## 4 Application of Nanofluid in PTC
### Numerical Studies
#### 4.2.2 Investigations
[73] simulated Al\({}_{2}\)O\({}_{3}\)/Therminol 66 nanofluid at different volume fraction (1-4%) inside the receiver tube using CFD. He reported a slight enhancement in thermal efficiency (around 0.5%). At the lowest Reynolds number (approximately 30,000) using 4 vol. % of Al\({}_{2}\)O\({}_{3}\) in nanofluid resulted in seven times greater friction coefficient compared to the base fluid. Also, this increase is approximately nine times bigger for the highest Reynolds number (>250,000). The same scenario is true for Nusselt number as it increases by a factor of 2 using 4% volume fraction of Al\({}_{2}\)O\({}_{3}\) in a nanofluid. [PERSON] et al. [62; 79] numerically modeled the effect of Al\({}_{2}\)O\({}_{3}\)/syltherm 800 and CuO/syltherm 800 nanofluids to study their effect on thermal enhancement of the PTC. In reference [79] up to 4% volume fraction of both Al\({}_{2}\)O\({}_{3}\) and CuO was examined. They found that CuO/syltherm 800 has the maximum thermal efficiency of 1.26% followed by 1.13% by application of Al\({}_{2}\)O\({}_{3}\)/syltherm 800. As for the heat transfer coefficient, the enhancements were 41% and 35% for CuO/syltherm 800 and Al\({}_{2}\)O\({}_{3}\)/syltherm 800, respectively. In reference [62] they used up to 6% volume fraction of both nanoparticles to investigate the effect of the nanofluids in PTC which is used in a trigeneration system. They realized, after optimization, that the use of CuO nanofluid with 4.35% volumetric concentration of CuO in the solar loop along with Toluene in ORC is the optimum choice. They also, found that the maximum energy efficiency enhancement was 1.91% and 1.17% for CuO/syltherm 800 and Al\({}_{2}\)O\({}_{3}\)/syltherm 800 nanofluid, respectively. They also, reported the maximum exergy enhancement of approximately 1.75% and 1% for CuO/syltherm 800 and Al\({}_{2}\)O\({}_{3}\)/syltherm 800 nanofluid, respectively. Two CFD simulations were carried out by [PERSON] et al. [37; 80]. In reference [80] the authors examined CuO with two base fluids, syltherm 800 and molten salt (60% NaNO\({}_{3}\)-40% KNO\({}_{3}\)) at 6 vol.%. They reported 0.76% and 0.26% thermal efficiency enhancement when using CuO/syltherm 800 and CuO/molten salt comparing with syltherm 800 and molten salt, respectively. As for convection heat transfer coefficient, 31.5% and 13.9% enhancement is observed for CuO/syltherm 800 and CuO/molten salt, respectively. Although, the hydraulic analysis also proved 50% and 16% pressure drop increase for CuO/syltherm 800 and CuO/molten salt cases, respectively, the demand for pumping work was still low. Hence, this pressure drop increase did not cause so much of a problem. Finally, they commented on exergy efficiency stating that nanofluid application, specifically molten salt nanofluid, can lead to better exergic efficiency. In reference [37] CuO/syltherm 800 nanofluid at 6 vol. % was used to evaluate the thermal analysis. They also studied the effect of different fins to investigate thermal efficiency enhancement. They realized that the combination of both nanofluids and fins could lead to higher efficiency enhancement. This combination can lead to 1.54% enhancement in thermal efficiency, whereas with the application of the only nanofluid and only fin this value was calculated as 0.76% and 1.1%, respectively, compared with smooth pipe with syltherm 800 as working fluid. Convection heat transfer coefficient enhanced by 130% at 300 K. Similar to their last study, the pressure drop increase (approximately 163% at 300 K) did not cause too much of a problem as the demand for pump work was still relatively low. [PERSON] et al. [58] carried out a CFD simulation to investigate the effect of SWCNT/Therminol VP-1 nanofluid on thermal and thermodynamic performance of the PTC at 0.25-2.5 vol. %. The resultssuggested that application of nanofluid enhances the heat transfer up to 234% compared with the base fluid due to the high thermal conductivity of SWCNT. Also, thermal efficiency using such nanofluid enhanced up to 4.4%.