## 2 Thermophysical Properties
### Thermal Conductivity
#### 2.3.1 Ethylene-Glycol-Based Nanofluids
Their experimental measurements can be correlated by a modified version of the Maxwell correlation:  
Figure 2: Thermal conductivity enhancement for \(TiO_{2}\) nanoparticles dispersed in pure ethylene-glycol at two temperatures 20 and 40 \({}^{\circ}\)C. After [52], with permission from Elsevier. \[k_{nf}=k_{bf}\frac{k_{np}+2k_{bf}-2(k_{bf}-k_{np})\varphi}{k_{np}+2k_{bf}+(k_{bf}- k_{np})\varphi}+5\times 10^{4}\beta\varphi\rho_{bf}Cp_{bf}f(T,\varphi)\sqrt{\frac{ \kappa T}{\rho_{np}d_{np}}} \tag{7}\]  
\[f(T,\varphi)=(2.8217\times 10^{-2}\varphi+3.917\times 10^{-3})\left(\frac{T}{T_{0} }\right)+(-3.0669\times 10^{-2}\varphi-3.91123\times 10^{-3}) \tag{8}\]  
where \(\beta\) is a function of \(\varphi\), which depends on the nanoparticle type, \(\kappa\) the Boltzmann constant and \(T_{0}=273\) K. This correlation is valid for three nanoparticle diameters (29, 53, and 77 nm) over a wide range of temperature \(298<T<363\) K. In terms of volume fraction, it varies between 1% and \(\varphi_{max}\), where \(\varphi_{max}=10\), 7, and 6% for \(Al_{2}O_{3}\), \(ZnO\), and \(CuO\) nanoparticles, respectively. [PERSON] et al. [58] investigated the thermal conductivity behaviour of \(SiC\) nanoparticle suspensions. Spherical \(SiC\) particles with an average diameter of \(d_{np}=26\) nm and cylindrical \(SiC\) particles with an average diameter of 600 nm were dispersed in water and ethylene-glycol separately. The measured data clearly indicated that the ratio of thermal conductivity (ratio of thermal conductivity of the mixture to that of the base liquid) depended on the nanoparticle concentration, size, and shape. They noticed that for the same nanoparticle morphology, the thermal conductivity ratios were independent of the base liquid, but the absolute value of the nanofluid thermal conductivity was proportional to that of the base liquid. A comparative study on the thermal performance of 4 vol.% \(SiC\) nanoparticles in water and 50:50 ethylene-glycol-water mixture was performed by [PERSON] et al. [59]. They noted that the thermal conductivity of \(SiC\)/EG-W nanofluids increased by increasing the particle size, which was similar to the behaviours reported for \(SiC\)-water nanofluids, but with different increment values. For example, at the same nanoparticle concentration, the thermal conductivity enhancement of \(SiC\)/EG-W increased from 11.5-17% by increasing the particle size from 16-90 nm, respectively, as displayed in Figure 3. The results indicated that the addition of \(SiC\) nanoparticles in EG-W resulted in a 4-5% higher enhancement than in pure water at the same operating conditions. The authors referred their findings to the lower values of the interfacial thermal resistance (better wettability) in EG-W than in water-based nanofluids. They mentioned also that such an effect could not be explained simply by the lower thermal conductivity of the EG-W base fluid since the difference in terms of the enhancement values expected from the effective medium theory was less than 0.1%. Figure 3: Comparison of the thermal conductivity enhancement in 4 vol.% SiC nanofluids with ethylene-glycol (EG)/\(H_{2}\)O and \(H_{2}\)O as base fluids at various particle sizes. After [59], with permission from AIP. For a suspension consisting of ethylene-glycol and carbon nanotubes (CNTs) at \(\varphi\) = 1 vol.%, 12.6%, and 12.4% thermal conductivity enhancements were reported by [PERSON] et al. [60] and [PERSON] et al. [61], respectively. They noted that the mixture thermal conductivity increased monotonously with the CNT volume fraction. For example, the EG thermal conductivity was enhanced by 1.6% and 12.4% compared to that of pure EG by adding 0.2 vol.% and 1 vol.% CNTs, respectively [61]. [PERSON] et al. [62] conducted measurements of the effective thermal conductivity of single-walled carbon nanotubes (SWCNTs) dispersed in ethylene-glycol. They reported that the thermal conductivity of the medium enhanced with respect to the nanotube loading.