## 4 Application of Nanofluid in PTC
### Numerical Studies
#### 4.2.2 Investigations  
The first study in this field was conducted in 2010 by [PERSON] and [PERSON] [63]. They conducted a CFD simulation to study the effect of Al\({}_{2}\)O\({}_{3}\)/synthetic oil nanofluid in PTC at 1-5 vol. % of Al\({}_{2}\)O\({}_{3}\). They found that the heat transfer coefficient enhances by nanoparticle volume fraction increase (approximately 14% enhancement, at 5% Al\({}_{2}\)O\({}_{3}\) volumetric concentration). Consequently, they concluded that increasing the temperature (from 300 K to 500 K) demolishes the effect of nanoparticle concentration on enhancing heat transfer coefficient in constant flow rate. Later, [PERSON] et al. [10] studied the effect of Al\({}_{2}\)O\({}_{3}\)/synthetic oil as a working fluid for PTC. They simulated the flow through absorber tube at three volumetric concentrations of 1-5%. Their results suggested that the application of the nanofluid at 5% volumetric concentration can enhance the convection heat transfer in the PTC by approximately 14-15%. Similar to the results suggested by them in [63] they realized that increasing the temperature (from 300 K to 500 K) has an adverse effect on enhancing the heat transfer coefficient. [PERSON] et al. [64] proposed an optimized model coupled with CFD analysis through which they investigated the effect of using Al\({}_{2}\)O\({}_{3}\)/synthetic oil (with 0-6.5 vol. % concentration) as working fluid on the thermal enhancement of PTC. They showed that using the proposed model, the maximum convection heat transfer coefficient of nanofluid could be enhanced by 36% at 300 K. Additionally, they showed that increasing the temperature (from 300 K to 500 K) decreases the heat transfer coefficient. Finally, they proposed optimum nanofluid concentration is 6.5 vol. %, for their studied range. [PERSON] et al. [61; 65; 66] conducted five studies using CFD simulations in PTC receive to investigate the effect of different nanofluids on PTC thermal performance. In Reference [65], they used Al2O3/synthetic oil nanofluid as working fluid with the volume fraction of up to 8% to investigate the enhancement of convection heat transfer coefficient as well as thermal efficiency. The results showed at 8% volume concentration 76% and 7.6% increase can be obtained for convection heat transfer and maximum thermal efficiency, respectively. Also the heat transfer coefficient at 6% and 4% volume concentration increased by 54% and 35%, respectively. A significant increase in pressure drop is also reported by the authors, as the volume concentration is reached beyond 4 vol. %, which in turn emphasized the necessity of more pumping power. This pressure drop increases up to approximately 40% at 4% vol. of Al2O3 in a nanofluid. The effect of temperature increase was on the favor of pressure drop as it causes less pressure drop along the tube with temperature increasing. However, this effect demolishes the effect of nanofluid in increasing thermal efficiency and heat transfer coefficient. In reference [61] the maximum heat transfer coefficient and thermal efficiency enhancement of 38% and 15% were found at 6% volume concentration of CuO in CuO/syltherm 800 nanofluid. Similar to [65] they reported an increase of in pressure drop. Additional simulations were conducted in Reference [66] on Al2O3/water nanofluid to minimize entropy generation and find optimum Reynolds number for different volume fractions of Al2O3 located at different sections of a circular tube. They showed that at a given Reynolds number the performance of heat transfer (Nusselt number) and the value for friction factor is almost the same regardless of the volume fraction. Also, it was proven that there is an optimum cross-section of the tube that causes minimum generation of entropy. An 18% enhancement in convection heat transfer coefficient was reported by [PERSON] et al. [67] in their numerical investigation. They tested the application of Al2O3/syltherm 800 nanofluid as working fluid in PTC at different volume concentrations of 1-5%.