## 2 Nanofluid Thermal Conductivity
### Effects of Carbon Nanotubes on Nanofluid Thermal Conductivity  
Researchers have observed significant enhancements in nanofluids containing nanotubes, also observing that the thermal conductivities of nanofluids containing carbon nanotubes increases non-linearly with nanoparticle volume concentration, even at low concentrations, which differs from nanofluids containing metal and metal oxide nanoparticles. Carbon nanotubes are made up of a series of hollow carbon molecules, which together form either a singular cylinder or multiple concentric cylinders. The thermal conductivity of carbon nanotubes is dependent upon their diameters. Therefore, it was suggested that the variance in experimental data between different studies may be a result of the varying diameters of nanotubes [2]. [PERSON] et al. [47] studied the thermal conductivity of multi-walled carbon nanotube (MWCNT)-synthetic poly (\(\alpha\)-olefin) oil suspensions using the transient hot-wire method. It was observed that the thermal conductivity increased significantly, having a non-linear relationship, with nanotube volume concentration. It was suggested that the significant increase was a result of the organized structure at the solid-liquid interface allowing more efficient heat conduction. Although the theoretical models suggested a linear relationship between thermal conductivity and nanoparticle concentrations at the tested concentrations, it was suggested that the non-linear relationship was caused by the size and shape of the nanotubes. It was observed that nanotubes lead to greater enhancement in thermal conductivity of nanofluids than other nanostructured materials, reaching an enhancement of 2.5% at a nanoparticle volume concentration of \(\varphi=1\%\). Similarly, [PERSON] et al. [2] measured the thermal conductivity of MWCNT-water nanofluid using a KD2 Pro Thermal Property meter, which worked based on the transient hot-wire method. Due to their hydrophobic surface, carbon nanotubes are prone to aggregation in water. Therefore, SDBS was added as a surfactant in a concentration of 20 \(W\%\) with respect to the MWNTs. The SDBS was able to maintain stability in the nanofluid up to approximately 60-70 \({}^{\circ}\)C. It was observed that the thermal conductivity of the nanofluid increased with temperature, having a linear relationship at temperatures below 30 \({}^{\circ}\)C, and a non-linear relationship at higher temperatures. It was observed that the thermal conductivity also increased with nanoparticle volume concentration, having a non-linear relationship even at low concentrations. This observation is consistent with the observations of [PERSON] et al. [47]. The non-linear increase at low concentrations differs from the common linear increase at low nanoparticle concentrations for nanofluids containing metal and metal-oxide nanoparticles. It was suggested  
Figure 23: Variation of the thermal conductivity of CuO–water nanofluid at various nanoparticle volume concentrations, as a function of temperature. that Brownian motion does not significantly contribute to the thermal conductivity enhancement in nanotube nanofluids. However, it was suggested that the ordered structure at the solid-liquid interface caused by interfacial layering allowed for more efficient heat transfer and, therefore, enhanced thermal conductivity. It was also suggested that nanotube networking contributed to the enhanced thermal conductivity, and may have also allowed ballistic transport of energy carriers, which also may have contributed to the increase in thermal conductivity. Additionally, [PERSON] et al. [52] studied the thermal conductivity of MWCNT-water suspensions at low nanoparticle volume concentrations, below \(\varphi=0.05\%\). Experimental data was collected using a hot-disk TPS 500 Thermal Constant Analyzer. SDS was used as a surfactant in small concentrations, in order to prevent agglomeration of the nanotubes.