Introduction

Solar energy utilization is a promising choice for facing numerous problems in the energy [1] and environmental domain [2]. Solar concentrating collectors are able to produce useful heat at medium and high-temperature levels. Parabolic trough collectors are among the most usual concentrating technologies and they can be exploited in many applications as solar cooling, industrial heat [3], desalination, methanol reforming and power production [4].

The last years, a lot of research has been focused on various ways for enhancing the thermal performance of parabolic trough collector (PTC) in order more useful heat to be exploited. These techniques generally aim to increase the heat transfer coefficient in the flow in order to achieve beneficial heat transfer conditions in the flow [5]. These techniques are separated into two great categories; the use of geometry modifications in the absorber tube or the use of nanofluids as working fluids [6]. In the first category, the use of dimpled tubes [7], the use of internal fins [8, 9], as well as the use on flow inserts [10] are very common techniques. These techniques try to increase the turbulence in the flow and thus the heat transfer between the absorber tube and the fluid to be improved. On the other hand, the use of nanofluids as working fluids is the other common technique [5]. The nanofluids are created by dispersing metallic or nonmetallic nanoparticles in the base fluid and this term has been introduced by Choi in 1995 [11]. The main idea of the nanofluid utilization is the increase in the conductivity of the fluid because the utilized nanoparticles have many times higher thermal conductivity than the base fluid (usually water or thermal oil) [12]. So, the heat transfer coefficient is enhanced because the heat can be easier to be transferred from the region close to the tube to the tube center. Moreover, the increased density of nanofluids, compared to the base fluids, leads to a higher product of density-specific heat capacity and this fact allows the nanofluids to carry higher heat amounts. So, the adoption of nanofluids combines two different positive factors for the thermal efficiency enhancement.

The use of nanofluids has been extensively examined in the literature by many researchers. Table 1 includes 27 different studies [13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39] which investigate different nanofluid types in parabolic trough solar collectors. These studies use water, thermal oil or molten salt as base fluids, while a great variety of nanoparticles is applied, usually in concentrations up to 6%. This table gives the thermal efficiency enhancement and the heat transfer coefficient enhancement in every case and where it is given in a clear way. These studies are experimental studies, computation fluid dynamic (CFD) studies and studies with developed thermal models. The thermal efficiency enhancement has been found up to 15% while the heat transfer coefficient enhancement up to 234%.

Table 1 Detailed literature review of studies about nanofluid-based PTC
Full size table

The experimental studies have been performed in Refs. [20, 21, 26, 34, 36, 37]. The study of Coccia et al. [21] found that the dispersion of nanoparticles in water does not lead to an adequate enhancement of the thermal efficiency which can be measured. On the other hand, the other experimental studies have been found significant thermal efficiency enhancement. Chaudhari et al. [20] found 7% thermal efficiency enhancement with Al2O3/water nanofluid, Kasaeian et al. [34] 8% with MCNT/oil nanofluid, Rehan et al. [34] 13% with Al2O3/water and 11% with Fe2O3/water, while similar enhancements close to 8.5% by Subramani et al. [36, 37] with Al2O3/water and TiO2/water.

The next part of the studies is associated with CFD works which can be found in Refs. [15, 18, 19, 23,24,25, 27,28,29,30,31,32,33, 35, 38, 39]. These studies give generally lower thermal efficiency enhancement values, compared to the experimental works. Bellos et al. [15] found thermal efficiency enhancement 4.25% with a low-quality PTC, while 0.76% [18] with a high-quality PTC. This result indicates that the type of the PTC creates different thermal efficiency margins. Moreover, Ghasemi and Ranjbar [14] found 0.5% thermal efficiency enhancement and Wang et al. [38] 1.2% for oil-based nanofluids. Mwesigye et al. [28,29,30,31,32,33] have found higher values for the thermal efficiency enhancement in PTC with various nanofluids, as well as Kaloudis et al. [25].

The use of thermal models for the prediction of PTC performance has been investigated in Refs. [13, 14, 16, 17, 22]. These studies indicate low thermal efficiency enhancements for various nanofluids. Allouchi et al. [13] found 1.06, 1.17 and 1.14% thermal efficiency enhancement with CuO/Oil, Al2O3/Oil and TiO2/Oil nanofluids, respectively. Bellos et al. [15] found 1.26 and 1.13% thermal efficiency enhancement with CuO/Oil and Al2O3/Oil, respectively. Moreover, they [16] found 1.31% thermal efficiency enhancement with the hybrid nanofluid Al2O3-TiO2/Oil. Ferraro et al. [22] found an extremely low enhancement close to 0.1% with Al2O3/Oil. It is generally obvious that the model-studies results give similar enhancement which takes relatively low values.

The previous literature review indicates the chaotic situation about the thermal efficiency enhancement margin with the use of nanofluids in PTCs. The experimental studies give high enhancements (7–13%), and the CFD studies give a bit lower enhancements (4–13%), while the model studies give enhancements close to 1%. There is the experimental work of Coccia et al. [21] which indicates negligible enhancement, while similar results can be found in Ref. [22]. So, it is not clear if and how the nanofluids can increase the thermal performance of PTC. A recent study in Ref. [40] proved that the heat transfer coefficient enhancement in PTCs can lead to a maximum thermal efficiency enhancement close to 3%. This result is based on the extremely low thermal losses of the PTC, especially in the cases with evacuated tubes with selective coatings. Moreover, this result corresponds to a reasonable flow rate which corresponds to an adequate thermal efficiency.

At this point, it would be interesting to examine the possible reasons for the present situation in the literature. The first problem is associated with the thermal properties of nanofluids. There are numerous equations for the determination of the thermal conductivity and of the dynamic viscosity and various equations have been used in the studies of Table 1. Moreover, there are two different models for the specific heat capacity determination which leads to different results, especially in the experimental studies. Furthermore, these models are usually valid for water-based nanofluids in generally low concentrations. There are no reliable models for oil-based nanofluids in medium–high temperatures which correspond to the real operating conditions in PTCs. Furthermore, the preparation methods play a significant role in the nanofluid properties. Another important problem is associated with the examined operating conditions of the various cases. In order to achieve reasonable conclusions, the main parameters of the system as flow rate, inlet temperature, nanoparticle concentration and solar irradiation have to be selected at usual values. However, many studies do not apply reasonable values for these parameters and so the obtained results are questionable in some cases. For instance, the PTC has to be investigated at high temperature with high flow rates in order to achieve turbulent flow, as in real concentrating power plants.

So, high heterogeneity among the examined studies is observed. For instance, in low-temperature levels, the thermal losses of PTC are extremely low in realistic systems and the thermal efficiency enhancement margins are approximately zero. However, if the PTC examined at extremely low flow rates or the examined system has low quality (for instance uncovered absorber), then the thermal losses are higher and there are higher margins for improvement.

The present study comes to examined different scenarios of PTC operation with nanofluids. Oil-based nanofluids are examined because the thermal oils are the most usual working fluids at medium–high temperatures. Moreover, the use of molten salt is not indicated according to the results of [18] because of their very good thermal properties. Six different nanoparticles (Cu, CuO, Al2O3, TiO2, SiO2 and Fe2O3) are selected to be examined in this work in order to investigate different nanofluids. Different concentrations up to 6% are examined, while the flow rate, the inlet temperature and the solar irradiation level are examined parametrically. The comparative study, among the nanofluids and the operating scenarios, is performed in a systematic way. This is something which is missing from the literature because in the majority of the studies only one or two nanoparticles are examined with the same model. In every case, the thermal efficiency enhancement is the main goal of this work and not the heat transfer enhancement because in PTC the increase in the useful heat production is the final objective by the nanofluid utilization. The results of this work can clearly indicate the cases where the thermal efficiency enhancement is important and when it has to be applied, something very important for the utilization of nanofluids in PTC. Moreover, a new evaluation index is introduced which takes into consideration the heat transfer coefficient and the density-specific heat capacity product. The analysis is performed with a developed thermal model in Engineering Equation Solver (EES) which has been validated in our previous studies [16, 17].

Materials and methods

The examined PTC module

In this work, the module of LS-2 PTC is investigated which has been used in various studies. This is a typical PTC with 22.74 concentration ratio, 39 m2 aperture with 7.8 m length and 5 m aperture. The evacuated tube collector has an absorber with 70 mm outer diameter and a glass cover with 115 m outer diameter. The optical efficiency of this collector is 57.7% for zero incident angle. More details about the examined PTC are given in Table 2 and in Ref. [41]. Moreover, the examined module can be seen in Fig. 1. There is an evacuated tube with a selective coating in the absorber. The emittance of the absorber, for the Cermet coating, is calculated as [42]:

Table 2 Parameters of the examined PTC [41]
Full size table
Fig. 1
figure 1

The examined module of LS-2 PTC

Full size image
$$ \varepsilon_{\text{r}} = 0.05599 + 1.039 \cdot 10^{ - 4} \cdot T_{\text{r}} + 2.249 \cdot 10^{ - 7} \cdot T_{\text{r}}^{2} . $$
(1)

The optical efficiency of the present collector is about 75.7%, and it is a result of 95% cover transmittance, 96% receiver absorbance and 83% mirror reflectance. The reduced value of the reflectance includes the possible optical losses due to errors, dust and other reasons as they have described in Ref. [41]. The intercept factor has been selected to be approximately 1 [40]. Equation 2 gives the calculation of the optical efficiency. In this work, the collector has been examined for zero incident angle in order to give the emphasis in the thermal analysis and in the comparison of various nanofluids. Thus, the incident angle modifier (K) is equal to 1 in all the cases.

$$ \eta_{\text{opt}} = \rho \cdot \gamma \cdot \tau \cdot \alpha \cdot {\rm K}\left( \theta \right). $$
(2)

The developed thermal model

The basic equations for the thermal modeling of the PTC are given in “The developed thermal model ” section. These equations are energy balances in the various subsystems. All these equations are used for the development of the thermal model. The same model, with the proper modifications in every case, has been applied in other studies [16, 17, 40, 43,44,45]. The validation of this model has been given in the previous references, and there is no reason for giving it again. The developed thermal model has been developed in Engineering Equation Solver (EES) [46].

The thermal efficiency (ηth) of the solar collector can be written as the ratio of the useful heat (Qu) to the available solar irradiation (Qs):

$$ \eta_{\text{th}} = \frac{{Q_{\text{u}} }}{{Q_{\text{s}} }}. $$
(3)

The solar energy in the collector aperture is the product of the direct beam irradiation (Gb) to the total aperture (Aa):

$$ Q_{s} = A_{\text{a}} \cdot G_{\text{b}} . $$
(4)

The nominal solar irradiation level in this study is at 1000 W m−2, while a parametric analysis is performed in order to examine the system in different solar potentials. The useful energy production (Qu) can be calculated in two ways. The first one is using the energy balance in the fluid volume (Eq. 5), and the second one is by using the heat transfer from the absorber tube to the fluid (Eq. 6):

$$ Q_{\text{u}} = m \cdot c_{\text{p}} \cdot \left( {T_{\text{out}} - T_{\text{in}} } \right), $$
(5)
$$ Q_{\text{u}} = h \cdot A_{\text{ri}} \cdot \left( {T_{\text{r}} - T_{\text{fm}} } \right). $$
(6)

The mean fluid temperature (Tfm) can be estimated as:

$$ T_{\text{fm}} = \frac{{T_{\text{in}} + T_{\text{out}} }}{2}. $$
(7)

The thermal losses of the collector can be calculated using Eqs. 8 and 9. The present study investigates the thermal performance in steady-state conditions, so it can be said that the thermal losses from the receiver to the cover (Eq. 8) are the same with the thermal losses of the cover to the ambient (Eq. 9):

$$ Q_{\text{loss}} = \frac{{A_{\text{ro}} \cdot \sigma \cdot \left( {{\rm T}_{\text{r}}^{4} - T_{\text{c}}^{4} } \right)}}{{\frac{1}{{\varepsilon_{\text{r}} }} + \frac{{1 - \varepsilon_{\text{c}} }}{{\varepsilon_{\text{c}} }} \cdot \left( {\frac{{A_{\text{ro}} }}{{A_{\text{ci}} }}} \right)}}, $$
(8)
$$ Q_{\text{loss}} = A_{\text{co}} \cdot h_{\text{out}} \cdot \left( {T_{\text{c}} - T_{\text{am}} } \right) + A_{\text{co}} \cdot \sigma \cdot \varepsilon_{\text{c}} \cdot \left( {T_{\text{c}}^{4} - T_{\text{sky}}^{4} } \right). $$
(9)

The ambient temperature has been selected at 300 K, while the sky temperature (Tsky) can be estimated as [47]:

$$ T_{\text{sky}} = 0.0553 \cdot T_{\text{am}}^{1.5} . $$
(10)

The heat convection coefficient between cover and ambient (hout) is estimated using Eq. 11 for a wind speed of 1 m s−1 [48]. This wind speed leads to heat convection coefficient close to 10 W m−2 K−1.

$$ h_{\text{out}} = 4 \cdot V_{\text{wind}}^{ 0. 5 8} \cdot D_{\text{co}}^{ - 0.42} . $$
(11)

The next important equation of the developed model is the energy balance in the absorber. According to this equation, the absorbed heat is separated into useful heat and to thermal losses:

$$ Q_{\text{s}} \cdot \eta_{\text{opt}} = Q_{\text{u}} + Q_{\text{loss}} . $$
(12)

The last parameter that has to be defined is the heat transfer coefficient between absorber and fluid (h). This parameter can be estimated using the Nusselt number. For turbulent flow conditions (Re > 2300), the Nusselt number can be calculated using the Dittus-Boelter equation [49].

$$ Nu = 0.023 \cdot Re^{0.8} \cdot Pr^{0.4} . $$
(13)

Below, the definitions of important parameters about this work are given.

Nusselt number (Nu):

$$ Nu = \frac{{h \cdot D_{\text{ri}} }}{k}. $$
(14)

Reynolds number (Re) for circular tube:

$$ Re = \frac{4 \cdot m}{{\pi \cdot D_{\text{ri}} \cdot \mu }}. $$
(15)

Prandtl number (Pr):

$$ Pr = \frac{{\mu \cdot c_{\text{p}} }}{k}. $$
(16)

The inlet temperature level is examined from 300 to 650 K with step 50 K and the flow rate from 50 to 300 L min−1 with step 50 L min−1. The reference operating conditions in this study are selected for inlet temperature equal to 600 K and flow rate equal to 150 L min−1.

Thermal properties of the examined nanofluids

“Thermal properties of the examined nanofluids” section is devoted to presenting the equations about the thermal properties of the examined nanofluids. The base fluid (bf) is the Syltherm 800 [50], a thermal oil which operates up to 400 °C with safety. The thermal properties of the examined nanoparticles (np) are listed in Table 3.

Table 3 Thermal properties of the examined nanoparticles
Full size table

The density of the nanofluids (nf) can be calculated proportionally with the volumetric concentration (φ) [12]:

$$ \rho_{\text{nf}} = \rho_{\text{bf}} \cdot \left( {1 - \phi } \right) + \rho_{\text{np}} \cdot \phi . $$
(17)

The specific heat capacity can be calculated using the following formula. This formula has proved to be the proper one according to the detailed analysis of Ref. [51].

$$ c_{\text{p,nf}} = \frac{{\rho_{\text{bf}} \cdot \left( {1 - \phi } \right)}}{{\rho_{\text{nf}} }} \cdot c_{\text{p,bf}} + \frac{{\rho_{\text{np}} \cdot \phi }}{{\rho_{\text{nf}} }} \cdot c_{\text{p,np}} . $$
(18)

The thermal conductivity can be calculated using the suggested equation by Yu and Choi [52]. This equation is the modified Maxwell equation which includes the parameter β. This parameter is the ratio of the nanolayer thickness to the original particle radius, and usually, this parameter is taken equal to 0.1 [53].

$$ k_{\text{nf}} = k_{\text{bf}} \cdot \frac{{k_{\text{np}} + 2 \cdot k_{\text{bf}} + 2 \cdot \left( {k_{\text{np}} - k_{\text{bf}} } \right) \cdot \left( {1 + \beta } \right)^{3} \cdot \phi }}{{k_{\text{np}} + 2 \cdot k_{\text{bf}} - \left( {k_{\text{np}} - k_{\text{bf}} } \right) \cdot \left( {1 + \beta } \right)^{3} \cdot \phi }}. $$
(19)

The dynamic viscosity can be calculated using the Batchelor model [54] which can be applied in low and high concentrations for spherical nanoparticles [53]:

$$ \mu_{\text{nf}} = \mu_{\text{bf}} \cdot \left( {1 + 2.5 \cdot \phi + 6.2 \cdot \phi^{2} } \right). $$
(20)

At this point, it is essential to state that the used equations for the determination of the thermal properties are general and they can be applied to all the nanoparticles. This fact makes the comparative analysis to be performed under similar conditions. The reason for not using more special equations for the determination of the thermal properties is the lack of experimental studies for oil-based nanofluids in temperature levels over 100 °C. So, there are no available experimental correlations at the present time. However, the selected Eqs. 17–20 are very usual selections which are acceptable and they give reasonable results.

The suggested evaluation index

In this work, a new evaluation index is introduced in order to evaluate the use of nanofluids in solar thermal systems. This index takes into account the heat transfer coefficient (h), as well as the density-specific capacity product (ρ·cp). This product indicates the amount of the heat that can be transferred from the fluid. Higher values of this product indicate that higher amounts of heat can be transferred and thus higher thermal performance to be achieved. The conventional studies evaluate only the heat transfer coefficient enhancement and they do not take into account the increase in the (ρ·cp). Moreover, other studies evaluate the increase in the Nusselt number and so they do not take into consideration the increase in the thermal conductivity of the nanofluids. Thus, the introduction of a more general index is vital for the proper and quick evaluation of the nanofluids in solar thermal systems.

Using Eqs. 5–7, the useful heat can be written as:

$$ Q_{\text{u}} = A_{{{\text{r}}_{\text{i}} }} \cdot U_{\text{r}} \cdot \left( {T_{\text{r}} - T_{\text{in}} } \right). $$
(21)

With the overall heat transfer coefficient (Ur) to be calculated as:

$$ U_{\text{r}} = \left[ {\frac{1}{h} + \frac{{A_{\text{r}} }}{{2 \cdot \left( {\rho \cdot c_{\text{p}} } \right) \cdot V}}} \right]^{ - 1} . $$
(22)

This overall heat transfer coefficient is the new introduced evaluation index which takes into consideration many parameters. This index evaluates the following parameters:

  • The heat transfer coefficient in the flow (h).

  • The density-capacity product (ρ·cp).

  • The flow rate of the collector.

Higher values of this parameter lead to lower receiver temperature if the useful heat is assumed constant. So, it can be said that when the overall heat transfer coefficient is high, the receiver temperature is lower, and the thermal losses are lower. This leads to thermal enhancement in the solar collector. This hypothesis will be verified with the numerical results of this works in the following section.

Followed methodology

The presented equations of this section have been inserted in EES [46], and a thermal model has been developed. This model has also been used in other studies [16, 17, 40, 43,44,45] where it has been validated many times. In this work, the use of six different nanofluids is performed using Syltherm 800 as the base fluid in all the cases [50]. The examined nanoparticles are Cu, CuO, Fe2O3, TiO2, Al2O3 and SiO2. These nanoparticles are examined for concentrations up to 6% with step 1%. In “Nanoparticle investigation” section, these nanoparticles, for all the concentrations, are compared for the reference operating conditions with flow rate 150 L min−1, inlet temperature 600 K and solar irradiation level 1000 W m−2. The flow rate of 150 L min−1 has been suggested as a reliable choice, after a simple sensitivity analysis with pure thermal oil (φ = 0%). The inlet temperature of 600 K is a high-temperature level which is representative for applications with PTCs. The comparative analysis of the nanofluids proved that Cu/Oil nanofluid is the best choice using the thermal efficiency enhancement criterion. Moreover, in the “Nanoparticle investigation” section, the suggested index (overall heat transfer coefficient) is presented and discussed.

“Parametric analysis” section is devoted to presenting a detailed parametric analysis with Cu/Oil nanofluid which is the most efficient nanoparticle according to the comparative analysis of “Nanoparticle investigation” section. The flow rate is studied from 50 L min−1 up to 300 L min−1 with step 50 L min−1, the inlet temperature from 300 K up to 650 K with step 50 K and the nanoparticle concentration from 0% up to 6% with 1% step. Furthermore, an extra parametric analysis with the solar irradiation from 500 W m−2 up to 1000 W m−2 is given.

Results

Nanoparticle investigation

The first presented results give the thermal efficiency of the PTC with pure thermal oil for various inlet temperatures and flow rates. Figure 2 shows the thermal efficiency curves for four different flow rates (100, 150, 200 and 250 L min−1). Higher inlet temperature leads to lower thermal efficiency, while higher flow rate leads to higher thermal efficiency. It is obvious that only the curve of 100 L min−1 gives a significantly lower performance. Moreover, Fig. 3 depicts the impact of the flow rate on the thermal efficiency in a clearer way. It is obvious that flow rates over 150 L min−1 give adequate thermal efficiency for all the examined inlet temperatures. This flow rate (150 L min−1) is selected as the most appropriate choice because higher values will lead to higher pressure drop with a negligible impact on the thermal efficiency. A similar analysis has been presented in Ref. [9]. Moreover, higher flow rate needs greater equipment and this leads to higher system cost. It can be also stated that the impact of the flow rate is greater in the higher inlet temperature levels because in these cases there are higher thermal losses.

Fig. 2
figure 2

Thermal efficiency curves for different flow rates

Full size image
Fig. 3
figure 3

The impact of the flow rate on the thermal efficiency for various inlet temperatures

Full size image

Figure 4 illustrates the impact of the nanoparticle concentration on the thermal efficiency of the collector for the six examined nanoparticles. These results are given for the operating case with inlet temperature equal to 600 K and 150 L min−1 flow rate. It is obvious that the Cu nanoparticle gives the highest performance with CuO and Fe2O3 to follow. TiO2 and Al2O3 are the next nanoparticles which lead to similar performance, while SiO2 gives the lowest performance. An interesting observation is the correlation of the thermal conductivity of the nanoparticles with their performance sequence. According to Table 3, Cu has the highest thermal conductivity, and it is the most efficient choice according to Fig. 4. On the other hand, SiO2 has the lowest thermal conductivity and the lowest thermal performance. This interesting observation aids to the proper nanoparticle evaluation using the thermal conductivity criterion.

Fig. 4
figure 4

Thermal efficiency enhancement for various nanofluids (Inlet temperature 600 K and flow rate 150 L min−1)

Full size image

Another interesting result is associated with the nanoparticle concentration. Higher concentration leads to higher thermal efficiency enhancement but the increasing rates are getting lower after the concentration of 3–4%. This result indicates the use of generally high concentrations, but not extremely high values. The thermal efficiency enhancement with Cu reaches up to 0.74%, with CuO up to 0.62%, with Fe2O3 up to 56%, with TiO2 up to 0.50%, with Al2O3 up to 0.49% and with SiO2 up to 0.26%.

Figure 5 depicts the overall heat transfer coefficient enhancement for all the examined nanofluids (all the cases of Figs. 4, 5). The trends of this figure are similar to the trends of Fig. 4 about the thermal efficiency enhancement. However, the curves of Fig. 5 have a more linear character. In any case, it is proved that higher values of the overall heat transfer coefficient lead to higher thermal efficiency.

Fig. 5
figure 5

Overall heat transfer coefficient enhancement for various nanofluids (Inlet temperature 600 K and flow rate 150 L min−1)

Full size image

The direct dependency between the overall heat transfer coefficient enhancement and the thermal efficiency enhancement is given in Fig. 6. Higher values of the overall heat transfer coefficient enhancement lead to higher thermal efficiency enhancement in a monotonic way. Equation (23) expresses this dependency with R2 equal to 99.95%, an extremely high value.

Fig. 6
figure 6

Thermal efficiency enhancement for different overall heat transfer coefficient enhancements (Inlet temperature 600 K and flow rate 150 L min−1)

Full size image
$$ \left( {\frac{{\eta_{\text{th}} }}{{\eta_{\text{th0}} }} - 1} \right) = 0.0272 \cdot \left( {\frac{{U_{\text{r}} }}{{U_{{{\text{r}}0}} }} - 1} \right) - 0.0192 \cdot \left( {\frac{{U_{\text{r}} }}{{U_{\text{r0}} }} - 1} \right). $$
(23)

Equation (23) is valid for the present collector and shows that the thermal efficiency enhancement is approximately a second degree polynomial of the overall heat transfer coefficient enhancement. It is essential to state that the results of Fig. 6 validate the initial hypothesis which states that the thermal efficiency enhancement is depended on the overall coefficient.

The last figure of this subsection is Fig. 7 where numerical values for the thermal efficiency enhancement and the overall heat transfer coefficient enhancement are given for the case of 4% nanoparticle concentration. The thermal efficiency enhancements are ranges from 0.19% for SiO2 up to 0.54% for Cu. Respectively, the enhancement of the overall heat transfer coefficient is ranged from 7.28% for SiO2 to 24.42% for Cu. It is again obvious that higher values of the overall heat transfer coefficient enhancement mean higher thermal efficiency enhancement. Thus, this parameter can be used for the quick evaluation of different nanofluids under the same operating conditions.

Fig. 7
figure 7

Thermal efficiency enhancement and overall heat transfer coefficient enhancement for 4% concentration (Inlet temperature 600 K and flow rate L min−1)

Full size image

Parametric analysis

The “Parametric analysis” section is devoted to giving a detailed parametric analysis of the collector performance with Cu/Oil nanofluid. This is the most efficient nanofluid, according to the results of “Nanoparticle investigation” section. The inlet temperature, the flow rate, the nanoparticle concentration, as well as the solar irradiation level are the investigated parameters of this analysis. The objective of this parametric analysis is to identify the cases with higher thermal efficiency margin with the utilization of nanofluids as working fluids. It is important to state again that all the comparisons are conducted using the pure oil case as the reference one.

Figure 8 illustrates the impact of the flow rate on the thermal efficiency enhancement for various concentrations and inlet temperature equal to 600 K. Higher flow rates allow lower thermal efficiency margins for all the examined nanoparticles. All the curves for the examined nanoparticles have the same trends, and in all the cases, higher concentration leads to higher performance. Generally, it can be said that for high flow rates the thermal efficiency enhancement is up to 0.4%, while it can reach up to 2.2% for low flow rates. In the cases with lower thermal efficiency, the thermal losses are higher and so the thermal efficiency enhancement margin is higher. These cases correspond to low flow rates (see Figs. 2, 3). So, when a system operates with low flow rates, then the use of nanofluids is recommended. Similar conclusions can be extracted from Fig. 9 where the results are given as a function of the concentration for four flow rates. Again, the thermal efficiency enhancement margin is higher for lower flow rates and higher nanoparticle concentrations.

Fig. 8
figure 8

Thermal efficiency enhancement for different flow rates with various Cu concentrations and inlet temperature equal to 600 K

Full size image
Fig. 9
figure 9

Thermal efficiency enhancement for different Cu concentrations with various flow rates and inlet temperature equal to 600 K

Full size image

The thermal efficiency enhancement margin for different inlet temperatures is given in Figs. 10 and 11. The curves of Fig. 10 seem to be parallel to each other, while the curves of Fig. 11 have variable distances which are more intense in higher concentrations. Both these figures make clear that the thermal efficiency enhancement margin is greater for higher inlet temperatures. This result is based on the higher thermal losses for higher inlet temperatures and to the greater improvement margin. So, the use of nanofluids is recommended for cases with higher inlet temperature levels. The obtained thermal efficiency enhancements are generally up to 1% which is low values. These low values are explained by the general high performance of PTC which cannot be increased in a great percentage.

Fig. 10
figure 10

Thermal efficiency enhancement for inlet temperatures with various Cu concentrations and flow rate equal to 150 L min−1

Full size image
Fig. 11
figure 11

Thermal efficiency enhancement for inlet temperatures with various Cu concentrations and flow rate equal to 150 L min−1

Full size image

At the end of this subsection, the impact of the solar irradiation level on the results is investigated. Figure 12 depicts this analysis for the case of 150 L min−1 flow rate and 600 K inlet temperature. It is obvious that the thermal enhancement does not present significant variation with the solar potential. A small increase in the efficiency is observed only for cases with high concentrations (5 and 6%). Thus, it can be said that the thermal efficiency enhancement is approximately constant and independent of the solar irradiation level. This result is explained by the generally high thermal performance of PTC for all the possible operating conditions. On the other hand, the thermal efficiency enhancement is found to be dependent on the other examined parameters (inlet temperature, flow rate and nanoparticle concentration) with a high way.

Fig. 12
figure 12

The impact of the solar irradiation level on the thermal efficiency enhancement for flow rate equal to 150 L min−1, inlet temperature equal to 600 K and Cu nanoparticle

Full size image

Conclusions

The objective of this work is to investigate the utilization of nanofluids in parabolic trough collectors. The module of LS-2 PTC is examined with a developed thermal model in EES. Six different nanoparticles are examined with Syltherm 800 as the base fluid for concentrations up to 6%. The inlet temperature level, the flow rate and the solar irradiation level are the investigated parameters, as well as the nanoparticle concentration. Moreover, a new evaluation index for the nanofluid evaluation in solar collectors is introduced. The most important findings of this work are listed below:

  • The Cu nanoparticle is found to lead to higher thermal efficiency enhancement while the SiO2 to the lowest. The thermal conductivity of the nanoparticles is found to be a determining factor in the respective nanofluid performance.

  • Higher concentration ratio is found to be beneficial for all the examined operating conditions. However, after 4% nanoparticle concentration, the thermal efficiency enhancement does not present high increasing rate.

  • The thermal efficiency margin is found to be higher for low flow rates and higher inlet temperatures. Thus, the use of nanofluids is recommended in the cases with these operating conditions. Practically, the use of nanofluids is recommended in cases with higher thermal losses because of the higher thermal efficiency enhancement margin.

  • It is found that the impact of the solar irradiation level has a negligible impact on the thermal efficiency enhancement.

  • The maximum thermal efficiency enhancement is found to be 2.2% for 6% Cu concentration, flow rate 50 L min−1 and inlet temperature 600 K. On the other hand, the thermal efficiency enhancement margin for high flow rates and low temperature is approximately negligible.

  • The suggested index for the evaluation of the performance enhancement is found to be directly connected with the thermal efficiency enhancement. Thus, its adoption can be made. This index takes into consideration the heat transfer coefficient, the density-specific heat capacity product and the flow rate level.