## 3 Results and Discussion
### Thermal Conductivity
Figure 4a,b evidence that a temperature rise leads to a thermal conductivity increase for both W- and PG:W-based nanofluids, respectively. These increases are around 6% for the former and 3-4% for the latter, which are very similar to those experienced by the corresponding base fluids. However, PG-based nanofluids show practically the same thermal conductivity values at 293.15 and 303.15 K (maximum 1% discrepancy within the temperature increase from 293.15 and 303.15 K), in accordance with the behaviour of pure PG. These findings are consistent with [PERSON] et al. [59], who conclude how thermal conductivity varies as a function of temperature follows that of the base fluid (in their work: water, EG and EG:W mixtures). Figure 5 shows that the nanofluid thermal conductivity improvements of the nine analysed nanofluids are practically independent of temperature. This behaviour is observed consistently across different base fluids, suggesting that the influence of temperature on microconvection effects and Brownian motion is minimal within the range studied. The stability of the nanofluid dispersions likely plays a crucial role in maintaining this temperature-independent behaviour, as a stable dispersion ensures consistent nanoparticle contribution across temperatures. This finding aligns with previous observations reported by our group [24; 60; 61], but it is important to note that the literature on this topic remains divided. Some studies corroborate our findings of temperature independence [62; 63; 64], while others report variations in conductivity enhancements with temperature [7; 65; 66; 67], particularly at higher temperature ranges. The observed stability in our experiments might be related to the controlled conditions and optimized dispersion quality, as high concentrations or elevated temperatures could compromise dispersion stability and result in varying thermal conductivity behaviour. Figure 5: _Cont._  
Figure 6 shows the improvements in nanofluids' thermal conductivity as a function of their own thermal conductivities. As can be seen, PG-based nanofluids show the highest enhancements for all cluster sizes, W-based nanofluids show the lowest enhancements, and PG:W-based nanofluids show intermediate improvements. This enables us to deduce that the lower the thermal conductivity of the base fluid, the greater the enhancement for the same size and mass concentration of a nanoadditive. A similar trend was previously reported by our group for the dynamic viscosity of nanofluids [68]: as the dynamic viscosity of the base fluid decreases, the enhancement for a given mass concentration of nanoadditive increases. The results evidenced here for thermal conductivity extend this theory to more transport properties of nanofluids. The specific surface area (SSA) of a particle is a function of size, shape, porosity, pore size distribution, and roughness. [PERSON] affirmed in a review [69] that several researchers accept that a smaller size of nanoparticle shows higher thermal-conductivity improvement, due to the high SSA observed. In order to explain the different trend here obtained for CoFe\({}_{2}\)O\({}_{4}\) cluster aqueous nanofluids, and in our previous work [24] for Fe\({}_{3}\)O\({}_{4}\)/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\) cluster aqueous nanofluids, Figure 7 shows the SSA of different-sized clusters of both types after being distributed in the base fluid (water) and then allowed to dry. In both cases, the higher thermal-conductivity increase corresponds to the clusters with higher SSA between those analysed: the smaller-sized clusters of CoFe\({}_{2}\)O\({}_{4}\) and the larger-sized clusters of Fe\({}_{3}\)O\({}_{4}\)/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\). Figure 5: Thermal conductivity enhancements as a function of size of cluster for (**a**) W, (**b**) PG:W and (**c**) PG-based nanofluids. The findings indicate a clear correlation between the thermal conductivity of the nanofluid and the SSA of the nanoadditive.