## 2 Nanofluid Thermal Conductivity
### Effects of Nanoparticle Size on Nanofluid Thermal Conductivity
Using the same method, [PERSON] et al. [42] studied the thermal conductivity of Al\({}_{2}\)O\({}_{3}\)-glycerol nanofluid. Experiments were conducted using Al\({}_{2}\)O\({}_{3}\) nanoparticles of three different diameters, including 31 nm, 55 nm, and 134 nm. The results showed a relatively significant increase in thermal conductivity with the decrease in nanoparticle size. It was suggested that this increase was related to increased Brownian motion in nanofluids containing smaller nanoparticles. The Brownian motion diffusion coefficient was calculated using the Einstein-Stokes equation. The coefficient increased as the nanoparticle size decreased, indicating more significant collisions between the nanoparticles and base liquid molecules for smaller nanoparticles, resulting in enhanced thermal conductivity. Moreover, using the KD2 Pro Thermal Analyzer, [PERSON] et al. [35] measured the thermal conductivity of Au-water nanofluid as a function of nanoparticle size. It was suggested that the thermal conductivity increased with the decrease of nanoparticle size, which is shown in Figure 9. It was suggested that this increase was a result of increased Brownian motion and greater surface area to volume ratio for smaller nanoparticles. The thermal conductivities of Ag\({}_{2}\)Al-water, Ag\({}_{2}\)Al-Ethylene Glycol, Al\({}_{2}\)Cu-water, and Al\({}_{2}\)Cu-Ethylene Glycol nanofluids were measured by [PERSON] et al. [4], as a function of nanoparticle size, within the range of 30-120 nm. The results indicated an increase in thermal conductivity with the decrease of nanoparticle size. It was suggested that this was a result of the larger surface area of nanoparticles and greater stability in suspensions in comparison to coarse particles. [PERSON] et al. [32] measured the thermal conductivities of SiO\({}_{2}\)-methanol and Al\({}_{2}\)O\({}_{3}\)-methanol nanofluids as a function of nanoparticle volume concentration, \(\varphi\). The SiO\({}_{2}\) nanoparticles had diameters of 10-20 nm, and the Al\({}_{2}\)O\({}_{3}\) nanoparticles had diameters of 40-50 nm. Dynamic light scattering was used to measure the cluster sizes of the nanoparticles dispersed in methanol, and it was observed that the clustering size of SiO\({}_{2}\) nanoparticles was 280-401 nm, while that of the Al\({}_{2}\)O\({}_{3}\) nanoparticles was 120-148 nm for a given condition. It was suggested that the larger formation of clusters in the SiO\({}_{2}\) nanofluid was a result of the smaller size of SiO\({}_{2}\) nanoparticles in comparison to the Al\({}_{2}\)O\({}_{3}\) nanoparticles. It was observed that for a given \(\varphi\), the SiO\({}_{2}\)-methanol nanofluid had a higher thermal conductivity. It was suggested that the higher thermal conductivity of SiO\({}_{2}\)-methanol nanofluid was a result of the larger cluster size of the nanoparticles in comparison to the clusters formed in the Al\({}_{2}\)O\({}_{3}\)-methanol nanofluid. [PERSON] et al. [36] measured the thermal conductivities of TiO\({}_{2}\)-water, Al\({}_{2}\)O\({}_{3}\)-water, Fe-Ethylene Glycol, and WO\({}_{3}\)-Ethylene Glycol nanofluids as a function of nanoparticle volume concentration, \(\varphi\). It was observed that TiO\({}_{2}\)-water nanofluid had a higher thermal conductivity than Al\({}_{2}\)O\({}_{3}\)-water nanofluid for a given \(\varphi\). It was also observed that Fe-Ethylene Glycol nanofluid had a higher thermal conductivity than WO\({}_{3}\)-Ethylene Glycol nanofluid for a given \(\varphi\). TiO\({}_{2}\) has a lower intrinsic thermal conductivity than Al\({}_{2}\)O\({}_{3}\); however, the TiO\({}_{2}\) nanoparticles (25 nm) were smaller in size than the Al\({}_{2}\)O\({}_{3}\) nanoparticles (48 nm), resulting in a higher thermal conductivity for TiO\({}_{2}\) nanofluid. It was also suggested that the smaller size of the Fe nanoparticles (10 nm) in comparison to that of the WO\({}_{3}\) nanoparticles (38 nm) contributed to the higher thermal conductivity of Fe-Ethylene Glycol nanofluid in comparison to that of WO\({}_{3}\)-Ethylene Glycol nanofluid.