#### 4.2.2. Investigations

The first study in this field was conducted in 2010 by Kasaeian and Sokhansefat [

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, Sokhansefat 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.

Mohammad Zadeh 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.

Mwesigye 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 Al

_{2}O

_{3}/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 Al

_{2}O

_{3} 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 Al

_{2}O

_{3}/water nanofluid to minimize entropy generation and find optimum Reynolds number for different volume fractions of Al

_{2}O

_{3} 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 Basbous et al. [

67] in their numerical investigation. They tested the application of Al

_{2}O

_{3}/syltherm 800 nanofluid as working fluid in PTC at different volume concentrations of 1–5%. The proposed model also predicted that increasing the temperature can cause an increase in convection heat transfer coefficient.

A CFD simulation was conducted by Bellos et al. [

68] on Al

_{2}O

_{3}/syltherm 800 nanofluid, at 2% volumetric concentration of Al

_{2}O

_{3}, 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 °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.

Wang et al. [

69] numerically studied with CFD simulation the effect of Al

_{2}O

_{3}/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.

Kaloudis, et al. [

70] conducted a CFD simulation to investigate the effect of different volume fraction (0.5–4%) of Al

_{2}O

_{3} in Al

_{2}O

_{3}/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 Al

_{2}O

_{3} volume fraction of 4%.

Benabderrahmane 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 (Al

_{2}O

_{3}/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, Al

_{2}O

_{3}/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].

Ghasemi et al. [

73] carried out a numerical simulation through which the application of Al

_{2}O

_{3}/ 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 Al

_{2}O

_{3}/ water and water itself. Although CuO/water nanofluid caused 7% more increase in heat transfer coefficient comparing with Al

_{2}O

_{3}/water nanofluid (35% compared with 28% enhancement), but the friction factor caused by application of Al

_{2}O

_{3} was lower than the one caused by CuO.

Mwesigye 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. 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.

Basbous et al. [

74] numerically modeled the thermal performance of PTC utilizing different metallic nanofluids. Syltherm 800 as base fluid and Cu, CuO, and Al

_{2}O

_{3}, 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.

Toghyani et al. [

75] modeled and optimized the effect of different nanoparticles on the performance of the PTC used in a Rankin cycle. CuO, SiO

_{2}, TiO

_{2}, and Al

_{2}O

_{3} 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 Al

_{2}O

_{3}/Therminol-55, caused the maximum enhancement in overall exergy efficiency of the system by 11%.

Nayak et al. [

76] modeled Al

_{2}O

_{3}/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 Al

_{2}O

_{3} was used comparing with Synthetic oil only.

Ferraro et al. [

77] used Al

_{2}O

_{3}/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 Al

_{2}O

_{3} for convection heat transfer coefficient.

Kharkah et al. [

78] conducted a CFD simulation on the receiver system of PTC using Al

_{2}O

_{3}/Synthetic oil nanofluid as working fluid at 5% volumetric concentration. The enhancement of 14.3% was reported in the system thermal efficiency.

Mwesigye 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 Al

_{2}O

_{3} 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%).

Ghasemi et al. [

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.

Bellos 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 Bellos 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.

Mwesigye 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 results suggested 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%. 70% reduction in entropy generation rate was observed due to the application of SWCNT. Pumping work, caused by pressure drop, did not increase too much for flow rates lower than 36.74 m

^{3}/h. They, finally, concluded that higher thermal conductivity does not necessarily lead to higher thermal efficiency, since the effect of specific heat capacity also should be considered.

Allouhi et al. [

81] numerically modeled the effect of TiO

_{2}, CuO, and Al

_{2}O

_{3} nanoparticles dispersed in Therminol VP-1 at 1–5 vol. % on thermal performance of PTC. Slight thermal efficiency enhancement was predicted by their model for 3 vol. %. CuO/ Therminol VP-1 nanofluid showed better exergy and energy performance comparing with other nanofluids. More specifically, it can enhance the convection heat transfer by a maximum 83%.

Bellos et al. [

82] numerically investigated the effect of TiO

_{2}/Syltherm 800, Al

_{2}O

_{3}/Syltherm 800, and TiO

_{2}/Al

_{2}O

_{3}/Syltherm 800 (hybrid nanofluid) at 3 vol. % for each TiO

_{2} and Al

_{2}O

_{3} as well as 1.5 vol. % for TiO

_{2}/Al

_{2}O

_{3} on PTC thermal performance at different temperature (300–650 K) and 150 L/min flow rate. It was found that the efficiency of PTC can be enhanced up to 0.74% when using hybrid nanofluid and 0.34 for both mono nanofluids. Enhancements of 142.1%, 35.2%, and 34.9% in heat transfer coefficient was observed for hybrid nanofluid, Al

_{2}O

_{3}/Syltherm 800, and TiO

_{2}/Syltherm, respectively. Finally, the model suggested higher exergy efficiency for nanofluids in comparison with base fluid at higher temperatures.

Bellos et al. [

38] studied numerically the effect of different nanoparticles, Cu, CuO, SiO

_{2}, Al

_{2}O

_{3}, Fe

_{2}O

_{3}, and TiO

_{2} dispersed into Syltherm 800 with different volume concentrations ranging 1–6 vol. % on PTC thermal efficiency. They found that the Cu/syltherm 800 nanofluid had the best thermal performance with the maximum thermal efficiency enhancement of 2.2% at 6 vol. %, 600 K inlet temperature, and 50 L/min flow rate. At 4% volume fraction Cu had the highest efficiency increase of 0.54% followed by 0.46% for CuO, 41% for Fe

_{2}O

_{3}, 0.35% for TiO

_{2}, 0.35% for Al

_{2}O

_{3}, and 0.19% for SiO

_{2}. The same trend is observed for enhancement in heat transfer coefficient with

Cu is having the highest enhancement with 24.42% and SiO_{2} with 7.28% the lowest enhancement at 4% volumetric concentration.

Kasaeian et al. [

83] modeled the effect of MWCNT/thermal oil nanofluid at 3, 6 vol. % of MWCNT on thermal performance of the PTC. They found 15% enhancement in heat transfer coefficient.

Bilal et al. [

84] modeled the effect of Fe

_{3}O

_{4}/water nanofluid at 0.6% vol. of Fe

_{3}O

_{4} on heat transfer behavior of the PTC. It was shown that the nanofluid could enhance the Nusselt number up to 56% at 6 vol. % of Fe

_{3}O

_{4}. Also, the maximum thermal efficiency enhancement (combination of nanofluid application with twisted tape) was 1.6%.

Khular et al. [

30] conducted numerical modeling in which they examined the effect of 0.05 vol. % Al

_{2}O

_{3} in Al

_{2}O

_{3}/Therminol VP-1 nanofluid on PTC thermal behavior. They suggested 5–10% enhancement in thermal efficiency due to the application of nanofluid.

A CFD simulation was conducted by Hatami et al. [

85] using 8% vol. of Cu, Fe

_{3}O

_{4}, Al

_{2}O

_{3}, and TiO

_{2} dispersed in water and investigated the effect of nanofluid in heat transfer of PTC. It was shown that Cu nanoparticles show better thermal enhancement comparing with Fe

_{3}O

_{4}, Al

_{2}O

_{3}, and TiO

_{2}.

Finally, Minea et al. [

86] simulated the effect of hybrid nanofluid on thermal performance of PTC. Three different hybrid nanofluids were selected: Ag/MgO (1.5 and 2 vol. %), Al

_{2}O

_{3}/Cu (0.1 and 1 vol. %), and GO/Co

_{3}O

_{4} (0.05 and 0.15 vol. %). The nanoparticles were dispersed in either water or the hybrid base fluid consisting of 60 vol. % EG and 40 vol. % water. It was found that although hybrid nanofluid with hybrid base fluid (water and EG) had better thermal enhancement (about 5–6%), it introduces higher pressure drop increase (approximately 5000%) to the system compared with hybrid nanofluid with water as the base fluid. Therefore, it was concluded that the application of hybrid water base nanofluid with acceptable heat transfer enhancement and lower pressure drop increase would be a better choice over hybrid nanofluid with hybrid base water. The water-based hybrid nanofluids with 2% Ag-MgO offers the highest values in collector efficiency (about 60%). Convection heat transfer coefficient increase between 115–125% using 0.15% GO/Co

_{3}O

_{4} dispersed in W:EG (40:60).

Table A2 at

Appendix A summarizes the details and important notes about the above studies.