynamics simulations of heat flow in a model nanofluid with well-dispersed particles. Our findings are consistent with the predictions of the effective medium theory as well as with recent experimental results on well-dispersed metal nanoparticle suspensions.

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A dispersive model is developed for wave propagation in periodic heterogeneous media. The model is based on the higher order mathematical homogenization theory with multiple spatial and temporal scales. A fast spatial scale and a slow temporal scale are introduced to account for the rapid spatial fluctuations as well as to capture the long-term behavior of the homogenized solution. By this approach the problem of secularity, which arises in the conventional multiple-scale higher order homogenization of wave equations with oscillatory coefficients, is successfully resolved. A model initial boundary value problem is analytically solved and the results have been found to be in good agreement with a numerical solution of the source problem in a heterogeneous medium.