## 2 Nanofluid Thermal Conductivity
### Effects of Nanoparticle Shape on Nanofluid Thermal Conductivity  
Researchers have observed that nanofluids having nanoparticles with greater surface area to volume ratios, have higher thermal conductivities [25; 43]. [PERSON] et al. [25] studied the thermal conductivity of TiO\({}_{2}\)-water nanofluid using cubic (51.87 nm), rod (43.08 nm), and spherical (22.9 nm) nanoparticles. It was observed that the nanofluid containing cubic nanoparticles had the highest thermal conductivity and that containing spherical nanoparticles had the lowest, which is shown in Figure 10. It was suggested that the significant impact of nanoparticle shape on thermal conductivity was related to the difference in surface area. Some benefits of using spherical nanoparticles in nanofluids include  
Figure 8: Variation of Al\({}_{2}\)O\({}_{3}\)–Ethylene Glycol nanofluid thermal conductivity as a function of temperature, for \(\varphi=1\%\) and \(\varphi=3\%\), with 11 nm diameter and 150 nm diameter particles. Figure 9: Variation of Au–water nanofluid thermal conductivity at room temperature as a function of nanoparticle size, for a nanoparticle volume concentration of \(\varphi=0.00026\%\). their superior stability to other shapes and fewer issues with clogging. A downside to using cubic nanoparticles is high cost. Similarly, using the transient hot-wire method, [PERSON] et al. [16] tested the thermal conductivity of TiO\({}_{2}\)-water nanofluid containing rod-shaped and spherical nanoparticles. The spherical nanoparticles had an average diameter of 15 nm. The rod-shaped nanoparticles had an average diameter of 10 nm and an average length of 40 nm. Cetyl trimethyl ammonium bromide (CTAB) was used as a surfactant to create a more stable nanofluid. For a given particle concentration, it was observed that the nanofluid containing rod-shaped nanoparticles had a higher thermal conductivity. It was suggested that this difference was related to the larger size of the rod-shaped nanoparticles in comparison to the spherical nanoparticles. [PERSON] et al. [24] measured the thermal conductivity of Al\({}_{2}\)O\({}_{3}\)-water nanofluid, using brick, platelet, and blade shaped nanoparticles. It was observed that nanofluid containing brick-shaped nanoparticles had the highest enhancement in thermal conductivity, while nanofluid containing blade-shaped nanoparticles had the lowest. It was suggested that thermal conductivity is related to suspension stability which is affected by nanoparticle shape. The nanofluid containing brick-shaped nanoparticles had the highest stability, while nanofluid containing blade-shaped nanoparticles had the lowest stability. [PERSON] et al. [43] measured the thermal conductivity of nanofluid composed of Al\({}_{2}\)O\({}_{3}\) nanoparticles dispersed in 50:50 volume Ethylene Glycol-water using the transient hot-wire method. It was observed that nanofluid containing cylinder-shaped nanoparticles (80 \(\times\) 10 nm) had the highest thermal conductivity, followed by that containing brick-shaped nanoparticles (40 nm). The nanofluid containing blade-shaped (60 \(\times\) 10 nm) nanoparticles had a lower thermal conductivity than those of cylindrical and brick-shaped nanofluids. It was suggested that increased nanoparticle surface area leads to higher thermal conductivity. [PERSON] et al. [40] conducted experiments to determine the thermal conductivity of ZnO-water nanofluid using both spherical and rectangular nanoparticles. The results are shown in Figure 11. The spherical nanoparticles had an average size of 20-40 nm, and rectangular nanoparticles had an average size of 90-210 nm. For a given volume fraction and temperature, the thermal conductivity of nanofluid containing rectangular nanoparticles was higher. It was suggested that the relationship between thermal conductivity and nanoparticle shape was related to the change in effective aggregate radius of the nanofluid with the change of nanoparticle shape. It was suggested that nanoparticle shape has a stronger influence on thermal conductivity than nanoparticle size.