An improved model for thermal conductivity of nanofluids with effects of particle size and Brownian motion

Based on the generalized distribution of the temperature field, an improved model for the thermal conductivity of nanofluid has been derived. The impact of particle size and Brownian motion is modeled through the effective volume fraction, based on particle radius. In the special case, the generalized relationship reduces to the classical Maxwell model. On the other hand, the effect of Brownian movement is equivalent to increasing the effective volume fraction of nanoparticles. The effective radius of the nanoparticle is proposed, where the switching time and the equivalent volume fraction depend on the Brownian velocity of the nanoparticles. Considering the above two effects, an effective model is obtained. Comparison of thermal conductivity for Al₂O₃–water nanofluid is made between the present model and several theoretical models. Theoretical predictions on CuO–water nanofluid, ZnO–TiO₂ hybrid nanofluids and MWCNTs nanofluid are also verified against experimental data.