## 4 Application of Nanofluid in PTC
### Numerical Studies
#### 4.2.2 Investigations
Furthermore, the pressure drop through the receiver at 400 K and Reynolds number of approximately 650,000 increase roughly by more than 100% (from nearly 3000 to 7734 Pa/m). Finally, the minimum entropy generation rate at a certain Reynolds number was obtained by their model. This point is crucial as it shows the Reynolds number in which we have the maximum heat transfer irreversibility and minimum friction irreversibility. Specifically, there is a maximum 30% decrease in entropy generation rate at 6% volume fraction comparing to the base fluid. [PERSON] et al. [74] numerically modeled the thermal performance of PTC utilizing different metallic nanofluids. Syltherm 800 as base fluid and Cu, CuO, and Al2O3, and Ag with 5% volumetric concentrations were considered as studied nanofluids. The results suggested that silver is the best nanoparticle to be used to induce the best thermal enhancement followed by copper, cupric oxide and aluminum oxide with convection heat transfer enhancement of 36%, 33%, 27%, and 18%, respectively. They also concluded that as the density of the nanoparticle increases, the thermal performance enhances better. Finally 21% decrease in heat loss was observed. [PERSON] et al. [75] modeled and optimized the effect of different nanoparticles on the performance of the PTC used in a Rankin cycle. CuO, SiO2, TiO2, and Al2O3 were dispersed in Therminol-55 at 2-5.5 vol. % for the numerical investigation. The results suggested that using nanofluids in the solution caused slight enhancement in thermal efficiency. Finally, the optimization results revealed that using Al2O3/Therminol-55, caused the maximum enhancement in overall exergy efficiency of the system by 11%. [PERSON] et al. [76] modeled Al2O3/Synthetic oil nanofluid up to 5% volumetric concentration to investigate and optimize thermal behavior of the PTC. They reported an approximately 7% enhancement in heat transfer coefficient when 5% volumetric concentration of Al2O3 was used comparing with Synthetic oil only. [PERSON] et al. [77] used Al2O3/Synthetic oil nanofluid to study the effect of the nanofluid on PTC performance numerically. Their results showed that the thermal efficacy and pressure drop almost stays the same. However, the maximum increase of approximately 60% was observed at 5% volumetric concentration of Al2O3 for convection heat transfer coefficient. [PERSON] et al. [78] conducted a CFD simulation on the receiver system of PTC using Al2O3/Synthetic oil nanofluid as working fluid at 5% volumetric concentration. The enhancement of 14.3% was reported in the system thermal efficiency. [PERSON] et al. [59] carried out a CFD simulation aiming to investigate the optimum thermal and thermodynamic performance of PTC. Three different nanofluids, Cu, Ag, and Al2O3 dispersed in Therminol VP-1, at different volume fractions, 1-6%, were used. It was found that the Ag/Therminol VP-1 had the highest thermal efficiency enhancement at 6% volumetric concentration by 13.9%, followed by Cu/Therminol VP-1 and Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1 by 12.5% and 7.2% enhancement, respectively. Also, it was shown that for a particular volume fraction, a maximum thermal efficiency point could be achieved at a certain Reynolds number or flow rate. Furthermore, convection heat transfer enhancement at 6% volumetric concentration is observed to be 7.9%, 6.4%, and 3.9% for Ag/Therminol VP-1 Cu/Therminol VP-1 and Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1, respectively. Finally, the entropy generation rate at lower Reynolds number was observed to reduce as the volume fraction of nanoparticle increases. This reduction is uppermost (24%) when Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1 nanofluid is used. It was mentioned by the authors that the reason for better entropy generation performance of Al\({}_{2}\)O\({}_{3}\)/Therminol VP-1 nanofluid was probably due to its relatively lower density comparing to silver/Therminol VP-1 (19%) and copper/Therminol VP-1 (17%). [PERSON] et al.