## 2 Nanofluid Thermal Conductivity
### Effects of Temperature on Nanofluid Thermal Conductivity  
Researchers have conducted experiments to determine the effects of temperature on the thermal conductivity of nanofluids, concluding that the thermal conductivity of nanofluids increases with temperature [5,8,10,12,13,22,25,28,30,31,33,38,39,40,41]. For example, the thermal conductivity of Al\({}_{2}\)O\({}_{3}\)-water and CuO-water nanofluids was measured and the results indicated that the rate of  
Figure 19: Variation of the thermal conductivity of water-based nanofluids at room temperature as a function of nanoparticle volume concentration, \(\varphi\). Figure 20: Variation of thermal conductivity of water-based nanofluids at room temperature as a function of nanoparticle volume concentration, \(\varphi\), at concentrations below \(\varphi=1\%\). enhancement of the effective thermal conductivity increased significantly with respect to increasing temperature [8; 41]. Also, [PERSON] et al. [13] measured the thermal conductivities of magnetic Fe\({}_{3}\)O\({}_{4}\) nanoparticles dispersed in 20%:80%, 40%:60% and 60%:40% by weight Ethylene Glycol/water-based nanofluids. It was observed that the thermal conductivity increased with temperature [13]. In addition, using a KD2 Pro analyzer which worked based on the transient line heat source method, [PERSON] et al. [31] measured the thermal conductivity of nanodiamond-water nanofluid as a function of temperature. A significant increase in thermal conductivity with the increase of temperature was observed. In the same way, [PERSON] et al. [39] studied the thermal conductivity of FeC-water nanofluid. An increase in thermal conductivity with temperature was observed. Similarly, [PERSON] et al. [22] measured the thermal conductivity of Al\({}_{2}\)O\({}_{3}\)-water nanofluid and observed an increase with the increase of temperature. It was suggested that this increase was a result of intensified Brownian motion at higher temperatures. Brownian motion is caused by the random collisions of liquid molecules resulting in the random motion of nanoparticles within the base liquid, which in turn leads to greater heat transfer. It was also suggested that the increased microscopic motion caused by Brownian, van der Waals, and electrostatic forces had a significant impact on the increase in thermal conductivity. Also, using a KD2 Pro instrument, [PERSON] et al. [33] measured the thermal conductivity of TiO\({}_{2}\)-water nanofluid as a function of temperature. The results are shown in Figure 21. For each tested nanoparticle volume fraction, the thermal conductivity increased with temperature. The results showed that the temperature had a stronger influence on thermal conductivity at higher temperatures. It was suggested that this relationship was related to enhanced Brownian motion at higher temperatures. Using the same method, [PERSON] et al. [12] measured the thermal conductivities of Al\({}_{2}\)O\({}_{3}\)-water and Al\({}_{2}\)O\({}_{3}\)-Ethylene Glycol nanofluids at temperatures ranging from 10-70 \({}^{\circ}\)C. For both nanofluids, at a given nanoparticle volume concentration, the thermal conductivity increased with temperature. The increase was less significant for Ethylene Glycol-based nanofluid. It was suggested that the increase in thermal conductivity with temperature was related to more significant Brownian motion at higher temperatures. It was suggested that water-based nanofluid would be a more appropriate choice for applications involving a significant temperature increase, because the thermal conductivity increased almost constantly with the increase of both temperature and nanoparticle concentration. Using the transient hot-wire method, [PERSON] et al. [5] measured the thermal conductivity of Ag-water nanofluids having nanoparticle volume concentrations less than 1%. It was observed that the thermal conductivity increased with the increase of temperature. It was suggested that the thermal conductivity of nanofluids has a stronger dependence on temperature than base fluid thermal conductivity.