Ramesh and Prabhu Nanoscale Research Letters 2011, 6:334 http://www.nanoscalereslett.com/content/6/1/334 of the particle. In that case diffusive thermal trans- port in nanoparticles is not valid and ballistic trans- port is more realistic. Keblinski et al. indicated that inside the solid particles, heat moves in a ballistic manner that involves multiple scattering from the solid/liquid interface, which plays a key role in trans- lating fast thermal transport in particles into high overall conductivity of the nanofluids. They also sug- gested that particles may be much closer due to Brownian motion and thus enhance coherent pho- non heat flow among the particles [43]. The esti- mated mean free path and the transition speed of phonons in nanofluids through density functional theory indicated that the speed of phonon transport will not be affected due to the existence of nanopar- ticles in the low volume fraction limit [59]. IV. Clustering of nanoparticles: Since nanoparticles in the fluid are in Brownian motion and the Van der Waals force against gravity results in clustering of nanoparticles into percolating patterns with lower thermal resistance paths. With decreasing packing fraction, the effective volume of the cluster increases thus enhancing the thermal conductivity. Clustering may also exert a negative effect on the heat transfer enhancement particularly at low volume fraction, by settling small particles out of the liquid and creating large regions of particle free liquid with high thermal resistance [43]. Using non-equilibrium molecular dynamics simulations, Eapen et al. showed that the thermal conductivity of a well-dispersed nanofluid was enhanced beyond the 3 Maxwell limit through a percolating amorphous-like fluid structure at the cluster interface [60]. Studies on clustering of nano- particles in the fluids suggest varying values of ther- mal conductivities, i.e. enhanced, reduce and unchanged thermal conductivity of nanofluids [61-63]. Ozerinc et al. mentioned that there should be an optimum level of clustering for maximum thermal conductivity enhancement [44]. The experimentally measured thermal conductivities of nanofluids deviate from conventional models such as Maxwell, Hamilton-Crosser, Jeffery, Davis, Bruggeman, Lu and Lin model. The important factors, which control the thermal conductivity of nanofluids, are particle volume concentration, particle material, particle size, particle shape, base fluid material, temperature, additive and acidity [17,44]. Due to these complex variables and different mechanisms, the exact model for effective ther- mal conductivity of nanofluid is difficult. Yu and Choi have modified the Maxwell equation for the effective thermal conductivity of solid/liquid suspensions to include the effect of this ordered nanolayer [51]. Wang et al. proposed fractal model for liquid with dilute Page 6 of 15 suspensions of nonmetallic nanoparticles, which involves the effective medium theory. The proposed model describes the nanoparticle clusters and their size distri- bution [64]. Xue presented a novel model considering the interface effect between the solid particles and the base fluid in nanofluids based on Maxwell theory and average polarization theory [65]. Jang and Choi devised a theoretical model that accounts for the role of Brow- nian motion of nanoparticles in nanofluid. This model also includes the concentration, temperature and size dependent conductivity [45]. By considering the particle dynamics (Brownian motion), Koo and Kleinstreuer expressed a model which consists of particle volume fraction, particle size, particle material and temperature dependence as well as properties of base liquid [46]. A comprehensive theoretical model has been developed by Kumar et al. which explains the enhancement in ther- mal conductivity of a nanofluid with respect to variation in particle size, particle volume fraction, and tempera- ture [66]. Xue and Xu derived a model which consists of the thermal conductivity of the solid and liquid, their relative volume fraction, the particle size and interfacial properties [67]. Patel et al. introduced a concept of micro-convection into Kumar et al. model for predicting the thermal conductivity accurately over a wide range of particle sizes (10 to 100 nm), particle concentrations (1 to 8%), particle materials (metal particles as well as metal oxides), different base fluids (water, ethylene gly- col) and temperature (20 to 50°C) [68]. By considering the effect of the interfacial layer at the solid particle/ liquid interface, Leong et al. proposed a model which accounts for the effects of particle size, interfacial layer thickness, volume fraction and thermal conductivity [54]. For carbon nanotube (CNT) nanofluids, Patel et al. presented a simple model which shows linear variation of the thermal conductivity of CNT nanofluid with volume concentration [69]. Feng et al. expressed a model as a function of the thermal conductivities of the base fluid and the nanoparticles, the volume fraction, fractal dimension for particles, the size of nanoparticles, and the temperature, as well as random number. Monte Carlo technique combined with fractal geometry theory is applied to predict the thermal conductivity of nano- fluids [70]. Shukla and Dhir developed a microscopic model based on the theory of Brownian motion of nano- particles in a fluid which account size of the particle and temperature [71]. Moghadassi et al. presented a novel model based on dimensionless groups which included the thermal conductivity of the solid and liquid, their volume fractions, particle size and interfacial shell prop- erties. The proposed model creates a non-linear relation between the effective thermal conductivity and nanopar- ticle volume fraction [72]. Wang et al. proposed a Novel Statistical Clustering Model to determine the