## 2 Thermophysical Properties
### Rheological Behaviour of Nanofluids
#### 2.4.1 Ethylene-Glycol-Based Nanofluids  
[PERSON] et al. [73] proposed viscosity measurements of \(SiO_{2}\) nanoparticles dispersed in an EG/water (60:40 by mass) mixture under sub-zero temperature operations. Their results showed that \(\upmu\) decreased monotonously from \(-35\)\({}^{\circ}\)C to \(50\)\({}^{\circ}\)C whatever the nanoparticle concentration between \(\varphi=2\) and 10 vol.%. \[\frac{\mu_{nf}}{\mu_{bf}}=-24.81+3.23T^{0.08014}e^{1.838}\varphi^{0.00234}-0.0006779T^ {2}+0.024\varphi^{3} \tag{11}\]  
[PERSON] et al. [52] studied the rheological behaviour of _TiO\({}_{2}\)_ nanoparticles (\(d_{np}=25\) nm) in pure ethylene-glycol for \(\varphi\) from 0.5-8 wt.%. After dispersing the nanoparticles into the base fluid, agglomerates were formed, and then, an ultrasonication treatment was done. Finally, they obtained a very stable nanofluid for over two months with nanoparticle diameters between 70 and 100 nm. They found that the _TiO\({}_{2}\)_-EG nanofluid exhibited a Newtonian behaviour over a shear rate range between 0.5 and 10\({}^{4}\) s\({}^{-1}\) and temperature varying between 20 \({}^{\circ}\)C and 60 \({}^{\circ}\)C. They noted that the nanofluid viscosity depended strongly on temperature and nanoparticle concentration, as shown in Figure 4. \(\upmu\) is a decreasing function of \(T\) in a logarithmic way and increases with \(\varphi\) following a second-order polynomial. For instance, adding 8 wt.% _TiO\({}_{2}\)_ nanoparticles increases the EG viscosity by 22.75%. They stated that the agglomeration phenomenon could be one of the key parameters responsible for the increase in viscosity. Their results compare fairly well with the following empirical correlation based on the aggregate diameter \(d_{agg}\):  
\[\frac{\mu_{nf}}{\mu_{bf}}=\left(1-\frac{\varphi}{0.605}\left(\frac{d_{agg}} {d_{np}}\right)\right)^{-1.5125} \tag{12}\]  
where the value 0.605 represents the maximum packing factor and \(d_{agg}=3.34d_{np}\). The rheological behaviour of _MgO_-EG nanofluid has been investigated by [PERSON] et al. [57] at ambient temperature. The experimental measurements showed a linear relation between the shear stress and the shear rate, which indicated a Newtonian behaviour of the nanofluid. They mentioned that the nanofluid viscosity decreased rapidly with temperature. However, it increased, at the same time, considerably with the nanoparticle volume fraction. An experimental investigation of the rheological properties of copper oxide nanoparticles suspended in a 60:40 ethylene-glycol and water mixture has been conducted by [PERSON] et al. [70] for temperatures ranging from \(-35\)\({}^{\circ}\)C-\(50\)\({}^{\circ}\)C and particle volume concentrations up to 6.12%. They noted that the base fluid freezes at \(-45\)\({}^{\circ}\)C, and therefore, the last measurement was done at \(-35\)\({}^{\circ}\)C. Their results revealed that the _CuO_-based nanofluids exhibited a Newtonian behaviour under all experimental conditions. They observed that the nanofluid viscosity increased with the increase of the nanoparticle concentration. For instance, at \(T=-35\)\({}^{\circ}\)C and \(\varphi=6.12\) vol.%, the viscosity of the base fluid increased by a factor of four. They also noted that the nanofluid viscosity decreased exponentially as the temperature increased. [PERSON] et al. [59] assessed the viscosity variations of water and EG-water mixture when adding 4 vol.% _SiC_ nanoparticles. They showed that the relative viscosity decreased with the increase of the  
Figure 4: Influence of the **(a)** temperature and **(b)** nanofluid volume fraction on the dynamic viscosity of _TiO\({}_{2}\)_ nanoparticles dispersed in pure ethylene-glycol. After [52], with permission from Elsevier. average particle size in both EG-water and water suspensions. However, at the same \(SiC\) nanoparticle volume fraction, the relative viscosity increase was smaller in the EG-water suspension than in pure water-based nanofluids, especially for suspensions containing smaller nanoparticles.