## 2 Nanofluid Thermal Conductivity
### Effects of Concentration of Nanoparticles on Nanofluid Thermal Conductivity
[PERSON] et al. [7] measured the thermal conductivity of Graphene-water nanofluid using 5000 nm graphene, 15,000 nm graphene, and oxidized 5000 nm graphene. The thermal conductivity increased non-linearly with increased nanoparticle volume fraction for all, with the oxidized 5000 nm graphene having the highest rate of increase. [PERSON] et al. [36] measured the thermal conductivities of TiO\({}_{2}\)-water, Al\({}_{2}\)O\({}_{3}\)-water, Fe-Ethylene Glycol, and WO\({}_{3}\)-Ethylene Glycol nanofluids as a function of nanoparticle volume fraction. For each nanofluid, the thermal conductivity increased non-linearly with the nanoparticle concentration. [PERSON] et al. [11] measured the thermal conductivities of nanofluids composed of Al\({}_{2}\)O\({}_{3}\) and CuO nanoparticles dispersed in water, Ethylene Glycol, engine oil, and vacuum pump fluid. It was observed that the thermal conductivity increased non-linearly with the nanoparticle concentration for all nanofluids tested. [PERSON] et al. [4] measured the thermal conductivities of Ag\({}_{2}\)Al-water, Ag\({}_{2}\)Al-Ethylene Glycol, Al\({}_{2}\)Cu-water, and Al\({}_{2}\)Cu-Ethylene Glycol nanofluids. The results showed a non-linear increase in thermal conductivity with nanoparticle concentration. However, some researchers have observed a linear relationship between nanoparticle concentration and thermal conductivity [3; 9; 15; 22; 37; 38; 39; 40]. [PERSON] et al. [37] studied the thermal conductivities of Al\({}_{2}\)O\({}_{3}\)-water, SiO\({}_{2}\)-water and ZrO\({}_{2}\)-water nanofluids. It was observed that the thermal conductivity increased almost linearly with the nanoparticle concentration for all tested nanofluids. It was suggested that this increase was related to increased activity between nanoparticles and the base fluid. [PERSON] et al. [3] measured the thermal conductivity of Fe-water nanofluid as a function of nanoparticle concentration. An almost linear increase in thermal conductivity with the increase of nanoparticle volume concentration was observed. It was suggested that this relationship was a result of the agglomeration of nanoparticles creating particle-free areas in the base liquid with high thermal resistance [3]. [PERSON] et al. [38] measured the thermal conductivity of CuO-R-134a nanofluid. The results showed a linear increase in thermal conductivity with concentration. It was observed that the increase in thermal conductivity with concentration was much sharper than the increase with temperature. Using a KD2 Pro Thermal Properties Analyzer, [PERSON] et al. [39] studied the thermal conductivity of Fe-water nanofluid as a function of nanoparticle weight concentration. It was observed that for a given temperature, the thermal conductivity increased almost linearly with nanoparticle concentration. It was suggested that this increase could be partially explained by the increased interaction between particles at higher concentrations. [PERSON] et al. [9] measured the thermal conductivities of CuO-water and CuO-Ethylene Glycol nanofluids using a differential heat-flow C80D microcalorimeter containing special calorimetric vessels, which worked based on the steady-state coaxial cylinder method. It was found that for a given temperature, the relative thermal conductivity increased almost linearly with volume fraction. Using the transient short hot-wire method, [PERSON] et al. [15] measured the thermal conductivities of aluminum nitride (AIN)-Ethylene Glycol and AIN-propylene glycol nanofluids. An almost linear increase in thermal conductivity with nanoparticle concentration was observed. [PERSON] et al. [22] measured the thermal conductivity of Al\({}_{2}\)O\({}_{3}\)-water nanofluid using a KD2 Pro Thermal Property Analyzer. It was observed that the thermal conductivity increased almost linearly with nanoparticle volume concentration. Using the transient hot-wire method, [PERSON] et al. [40] measured the thermal conductivity of ZnO-water nanofluid as a function of nanoparticle concentration.