## 2 Nanofluid Thermal Conductivity
### Effects of Carbon Nanotubes on Nanofluid Thermal Conductivity
By functionalizing the nanotubes, the need for surfactant was eliminated, thus preventing any negative effects that a surfactant may have. It was observed that the thermal conductivity increased non-linearly with temperature. It was also observed that the thermal conductivity increased with nanotube concentration. It was suggested that this increase was a result of a greater area for heat transfer with a greater concentration. Similarly, [PERSON] et al. [58] studied the thermal conductivity of 50-50 water-ethylene mixture containing COOH functionalized SWCNTs. It was observed that the thermal conductivity increased non-linearly with temperature, with a greater slope in the increase of temperature, for nanofluids have a higher nanotube concentration. It was suggested that the increase with temperature was a result of Brownian motion. Thus, at higher concentrations, the frequency of collisions of the nanoparticles increased, leading to greater enhancement in thermal conductivity. It was also observed that the nanofluid thermal conductivity increased with nanotube concentration, having a greater slope of increase below \(\varphi=0.125\%\). It was suggested that at lower concentrations, the thermal conductivity increase with nanotube concentration was a result of increased interaction between the nanotubes, while at higher concentrations, the nanotubes may have formed larger chains, leading to a lower surface area to volume ratio, and therefore a less significant increase in thermal conductivity. Additionally, the thermal conductivity of nanofluid composed of Al\({}_{2}\)O\({}_{3}\) nanoparticles dispersed in the same base liquid was compared with the thermal conductivity of the SWCNT nanofluid. It was observed that the thermal conductivity of the nanofluid containing nanotubes was significantly higher. It was suggested that this was a result of the much higher thermal conductivity of the SWCNTs in comparison to Al\({}_{2}\)O\({}_{3}\), and the higher specific surface area of the SWCNTs. However, some experimental data has been collected which shows a linear increase in the thermal conductivity of nanotube nanofluids with temperature. [PERSON] et al. [6] studied the thermal conductivities of nanofluids composed of short SWCNTs, long SWCNT, and MWCNTs dispersed in water. It was observed that the thermal conductivity increased almost linearly with both temperature and nanotube concentration. It was also observed that for a given temperature and nanotube concentration, the long SWCNTs had the highest thermal conductivity, while the MWCNTs had the lowest. It was suggested that this was a result of the higher aspect ratio and surface area of the long SWCNTs. From the above discussed experimental findings, it can be suggested that the addition of carbon nanotubes to a base liquid results in significant thermal conductivity enhancement with both temperature and nanotube concentration. It can also be suggested that the increase in thermal conductivity with nanotube concentration differsfrom that of nanofluids containing metal and metal-oxide particles, by increasing non-linearly at low concentrations. However, further experimentation should be completed in order to determine whether the addition of surfactant or an oxidation treatment of the nanotubes leads to greater stability and thermal conductivity of the nanofluid. Figure 25 shows the effect of various surfactants on the thermal conductivity of MWCNT-water nanofluid as a function of nanoparticle volume concentration, \(\varphi\). It is observed that the nanofluid containing Gum Arabic surfactant has a significantly higher thermal conductivity than the nanofluids containing SDS, SDBS, and PVP surfactants. However, it is observed that in each case, the thermal conductivity increases almost linearly with nanoparticle concentration, which contradicts with the statement of [PERSON] et al. [47], that the thermal conductivity of nanofluids containing carbon nanotubes increases non-linearly, even at low concentrations.