In this paper a new equation for calculating the nanofluid viscosity by considering the Brownian motion of nanoparticles is introduced. The relative velocity between the base fluid and nanoparticles has been taken into account. This equation presents the nanofluid viscosity as a function of the temperature, the mean nanoparticle diameter, the nanoparticle volume fraction, the nanoparticle density and the base fluid physical properties. In developing the model a correction factor is introduced to take into account the simplification that was applied on the boundary condition. It is calculated by using very limited experimental data for nanofluids consisting of 13 nm Al 2 O 3 nanoparticles and water and 28 nm Al 2 O 3 nanoparticles and water. The predicted results are then compared with many other published experimental results for different nanofluids and very good concordance between these results is observed. Compared with the other theoretical models that are available in the literature, the presented model, in general, has a higher accuracy and precision.

A simple mathematical model for calculating the effective thermal conductivity of nanofluids has been developed based on the thermal resistance approach. The model is developed by considering both effects of a solid-like nanolayer and convective heat transfer caused by Brownian motion which have not been considered simultaneously by most available models in the literature. In addition the correlation of Prasher and Phelan for the convective heat transfer coefficient is modified to take into account the effect of the solid-like nanolayer. In addition a general value for n (different from the one presented by Tillman and Hill) is introduced to modify the thickness of the solid-like nanolayer. The latter is done by considering both conduction and convection heat transfer mechanisms. Comparisons with previously published experimental results and other mathematical models show that the presented model could well predict a nanofluids effective thermal conductivity as a function of the nanoparticles mean diameter, volume fraction, and temperature for different kinds of nanofluids.