## 4 Application of Nanofluid in PTC
### Numerical Studies
#### 4.2.2 Investigations
The proposed model also predicted that increasing the temperature can cause an increase in convection heat transfer coefficient. A CFD simulation was conducted by [PERSON] et al. [68] on Al2O3/syltherm 800 nanofluid, at 2% volumetric concentration of Al2O3, to examine its effect on the thermal performance of PTC. It was concluded that the nanofluid could increase the efficiency of PTC by 4.25%. An interesting result reported by them was the effect of pressurized water as working fluid which enhanced the thermal efficiency by 6.34%. However, authors mentioned that the application of pressurized water requires some effort which makes nanofluid utilization more advantageous overpressure water. It was also suggested a new design for absorber geometry shape of which had a wavy trend, which improved the efficiency by 4.55% and this design. Furthermore, it was shown that higher temperature levels increase efficiency. This led to heat transfer coefficient improvement (maximum increase of 10.92% at 350 \({}^{\circ}\)C). Finally, application of nanofluid did not cause too much pressure drop increase comparing to base fluid (syltherm 800). The pressure drop increase was around 125 Pa to 202 Pa for nanofluid and 118 Pa to 192 Pa for syltherm 800. [PERSON] et al. [69] numerically studied with CFD simulation the effect of Al2O3/thermal oil nanofluid with different volume fractions ranging 0.5-5% on the performance of PTC. It was reported the efficiency enhancement around 1.2% in their model (at 5% volume fraction). They also found that increasing the nanofluid volume fraction can lead to a slight decrease in longitudinal displacement of the absorber. Similarly, the horizontal displacement of the absorber was reported to slightly decrease by volume fraction increase. [PERSON], et al. [70] conducted a CFD simulation to investigate the effect of different volume fraction (0.5-4%) of Al2O3 in Al2O3/syltherm 800 nanofluid on PTC performance. They used two different modeling for nanofluid: two-phase simulation and one phase simulation. They concluded that utilizing two-phase modeling of nanofluid had more accuracy in the results. More specifically, the numerical results suggested a maximum of 10% thermal efficiency enhancement at maximum Al2O3 volume fraction of 4%. [PERSON] et al. [71; 72] numerically modeled the effect of utilizing nanofluid as well as internal fins in the receiver of PTC using CFD. In Reference [72], it was concluded that combining both internal fins and nanofluid application can enhance the heat transfer behavior of the PTC greatly. To be specific, they utilized four different nanofluids (Al2O3/Dowtherm A, Cu/Dowtherm A, SiC/Dowtherm A, C/Dowtherm A) at different volumetric concentration of 1% and found that the metallic nanofluids (Cu/Dowtherm) had better thermal enhancement performance comparing with non-metallic ones (SiC/Dowtherm A, C/Dowtherm A, Al2O3/Dowtherm A). Also, the friction factor reported to be higher when nanofluid is applied. A 68% increase in convection heat transfer coefficient was reported [37]. [PERSON] et al. [73] carried out a numerical simulation through which the application of Al2O3/ water and CuO/water as a working fluid at different volume fractions, 0.5-3%, in PTC were investigated. They realized that the application of 3% CuO/water nanofluid could lead to higher convection heat transfer coefficient comparing with Al2O3/ water and water itself. Although CuO/water nanofluid caused 7% more increase in heat transfer coefficient comparing with Al2O3/water nanofluid (35% compared with 28% enhancement), but the friction factor caused by application of Al2O3 was lower than the one caused by CuO. [PERSON] et al. [60] conducted another CFD simulation on Cu/Therminol VP-1 nanofluid to study the application of nanofluid at different volume fraction (1-6%) on thermal and thermodynamic performance of PTC. At a maximum 6% volumetric concentration of Cu, it was observed that the convection heat transfer coefficient and thermal efficiency increase up to 32% and 12.5%, respectively.