In this paper, Brownian motion of nanoparticles and clusters and resulted micromixing are combined with the aggregation kinetics of nanoparticles and formation of clusters to capture the effects of added nanoparticles on k eff . Results show that the observed anomalies reported in experimental works can be well described by taking aggregation kinetics into account. The proposed model, attribute the effective thermal conductivity not only to the intrinsic physical properties such as thermal conductivity of the liquid and nanoparticles, viscosity of the liquid, and radius of the nanoparticles, as well as temperature and time, but also to physicochemical parameters which affect stability state of nanofluids such as the Hamaker constant, the surface charge, pH , and ion concentration. The more nanofluid is stabilized, the more k eff will increase. We have also demonstrated that the thermal conductivity ratio can also increase with particle size depending on the chemistry of the solution and an optimized radius in a suspension with certain temperature and pH can be achieved. This behavior is not feasible without including the effects of aggregation kinetics combined with Brownian motion and induced micro-convection.
