Simultaneous effects of Brownian motion and clustering of nanoparticles on thermal conductivity of nanofluids*

In this paper, Brownian motion of nanoparticles and clusters and resulted micromixing are combined with the aggregation kinetics of clusters to capture the effects of nanoparticles on the thermal conductivity of nanofluids. Starting from kinetic theory, random motion of nanoparticles and induced micro-convection were combined with the kinetics of aggregates and a theoretical model which depends on two semi-empirical parameters was derived. The proposed model attributes the thermal conductivity of nanofluids not only to the intrinsic physical properties, but also to physicochemical parameters which affect the stability state of nanofluids. The more nanofluid is stabilized, the more keff increases. We have also demonstrated that the thermal conductivity either increases or decreases with respect to the particle size and there is an optimum value for the particle radius at which the thermal conductivity of the nanofluid is maximum. Depending on the chemistry of the solution, the optimized radius of the nanoparticles in a suspension depends on the temperature and pH of the suspension and the volume fraction of the nanoparticles. This behaviour is not feasible without including the effects of aggregation kinetics combined with Brownian motion and induced micro-convection.