## 3 Results and Discussion
### Thermal Conductivity  
The experimental values of thermal conductivity obtained for the base fluids (W, PG:W and PG) and shown in Table 2 exhibit strong concordance with the literature data. Average deviations of 0.5% (W), 0.9% (PG:W) and 1.2% (PG) were obtained with respect to [PERSON] et al. (2010), [PERSON] (2011) and Sun and Teja (2012), respectively. Figure 4 and Table 2 show the obtained experimental thermal conductivities for the different nanofluid sets. A decreasing trend with the increasing size of cluster is observed, with maximum thermal conductivity increases of 2.6%, 3.9% and 4.2% for W-, PG:W- and PG-based nanofluids, respectively. It should be noted that the reported behaviour is evidenced for all the temperatures analysed. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Nanofluid Set**} & \multirow{2}{*}{**Temperature [K]**} & \multicolumn{4}{c}{**Thermal Conductivity [W/(m\(\cdot\)K)]**} \\ \cline{3-6}  & & **Base Fluid** & **0.50 wt\% CoFe\({}_{2}\)O\({}_{4}\)** & **0.50 wt\% CoFe\({}_{2}\)O\({}_{4}\)** & **0.50 wt\% CoFe\({}_{2}\)O\({}_{4}\)** \\  & & & **97 nm Nanofluid** & **155 nm Nanofluid** & **192 nm Nanofluid** \\ \hline \multirow{2}{*}{W-based} & 293.15 & 0.601 & 0.616 & 0.607 & 0.605 \\  & 303.15 & 0.619 & 0.635 & 0.627 & 0.625 \\  & 313.15 & 0.636 & 0.653 & 0.645 & 0.641 \\ \hline \multirow{2}{*}{PG:W-based} & 293.15 & 0.418 & 0.433 & 0.429 & 0.424 \\  & 303.15 & 0.426 & 0.443 & 0.437 & 0.432 \\  & 313.15 & 0.433 & 0.450 & 0.443 & 0.438 \\ \hline \multirow{2}{*}{PG-based} & 293.15 & 0.200 & 0.207 & 0.204 & 0.202 \\  & 303.15 & 0.199 & 0.206 & 0.204 & 0.202 \\ \cline{1-1}  & 313.15 & 0.197 & 0.205 & 0.202 & 0.200 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental thermal conductivity of the base fluids and the difference-based nanofluids for various cluster sizes and temperatures. Figure 3: Average \(Z\)-size versus time from preparation for the 0.10 wt% (**a**) W-based and (**b**) PG:W-based static and shaken nanofluids. Several authors reported an indirect relation between thermal conductivity of nanofluids and size of metal oxide nanoparticles: [PERSON] et al. [43], [PERSON] and [PERSON] [44], [PERSON] et al. [45], [PERSON] et al. [46] or [PERSON] et al. [47] for Al\({}_{2}\)O\({}_{3}\)/water nanofluids; [PERSON] et al. [48] and [PERSON] et al. [49] for TiO\({}_{2}\)/water nanofluids; [PERSON] et al. [50] for TiO\({}_{2}\)/ethylene glycol (EG) and ZnO/EG nanofluids; [PERSON] et al. [51] for Al\({}_{2}\)O\({}_{3}\) dispersions in an EG and W  
Figure 4: Thermal conductivities as a function of size of cluster for W (**a**), PG:W (**b**) and W-based (**c**) nanofluids. mixture at 50:50 wt%; and [PERSON] and [PERSON] [52] for Al\({}_{2}\)O\({}_{3}\), Cu\({}_{2}\)O and ZnO dispersions in an EG and W mixture at 40:60 wt%. Nevertheless, other authors reported the contrary trend, a direct relation between thermal conductivity of nanofluids and size of metal oxide nanoparticles: [PERSON] et al. [53] and [PERSON] et al. [54] for SiO\({}_{2}\)/water nanofluids; [PERSON] et al. [55] for TiO\({}_{2}\)/water nanofluids; [PERSON] et al. [56] for Al\({}_{2}\)O\({}_{3}\), SiO\({}_{2}\), TiO\({}_{2}\), ZrO\({}_{2}\), and CuO/water nanofluids; or [PERSON] et al. [57] for Al\({}_{2}\)O\({}_{3}\), SiO\({}_{2}\), TiO\({}_{2}\), ZnO, and CuO dispersions in a PG and W mixture at 40:60 wt%. Our previous work [24] on aqueous dispersions of Fe\({}_{3}\)O\({}_{4}\)/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) clusters also showed this direct relationship. [PERSON] and [PERSON] concluded recently, in a review [58], that most studies found that the thermal conductivity of nanofluids increases as the particle size decreases (especially below 100 nm). They also affirm that the theoretical explanations by interfacial fluid layering, particle clustering, Brownian motion and nano-convection justify this indirect relation between thermal conductivity and size.