## 2 Nanofluid Thermal Conductivity
### Effects of Carbon Nanotubes on Nanofluid Thermal Conductivity
The results are shown in Figure 24. It was observed that at \(\varphi=0.01\%\), the nanofluid thermal conductivity was only slightly higher than that of the base liquid for a given temperature. However, a much more significant enhancement was observed when the nanoparticle volume concentration was increased to \(\varphi=0.03\%\). It was suggested that at very low concentrations, carbon nanotubes will not form long chains. As the nanotube concentration increases, a percolation threshold will eventually be reached, at which the nanotubes will begin to network, and in turn the thermal conductivity enhancement will increase. It was suggested that in this experiment, the percolation threshold was at \(\varphi=0.03\%\). It was also suggested that at higher temperatures, Brownian motion significantly contributed to the increase in thermal conductivity, due to the inability of nanotubes to form chains at higher temperatures, as a result of nanofluid instability. [PERSON] et al. [53] measured the thermal conductivity of MWCNT-water nanofluid using a KD2 Pro Thermal Analyzer. For each given nanotube concentration, the thermal conductivity of the nanofluid containing no surfactant was measured and compared with the nanofluid containing 0.1 W% PVP surfactant. It was observed that in each case, the nanofluid containing surfactant had a higher thermal conductivity than that without. It was also observed that the thermal conductivity of the nanofluid increased with nanotube concentration. The low weight concentration of surfactant was chosen due to the surfactant resulting in a reduction of the thermal conductivity of water. It was suggested that the increased thermal conductivity with the addition of surfactant was a result of the surfactant increasing repulsive forces between the nanotubes, which minimized agglomeration, and  
Figure 24: Variation of the thermal conductivity of multi-walled carbon nanotube (MWCNT)–water nanofluid at various nanoparticle volume concentrations, as a function of temperature. thus prevented sedimentation. Therefore, it was suggested that the addition of surfactant, in order to increase the stability of nanofluids containing carbon nanotubes, is very important in producing carbon nanotube nanofluids with high thermal conductivity. In the same way, [PERSON] et al. [54] measured the thermal conductivity of MWCNT-water nanofluid containing Gum Arabic surfactant. It was observed that the optimal concentration of surfactant in increasing the stability of the nanofluid was 1.0-2.5 W\(\%\). At higher surfactant concentrations, it was observed that the nanofluid stability decreased due to the aggregation of the Gum Arabic molecules. With the optimal surfactant concentration, it was observed that the nanofluid thermal conductivity increased non-linearly with the nanotube concentration. However, it was stated that the exact mechanism for this non-linear increase is unknown. In addition, [PERSON] et al. [55] measured the thermal conductivity of oxidation treated carbon nanotube (CNT)-water nanofluids. A non-linear increase with concentration was observed. It was suggested that the non-linear trend was a result of the unpredictable size and shape of the nanotubes due to their tendency toward agglomeration as a result of their high aspect ratio. Also, using a KD2 Pro Thermal Properties Analyzer, [PERSON] et al. [56] measured the thermal conductivity of MWCNTs dispersed in hydrogenated oil-based drilling fluid. It was observed that the thermal conductivity enhancement was greater at higher nanoparticle concentrations than at lower concentrations. Thus, it was suggested that nanotube concentration plays a significant role in nanofluid thermal conductivity enhancement. In the same way, [PERSON] et al. [57] conducted experiments to study the thermal conductivity of single-walled carbon nanotubes (SWCNTs) dispersed in Ethylene Glycol. The nanotubes were functionalized with COOH groups, making them hydrophilic and, therefore, creating a more stable nanofluid.