## 2 Thermophysical Properties
### Rheological Behaviour of Nanofluids
#### 2.4.1 Ethylene-Glycol-Based Nanofluids
For example, for a nanoparticle diameter equal to 16 nm and \(\varphi\) = 4 vol.%, the viscosities of water and EG-water were increased by 75% and 48%, respectively, compared to that of the base fluids. They affirmed that the observed phenomena could be related to the difference in the structure and thickness of the diffuse fluid layers around the nanoparticles in various base fluids, which affects the effective volume concentration and ultimately the viscosity of the suspensions. The Newtonian behaviour of diamond nanoparticles dispersed in a 45:55 EG-W solution was reported by [PERSON] et al. [53] for nanoparticle volume fractions varying from 0.5-2 vol.%. They indicated that  
fractions of copper oxide nanoparticles (\(d_{np}\) = 29 nm) had been measured by [PERSON] et al. [3] over a temperature range from \(-\)35 \({}^{\circ}\)C-50 \({}^{\circ}\)C. They noted that the nanofluid viscosity increased with the increase of \(CuO\) nanoparticle concentration, and as expected, it diminished as the temperature increased. As an example, at \(T\) = \(-\)35 \({}^{\circ}\)C, the viscosity increased from 0.736-3.291 Pa\(\cdot\)s by adding 1 vol.% and 5.9 vol.% of \(CuO\) nanoparticles to PG-water, respectively. The effective viscosity decreased by about 100-times when the temperature increased from \(-\)35 \({}^{\circ}\)C-50 \({}^{\circ}\)C at \(\varphi\) = 1 vol.%. All nanofluids exhibited a Newtonian behaviour for \(\varphi\) = [0-5.9 vol.%] in the whole temperature range considered. They proposed the following correlation covering all of the parameter range they considered:  
\[\mu_{nf}=Ae^{B\varphi} \ln A=736.9e^{-0.0199T} \tag{14}\] \[B=44.794-0.0765T\]  
[PERSON] et al. [4] investigated the rheological behaviour of copper oxide nanoparticles (\(\varphi\) = [0.025-1.2 vol.%]) dispersed in a 60:40 PG-water solution for \(T\) = [\(-\)15; 60 \({}^{\circ}\)C]. They reported also a Newtonian behaviour of the nanofluids under all the operating conditions. They obtained similar trends for the variations of the nanofluid viscosity as a function of \(T\) and \(\varphi\) as in [3]. It has also been confirmed later by [PERSON] and [PERSON] [66] for \(TiO_{2}\) nanoparticles dispersed in a 70:30 (% by weight) water-propylene-glycol mixture. These last authors proposed correlations for the dynamic viscosity of these nanofluids over \(\varphi\) = [0.1; 0.8%] and discussed the potential heat transfer benefits of their use in laminar and turbulent flow conditions. Viscosity measurements of zinc oxide nanoparticles dispersed in a 10:90 propylene-glycol and water mixture were recently conducted by [PERSON] et al. [71] for different temperatures (\(T\) = 30, 35, and 40 \({}^{\circ}\)C). They stated that the nanofluid viscosity increased by increasing the \(ZnO\) nanoparticle concentration up to 0.04 wt.% because of the increasing molecular interactions between \(ZnO\), water, and PG. After that, the viscosity decreased by increasing the nanoparticle concentration up to 0.08 wt.%, which may be attributed to stronger molecular interactions between \(ZnO\) with water and propylene-glycol and to lower molecular interactions between water and propylene-glycol. With further loading of \(ZnO\) nanoparticles (0.1 wt.%), the nanofluid viscosity started increasing again because of the nanoparticle agglomeration. [PERSON] et al. [7] studied experimentally the rheological behaviour of different dispersions of functionalized graphene nanoplatelets, f-GnPs (from 0.25-1 wt.%) in two propylene-glycol-water mixtures (10:90 and 30:70) within the temperature range [5-50 \({}^{\circ}\)C]. They reported also a Newtonian behaviour over all the concentrations, temperatures and shear rate ranges they considered. They found that a less viscous base fluid implied higher viscosity increments of the constituted nanofluids, especially at lower temperatures.