## 3 Heat Transfer Enhancement
### Numerical Simulations  
The purpose of the present section is to report on the most important numerical results regarding the thermal and hydraulic performances of EG- and PG-based nanofluids in realistic configurations. The interested reader can refer to the review of [PERSON] (2018) for a detailed description of the numerical methods currently used to model the multiphase nature of nanofluids. Turbulent flow and heat transfer of three different nanofluids, \(Al_{2}O_{3}\),\(CuO\), and \(SiO_{2}\), based on a 60:40 (by mass) EG/W mixture flowing through a circular tube under constant heat flux conditions have been numerically studied by [PERSON] et al. [PERSON] et al. (2018). The heat transfer coefficient \(h\) increased by increasing both the nanoparticle concentration and the Reynolds number. As an example, at \(Re=20\),000, the Nusselt number was enhanced by about 1.35-times by adding 6. vol.% of \(CuO\) nanoparticles compared to the base fluid. For the same operating conditions, the \(CuO\) nanofluid exhibited higher heat transfer performances followed successively by the \(Al_{2}O_{3}\)- and \(SiO_{2}\)-based nanofluids. The performances of finned tube heating units with nanofluids have been compared to that of a conventional HTF composed of 60% ethylene-glycol and 40% water by [PERSON] and [PERSON] and [PERSON] (2018), \(Al_{2}O_{3}\) and \(CuO\) nanoparticles were suspended in the 60:40 EG/W mixture at different concentrations ranging from 1-4 vol.%. The incoming fluid conditions were typical of heating systems in subarctic and Arctic regions. The results indicated that finned tube heating performance was enhanced by employing nanofluids as a heat transfer medium. For instance, their model predicted enhancements by 11.6% and 8.7% in terms of the finned tube heating output by adding 4 vol.% of \(Al_{2}O_{3}\) and \(CuO\) nanoparticles to EG-water, respectively. They noted also that the pumping power required for a given heating output and a given finned tube geometry was reduced with both the \(Al_{2}O_{3}\)/EG-water and the \(CuO\)/EG-water nanofluids compared to the base fluid. For all these fluids, the finned tube with \(\varphi=4\) vol.% of \(Al_{2}O_{3}\) nanoparticles in the EG-water mixture offered the lowest liquid pumping power. [PERSON] et al. [PERSON] et al. (2018) investigated the heat transfer enhancement in an automotive car radiator operating with copper/EG-based nanofluids. Their analysis showed that such nanofluids enhanced the overall heat transfer rate in an engine cooling system. They noted that the heat transfer coefficient \(h\) increased by increasing the nanoparticle volume fraction. At a Reynolds number \(Re=5000\), adding 2 vol.% of copper nanoparticles to EG was found to enhance the heat transfer rate by roughly 4% and reduce the air frontal areas by nearly 19%. However, for the same flow rate, a 12.13% increase in the pumping power was reported. A three-dimensional laminar flow and the associated heat transfer were investigated numerically by [PERSON] et al. [9] for two different nanofluids, composed either of \(Al_{2}O_{3}\) or \(CuO\) nanoparticles dispersed into a 60:40 EG/W mixture. The geometry corresponds to flat tubes within a car radiator. The results showed that at various Reynolds numbers, the heat transfer coefficient, the friction factor and the pressure drop increased by increasing the nanoparticle volume concentration. However, they mentioned that due to the reduced volumetric flow needed for the same amount of heat transfer, the required pumping power diminished. As an example, for the same amount of heat transfer, the pumping power requirement was 82% lower for \(Al_{2}O_{3}\) nanofluid at \(\varphi=10\) vol.% and 77% lower for \(CuO\) nanofluid with \(\varphi=6\) vol.% with respect to the base fluid. They proposed new Nusselt number correlations for both the entrance and fully-developed flow regions.