## 2 Nanofluid Thermal Conductivity
### Effects of Nanoparticle Size on Nanofluid Thermal Conductivity
It was stated that these results showed the strong effect of surface area-to-volume ratio of nanoparticles on the thermal conductivity of nanofluids [36]. Using the transient hot-wire method, [PERSON] et al. [25] conducted experiments to determine the thermal conductivity of TiO\({}_{2}\)-water nanofluid. It was observed that the thermal conductivity increased with decrease in nanoparticle size. It was suggested that this relationship was related to greater Brownian motion for smaller nanoparticles. [PERSON] et al. [20] measured the thermal conductivities of Al\({}_{2}\)O\({}_{3}\)-water nanofluids, using 13 nm and 20 nm Al\({}_{2}\)O\({}_{3}\) particles, containing both sodium dodecyl sulphate (SDS) and polyvinyl pyrrolidone (PVP) as surfactants. For a given surfactant concentration, it was observed that the nanofluids containing 13 nm particles had higher thermal conductivities. However, in some cases, researchers found that the thermal conductivity of nanofluids did not increase with the decrease in nanoparticle size. [PERSON] et al. [48] measured the thermal conductivities of Al\({}_{2}\)O\({}_{3}\)-Ethylene Glycol nanofluids containing 5 nm, 25 nm, 58 nm, and 101 nm particles using the transient hot-wire method. It was observed that the thermal conductivities of the nanofluids, from highest to lowest, were those containing 25 nm particles, 5 nm particles, 58 nm particles, and finally 101 nm particles. It was suggested that these results were caused by a combination of the surface area to volume ratio and phonon scattering. The scattering of the primary carriers of energy at the boundaries of nanoparticles is called phonon scattering [48]. As the nanoparticle size decreases, the surface area to volume ratio increases, which allows for more effective heat transfer at the solid-liquid interface, leading to increased thermal conductivity. However, the intrinsic thermal conductivity of the nanoparticles decreases due to phonon scattering when the nanoparticle size is close to that of the mean free path, which was estimated to be around 35 nm. Although existing experimental data indicates that the effect of nanoparticle material on the thermal conductivity of nanofluids is not very strong [26; 32; 36], it was suggested that phonon scattering had a significant impact on these experimental results. [PERSON] et al. [49] measured the thermal conductivities of nanofluids composed of 8 nm, 12 nm, 16 nm, 46 nm, 71 nm, 245 nm, and 282 nm Al\({}_{2}\)O\({}_{3}\) particles dispersed in water, and 12 nm, 16 nm, 245 nm, and 282 nm Al\({}_{2}\)O\({}_{3}\) particles dispersed in Ethylene Glycol using a liquid metal transient hot-wire device. It was observed that the thermal conductivity was almost constant with the decrease in nanoparticle size for nanofluids containing nanoparticles with a size greater than 50 nm. For nanofluids containing particles having a size smaller than approximately 50 nm, it was observed that the thermal conductivity of the nanofluid decreased with decrease in nanoparticle size. It was suggested that this was a result of the decreased intrinsic thermal conductivity of nanoparticles when the nanoparticles became small enough to be affected by phonon scattering. [PERSON] et al. [50] measured the thermal conductivities of nanofluids composed of TiO\({}_{2}\) nanoparticles dispersed in water and polyvinyl alcohol (PVA) as a function of nanoparticle size, for nanoparticles, ranging from 5-100 nm. It was observed that the thermal conductivity of TiO\({}_{2}\)-PVA nanofluid increased with the decrease of nanoparticle size. It was suggested that this increase was a result of liquid adsorption layers forming around the surfaces of the nanoparticles. At smaller nanoparticles sizes, the adsorption layers formed an easy path for heat transfer, due to the large surface area to volume ratio of the nanoparticles and the high viscosity of the base fluid. As the nanoparticle size increased, the adsorption layers became thinner, making a less effective heat transfer path.