## 2 Nanofluid Thermal Conductivity
### Effects of Nanoparticle Size on Nanofluid Thermal Conductivity  
Researchers have observed that a greater surface area to volume ratio in nanofluids, resulting from nanoparticles of smaller sizes, leads to increased thermal conductivity [3; 4; 28; 35; 36]. [PERSON] et al. [11] measured the thermal conductivities of Al\({}_{2}\)O\({}_{3}\) and CuO nanoparticles dispersed in water, Ethylene Glycol, engine oil, and vacuum pump fluid. Measurements were obtained using the one-dimensional steady-state parallel-plate method. An increase in thermal conductivity with the decrease of nanoparticle size was observed. It was suggested that this relationship could be partially explained by stochastic and electrostatic forces only, having a strong influence on very small particles. Also, [PERSON] et al. [7] measured the thermal conductivity of graphene-water nanofluid, using 5000 nm graphene, 15,000 nm graphene, and oxidized 5000 nm graphene. The thermal conductivity of the \begin{table}
\begin{tabular}{c c c} \hline \hline
**Reference** & **Nanoparticle Material** & \begin{tabular}{c} **Nanoparticle Thermal Conductivity at Room** \\ **Temperature W/_m.k_** \\ \end{tabular} \\ \hline [PERSON] et al. [7] (2014) & Graphene & 3000 \\ \hline [PERSON] et al. [23] (2017) & Ag & 429 \\ \hline [PERSON] et al. [37] (2017) & \begin{tabular}{c} SiO\({}_{2}\) \\ ZrO\({}_{2}\) \\ \end{tabular} & 1.4 \\ \hline [PERSON] et al. [26] (2010) & \begin{tabular}{c} MgO \\ TiO\({}_{2}\) \\ ZnO \\ \end{tabular} & 8.4 \\  & \begin{tabular}{c} ZnO \\ Al\({}_{2}\)O\({}_{3}\) \\ SiO\({}_{2}\) \\ \end{tabular} & 36 \\ \hline [PERSON] et al. [34] (2011) & SiC & 490 \\ \hline [PERSON] et al. [4] (2008) & \
\begin{tabular}{c} Al\({}_{2}\)Cu \\ Ag\({}_{2}\)Al \\ \end{tabular} & 319 \\ \hline [PERSON] et al. [28] (2010) &
\begin{tabular}{c} Al \\ Cu \\ \end{tabular} & 204 \\ \hline [PERSON] et al. [29] (2016) & Nanodiamond & 1000 \\ \hline [PERSON] et al. [46] (2015) & CuO & 30 \\ \hline [PERSON] et al. [47] (2001) & Multi-walled Carbon Nanotube & 2000 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Nanoparticle thermal conductivity. Figure 7: Variation of Ethylene Glycol-based nanofluid thermal conductivity as a function of nanoparticle volume concentration, \(\varphi\), for different nanoparticles at room temperature. 5000 nm graphene nanofluid was higher for a given nanoparticle volume concentration. It was suggested that the thermal conductivity of nanofluids increases with the decrease of nanoparticle size. In addition, [PERSON] et al. [28] measured the thermal conductivities of Al\({}_{2}\)O\({}_{3}\)-water and Al\({}_{2}\)O\({}_{3}\)-Ethylene Glycol nanofluids as a function of nanoparticle size. The results, which are shown in Figure 8, indicated an increase in thermal conductivity with the decrease of nanoparticle size. It was suggested that the thermal conductivity enhancement was a result of the increased surface area to volume ratio, A/V, with the decrease of nanoparticle size, allowing more effective heat transfer to the base fluid. It was also suggested that increased Brownian motion with smaller nanoparticles led to the increased thermal conductivity. It was observed that the magnitude of Brownian motion was on the order of \(10^{-4}\) (\(m/s\)) for Al\({}_{2}\)O\({}_{3}\)-water nanofluid containing 150 nm particles and increased to the order of \(10^{-2}\) (\(m/s\)) for Al\({}_{2}\)O\({}_{3}\)-water nanofluid containing 11 nm particles. Using a KD2 Pro Thermal Property Analyzer, [PERSON] et al. [3] measured the thermal conductivity of Fe-water nanofluid as a function of nanoparticle volume concentration (\(\varphi\)), using 37 nm, 71 nm, and 98 nm Fe particles. The KD2 Pro Thermal Property Analyzer works based on the transient short hot-wire method. It was observed that for a given \(\varphi\), the thermal conductivity increased with the decrease of nanoparticle size. It was suggested that this increase was caused by the increased interfacial area between nanoparticles and base liquid for smaller particle sizes.