Introduction

Depletion of fossil fuels, the release of enormous amounts of greenhouse gases, and subsequent global warming are the pendulum points for both the scientists and researchers, to focus on renewable sources of energy like solar energy, wind energy, ocean energy, and geothermal energy, which are clean, evergreen, and available abundantly. Even though many renewable sources of energy are available, solar energy is the most promising one, to utilize in an easy way with a low cost. For most of the thermal applications, it is required to generate the energy at a higher level than that of the flat plate solar collectors. The concentrated solar collectors like parabolic trough or dish types are used to attain a higher energy level. Maximum heat energy is achieved by decreasing the absorber area which will decrease the heat loss and increase the useful heat gain at a higher concentration ratio. Solar energy is widely used for hot water, industrial process heat, steam generation and electricity production [1]. Encapsulated phase material-based thermal energy storage system for concentrating solar power plant was analyzed for uninterrupted operation as well as to ensure the techno-economic status of storage material [2]. Sheikholeslami et al. [3] designed clean energy storage unit to reduce the energy consumption through civil structural instead of increasing the space between air passage and phase change material. Curing process completed 21.4% faster than other case, which ensured the system validation. Conical geometry solar collector was designed and tested for its thermal performance for producing hot water where deionized water-based alumina nanofluid as heat transfer medium [4]. The solar parabolic trough collector (SPTC) is the most mature technique for steam production where different types of nanofluid with various concentrations used. Vijayan and Karunakaran [5] investigated the performance of unshielded receiver type SPTC, where water as HTF. They observed the maximum difference in temperature as 24 °C. The mixed type storage tank integrated SPTC model was developed using MATLAB software. The model is experimentally verified and analyzed for its performance. The enhancement of maximum temperature difference between analytical and experimental storage tank was observed as 9.59% [6]. Valanarasu and Sornakumar [7] carried out the experimental work on SPTC and recorded the temperature difference of 38.84º, during the test time period of 9.30–4.00 pm, where no heat energy was removed. Bellos et al. [8] experimentally analyzed various HTFs such as pressurized water, molten nitrate salt, carbon dioxide, air, sodium liquid, and helium on SPTC for higher temperature range. Bellos et al. [9] investigated the performance of various Syltherm 800-based nanofluids (Cu, CuO, Fe2O3, TiO2, Al2O3, and SiO2) on SPTC and observed Cu as an efficient one among various types of nanofluids, where the fluid flow rates vary from 50 to 300 L min−1. The thermal efficiency enhancement of Cu nanofluid was 0.74% at 6.0% concentration. The latest developments in solar concentrator and performance enhancement methods such as nanofluid, turbulator, insert, and absorber geometry modification are discussed [10]. The deionized (DI) water and ethylene glycol-based aluminum oxide nanofluid were synthesized using magnetic stirrer cum ultrasonication, and thermal properties were analyzed [11]. Murshed et al. [12] analyzed the variation, trend, and influence of temperature on thermophysical properties such as thermal conductivity, specific heat and viscosity.

Sadaghiyani et al. [13] developed two new compound type SPTC collector models to determine the efficiency and compared the results with LS-2 and Dudley’s model. Stefanovic et al. [14] developed photovoltaic panel integrated hybrid solar collectors to investigate the conversion ability of solar radiation into heat and electricity. Marco et al. [15] investigated the technical difficulties related in utilizing the CuO nanofluid as HTF flowing through transparent quartz receiver. They reached the maximum fluid temperature of 180 °C and an average efficiency of 65%. Visconti et al. [16] designed an electronically operating system to monitor and control two similar solar collectors precisely under the same environment where water and Al2O3 nanofluid were used as HTF for exact performance comparison. Colangelo et al. [17] analyzed and compared the thermal efficiency of simulated results with actual experimental results. They proved efficiency enhancement of 7.54% while using Al2O3 nanofluid as HTF.

Ghasemi et al. [18] detailed the influence and performance of Al2O3/H2O and CuO/H2O nanofluid of various concentrations on SPTC. The experimental work was carried out on parabolic trough solar collector to study the thermal and thermophysical properties of Al2O3/DI water nanofluid at very low concentration and mass flow rates [19]. Al2O3 nanofluid was used as HTF on a SPTC to arrive the techno-commercial analysis of steam power plant [20]. Thomas [21] brought out a straightforward construction and conducted a static load test on collector structure to ensure the stability [21]. The experiment was conducted by Kalogirou [22] on concentrated solar collector as per ASHRAE standard, and they studied the efficiency and incident angle. Thermal performance of therminol on SPTC system was experimentally studied [23]. The performance of SPTC was enhanced with nanofluid concentration and inverse with a mass flow rate of nanofluid [24]. Senthil and Cheralathan carried out experimental works on parabolic dish solar collector’s receiver, to analyze the effect of absorber, heat gain and losses. Absorber surface temperature has a positive effect with increased concentration ratio, beam radiation, ambient temperature but opposite sense to air velocity [25]. Impact of thermal energy storage materials in concentrated solar absorbers resulted in improved thermal energy capacity [26].

Farshad and Sheikholeslmi [27] studied the effect of Reynolds number, number of revolutions, diameter ratio, concentration of nanoparticle and wind velocity on exergy loss and heat transfer parameters on flat plate collector, where twisted helical tape and alumina/H2O nanofluid were used for performance enhancement. Most of the work was carried out in the range of 1.0–5.0% (concentration) and 0.02 kg s−1 as the minimum nanofluid flow rate with uneven incremental step in both fluid concentration and mass flow rate.

Based on the above literature, we practiced an attempt to synthesize and analyze Al2O3/DI water nanofluid’s thermal performance at low concentration (0.2–1.0%) and mass flow rate (0.010 kg s−1 and 0.015 kg s−1) at an equal incremental step on unshielded receiver (USR) type SPTC. The significant results are reported in this work.

Experimental

Construction of SPTC and working procedure

The photographic view of USR type SPTC system for hot water generation test setup and its schematic diagram is shown in Figs. 1 and 2. The test setup consists of SPTC system, heat energy storage tank, nanofluid collection cum recirculation tank, submersible pump, and tracking module. The collector system is included with aperture, receiver, and reflector. The aperture is in the shape of parabolic, where the polished aluminum is fixed, to reflect the solar radiation toward the receiver, which falls on it. The total area of collector aperture or reflector is 1.08 m2, the length is 1.2 m, and the width is 0.9 m. But the approached effective reflector area is only 1.0593 m2. The absorber is made of any material (we used copper), but cost, ease of availability, and absorbance capability (varied depends upon the material) must be considered. The copper tube of standard size is used here as an absorber and not shielded by any means. Concentration ratio (ratio of aperture area and absorber area) is a critical parameter that is influencing the useful heat gain. The heat energy collection tank is made up of rigid plastic with proper insulation, to reduce the heat loss. DI water-based alumina nanofluid is selected and utilized as heat transfer fluid due to its extensive experimental reports by researchers, low cost, thermal conductivity, low-pressure drop, low sedimentation and ease of availability.

Fig. 1
figure 1

Experimental platform of solar collector

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Fig. 2
figure 2

Schematic diagram of solar collector

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The USR tube is exposed to reflected radiation coming from the collector aperture, and the heat energy is transferred to HTF. The alumina/DI water nanofluid is heated due to heat transfer from the USR tube by convection mode. The heated alumina/DI water nanofluid is cooled while flows through the heat exchanger where HTF releases the heat energy to hot water by conduction–convection heat exchange mode. A mini submersible pump is used for recirculation and to close the HTF circuit. The experimental work is carried out for two mass flow rates (0.010 kg s−1 and 0.0150 kg s−1) controlled by a control valve. The mass flow rates maintain the HTF in the laminar region, up to a certain temperature level. The calculated bulk mean temperature of the fluid is 88 °C and 56 °C for the mass flow rate of 0.010 kg s−1 and 0.015 kg s−1, respectively. The bulk mean temperature of HTF is restricted to keep the flowing fluid in the laminar region. SPTE is oriented in the north–south direction, and tracking is carried out in the east–west direction at an angle of 15° automatically for every 1-h time gap, to absorb the maximum radiation. The parametric values are given in Table 1.

Table 1 Specifications of collector system
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Synthesis of nanofluid

The nanofluid is prepared by dissolving the Al2O3 nanoparticle (Alfa Aesar) in DI water at five different concentrations from 0.2 to 1.0% v/v. Main properties of alumina nanoparticles are given in Table 2. First, the mass of nanoparticles is calculated using Eq. (1), and then it is mixed with DI water manually and followed by a magnetic stirrer (Remi). Finally, the nanofluid is transferred from magnetic stirrer to ultrasonic bath (Maxsell) for homogeneous mixing. The same procedure is adopted for all concentrations as shown in Fig. 3. The prepared nanofluid has good stability not only due to the two-step preparation procedure, also due to low concentration and mass flow rate.

$$ W_{\text{np}} = \left[ {{\raise0.7ex\hbox{${V_{\text{np}} }$} \!\mathord{\left/ {\vphantom {{V_{\text{np}} } {V_{\text{np}} + V_{\text{bf}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${V_{\text{np}} + V_{\text{bf}} }$}}} \right] $$
(1)
Table 2 Properties of Al2O3 nanoparticles
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Fig. 3
figure 3

Synthesis of nanofluid

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Thermal performance analysis

The instantaneous efficiency of SPTC is determined based on recorded quantities such as solar radiation intensity, ambient temperature, nanofluid inlet temperature, and wind velocity. The absorbed solar radiation depends on the reflectivity of reflector material, and a higher reflectivity leads to higher heat absorption by the fluid as per Eq. (2) [28]. Both the wind loss and radiation loss coefficient are playing a vital role in loss coefficient calculation, which can be determined as per Eq. (3). Wind loss coefficient is proportional to Nusselt number, and thermal conductivity of air, but inverse to receiver diameter. The radiation loss coefficient depends on the emissivity of receiver material, surface temperature and ambient temperature. The properties such as density, kinematic viscosity, dynamic viscosity, specific heat, Prandtl number, and thermal conductivity were taken from thermo-physical property data. The status of flowing fluid is calculated based on its Reynolds quantity. If the value of Re < 2300, then the flow is laminar and coming under fully developed hydrodynamic as well as thermal profile mode. Therefore, Nu = 3.7 is considered for constant wall temperature [29]. If the values are in the range of 2300 < Re < 5 × 106 and 0.5 < Pr < 2000, then the nanofluid ensures fully developed turbulent flow status. Equations 4 and 5 are represented by Filonienko [30] and Gnielinski [31], used to calculate the friction factor and Nu for turbulent flow, respectively.

$$ S = I_{\text{b}} R_{\text{b}} \rho \gamma \left( {\tau \alpha } \right) + I_{\text{b}} R_{\text{b}} \left( {\tau \alpha } \right)\left( {{\raise0.7ex\hbox{${D_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{D_{\text{o}} } {\left( {W + D_{\text{o}} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {W + D_{\text{o}} } \right)}$}}} \right) $$
(2)
$$ U_{\text{l}} = \left[ {\left( {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {h_{\text{w}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${h_{\text{w}} }$}}} \right) + \left( {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {h_{\text{r}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${h_{\text{r}} }$}}} \right)} \right]^{ - 1} $$
(3)
$$ f = \left( {1.58 \times \ell n\left( {\text{Re} - 3.28} \right)} \right)^{ - 2} $$
(4)
$$ {\text{Nu}} = \frac{{\left( {{\raise0.7ex\hbox{$f$} \!\mathord{\left/ {\vphantom {f 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} \right)\left( {\text{Re} - 1000} \right)\Pr }}{{1.0 + 12.7\left( {\sqrt {{\raise0.7ex\hbox{$f$} \!\mathord{\left/ {\vphantom {f 2}}\right.\kern-0pt} \!\lower0.7ex\hbox{$2$}}} } \right)\left( {\Pr^{{{\raise0.7ex\hbox{$2$} \!\mathord{\left/ {\vphantom {2 3}}\right.\kern-0pt} \!\lower0.7ex\hbox{$3$}}}} - 1} \right)}} $$
(5)

Due to the absence of variation in the receiver dimension and its thermal conductivity, the heat loss coefficient and inside heat transfer coefficient influenced on overall heat loss coefficient given in Eq. (6). The actual useful heat gain is the difference between useful heat gain and total heat loss which is determined by Eq. (7). The instantaneous collector efficiency is proportional to the actual useful heat gain available as per Eq. (8). Now, the optical efficiency is determined for the various angles of incident by Eq. (9). The optical efficiency (ηopt) only depends on the reflectivity (ρ) of aperture material, intercept factor (γ), the transmittance-absorption product of the receiver (τα). Both the incident angle modifier and end loss were also considered as shown in Eq. (10) to calculate the optical efficiency. The transmittance parameter can be taken 1.0 due to the unshielded type receiver. The inlet–outlet temperature of nanofluid, ambient temperature, and water temperature are observed using the PT-100 resistance temperature detector. The solar power meter, vane-type anemometer, and rotameter are used to measure the beam radiation, wind speed, and mass flow rate. The uncertainty of these measuring instruments is given in Table 3. Each concentration was tested for 3 days. Before charging the next concentration, the existing nanofluid is fully drained. To complete the cleaning process, the test run was conducted with DI water, and then the system is kept in ideal condition. All these parameters are observed at every five minutes.

$$ U_{\text{o}} = \left[ {\left( {{\raise0.7ex\hbox{$1$} \!\mathord{\left/ {\vphantom {1 {U_{\text{l}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${U_{\text{l}} }$}}} \right) + \left( {{\raise0.7ex\hbox{${D_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{D_{\text{o}} } {\left( {D_{\text{i}} \times h_{\text{fi}} } \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {D_{\text{i}} \times h_{\text{fi}} } \right)}$}}} \right) + \left( {{\raise0.7ex\hbox{${D_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{D_{\text{o}} } {2K_{\text{r}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${2K_{\text{r}} }$}}} \right)\ell n\left( {{\raise0.7ex\hbox{${D_{\text{o}} }$} \!\mathord{\left/ {\vphantom {{D_{\text{o}} } {D_{\text{i}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${D_{\text{i}} }$}}} \right)} \right]^{ - 1} $$
(6)
$$ \frac{\partial }{{\partial x_{\text{j}} }}\left( {\rho U_{\text{j}} k} \right) - \frac{\partial }{{\partial x_{\text{j}} }}\left( {\frac{{\mu_{\text{eff}} }}{{\sigma_{\text{k}} }}\frac{{\partial U_{\text{i}} }}{{\partial x_{\text{j}} }}} \right) = G_{{{\text{k}}_{1} }} - \rho \varepsilon $$
(7)
$$ \eta_{\text{ins}} = \left[ {{\raise0.7ex\hbox{${Q_{\text{u}} }$} \!\mathord{\left/ {\vphantom {{Q_{\text{u}} } {\left( {I_{\text{b}} R_{\text{b}} WL} \right)}}}\right.\kern-0pt} \!\lower0.7ex\hbox{${\left( {I_{\text{b}} R_{\text{b}} WL} \right)}$}}} \right] $$
(8)
$$ \eta_{\text{opt}} = \left( {\rho \gamma \tau \alpha } \right) \times K\left( \theta \right) \times \left( {X_{\text{end loss}} } \right) $$
(9)
Table 3 Uncertainty of measurement
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The parametric values measured using the instruments discussed here have not deviated over the limit specified by the ASHRAE standard, which confirms that the experimental works are standard conditions. An uncertainty analysis was carried out based on the procedure suggested by Kline and McClintock [32] and Moffat [33] to validate the experimental measurements. Equation (10) is used to determine the overall uncertainty of the experiment. Equations (10) and (11) are used to determine the overall energy and exergy uncertainty of the experiment.

$$ \delta \eta^{2} = \left( {\frac{\delta \eta }{{\delta \dot{m}}}} \right)^{2} \left( {\delta \dot{m}} \right)^{2} + \left( {\frac{\delta \eta }{{\delta I_{\text{b}} }}} \right)^{2} \left( {\delta I_{\text{b}} } \right)^{2} + \left( {\frac{\delta \eta }{{\delta T_{\text{i}} }}} \right)^{2} \left( {\delta T_{\text{i}} } \right)^{2} + \left( {\frac{\delta }{{\delta T_{\text{o}} }}} \right)^{2} \left( {\delta T_{\text{o}} } \right)^{2} $$
(10)
$$ \left( {\delta \eta_{\text{ex}} } \right)^{2} = \left( {\frac{{\delta \eta_{\text{ex}} }}{{\delta \dot{m}}}} \right)^{2} \left( {\delta \dot{m}} \right)^{2} + + \left( {\frac{{\delta \eta_{\text{ex}} }}{{\delta I_{\text{b}} }}} \right)^{2} \left( {\delta I_{\text{b}} } \right)^{2} + \left( {\frac{{\delta \eta_{\text{ex}} }}{{\delta T_{\text{i}} }}} \right)^{2} \left( {\delta T_{\text{i}} } \right)^{2} + \left( {\frac{{\delta \eta_{\text{ex}} }}{{\delta T_{\text{o}} }}} \right)^{2} \left( {\delta T_{\text{o}} } \right)^{2} + \left( {\frac{{\delta \eta_{\text{ex}} }}{{\delta T_{\text{a}} }}} \right)^{2} \left( {\delta T_{\text{a}} } \right)^{2} $$
(11)

By considering the uncertainty of the measuring instruments, while HTF flow rate varied from 0.010 to 0.0150 kg s−1, the experimental energy and exergy uncertainty varied from 5.6 to 4.2% and 3.8 to 2.5%, respectively.

Results and discussion

The results observed from the experimental work are used to analyze the performance of the low volume fraction of alumina/DI water nanofluid on the SPTC with the hot water generation system discussed and presented here.

The variation of ambient temperature and bulk mean temperature for both the mass flow rate of HTF (nanofluid) with respect to the working time of the whole day is given in Fig. 4. There is no abrupt increase in ambient temperature observed for the total module. The ambient temperature starts from 29.0 °C at 8.00 am, and it reaches a maximum of 33.0 °C at 2.00 pm. The difference is only 4.0 °C and it depends on the location [23]. At 1.00 pm the bulk mean temperature difference of mass flow rates is zero, before and after this test time it is gradually increased. The bulk mean temperature gradually increases from 30 to 56 °C, and then it is reached to 36 °C. The enhancement of mean temperature is 86.7% for the test duration of 8.00 am to 1.00 pm, and then it is reduced gradually by 55.6%. Variation of the temperature difference between the inlet and outlet for both the mass flow rate of the total test period is given in Fig. 5. The inlet temperature of nanofluid depends not only on the environment but also on the energy absorption capacity of fluid. The fluid outlet temperature depends on the receiver tube temperature and heat transfer coefficient. The receiver temperature is increased by incident solar radiation and the heat transfer coefficient influences outlet temperature. Exactly at 1.00 pm, the temperature difference is equal to both the mass flow rate. The minimum temperature is 4.0 °C, and the maximum difference is 46 °C.

Fig. 4
figure 4

Variation of Ta and Tm over time

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Fig. 5
figure 5

Temperature rise trend with time

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Variation of heat loss coefficient for both the DI water and nanofluid during the test period is shown in Fig. 6. Heat loss is included both wind loss coefficient (hw) and radiation loss coefficient (hr). hw depends on ambient temperature and wind speed. hr depends on the receiver temperature and emissivity of the receiver. But heat loss coefficient (Ul) is independent of the flowing fluid. Consequently, the observed values apply to both mass flow rates of DI water and nanofluid with various concentrations. Ul is varied from 4.64 to 5.433 W m−2 K−1 for the whole testing period. At 1.00 pm, the minimum and maximum heat losses are 4.64 W m−2 K−1, 6.646 W m−2 K−1 which is the combined effect of both the loss coefficients. hr is influenced more and hw is having a little impact on Ul. Increase in receiver temperature will increase the Ul.

Fig. 6
figure 6

Heat loss coefficient over time

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The variation of overall heat loss coefficient (Eq. 5) with the various volume fractions of HTF at defined mass flow rate is given in Fig. 7. The first point, 0% volume fraction means the fluid is only (absence of nanoparticles) DI water. The overall heat loss coefficient is increased with the increase in volume fraction, and it is the combination of heat loss coefficient and inside heat transfer coefficient. The overall loss coefficient for 0.015 kg s−1 is more than the mass flow rate of 0.010 kg s−1. It is 5.6369 W m−2 K−1 and 5.6377 W m−2 K−1 for water of mass flow rate 0.010 kg s−1 and 0.015 kg s−1. For the concentration of 1.0%, the loss coefficients are 5.6507 W m−2 K−1 and 5.6518 W m−2 K−1 corresponding to the given flow rates. The maximum difference for 1.0% volume fraction was meager, i.e. 0.11%. This optical efficiency not varied depends on solar radiation. It belongs and is proportional to the reflective material, absorber material, absorber position, and an incident angle of solar radiation. To obtain the maximum possible optical efficiency, it requires the aperture with high reflectivity, a maximum absorbance-transmittance product and accurate alignment of the receiver. The optical efficiency of the collector has varied from 31.57% in the morning (8.00 am), and it has reached the maximum value (60.75%) in the noon (12.00 pm) again it comes back to the starting point. The overall loss coefficient is high, due to the unshielded receiver and mass flow rate of the liquid. Wind velocity plays a vital role which is considered.

Fig. 7
figure 7

Overall heat loss coefficient versus concentration

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Changes in the quantity of the receiver tube temperature, total available solar radiation (Eq. 6) and the beam radiation with respect to time are given in Fig. 8. The beam radiation is slowly increased, 250 W m−2 as a minimum and 850 W m−2 as maximum. It depends upon the location of the test setup. The total available solar radiation is also increased proportionally to solar radiation. It depends not only on the solar radiation, but also on the tilt factor and the reflectance of collector material, the intercept factor, absorptive and transmittance of the absorber. Other than the tilt factor, the remaining parameters are influenced more by the total available solar radiation. It performs an influence on the useful heat gain. In the test period of the whole day, the receiver temperature is observed as low in the morning and reached the maximum at noon and near noontime. It is due to the increased quantity of direct solar radiation.

Fig. 8
figure 8

Variation of receiver temperature, solar flux and beam radiation

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Figure 9 shows the variation of the heat transfer coefficient of the flowing fluid through the absorber with various concentrations. The values are absorbed for the mass flow rate of 0.010 kg s−1 and 0.0150 kg s−1 with different concentrations. Two opportunities exist to enhance the inside heat transfer coefficient, namely, by increasing the concentration and increasing the mass flow rate. The velocity of the fluid is increased due to mass flow rate; in turn, the inside heat transfer coefficient is increased. An increase in nano-concentration will increase the thermal conductivity of the liquid and heat transfer.

Fig. 9
figure 9

Variation of heat transfer coefficient with concentration

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Heat transfer coefficient variation of DI water with time for the mass flow rates are given in Fig. 10. The change in mass flow rate has shown the influence on the heat transfer coefficient. When the mass flow rate is increased, it leads to an increase in heat transfer. The increment is also very gradual from 136.61 to 144.13 W m−2 K−1. Here, Nusselt number is constant because flowing fluid is in the laminar region and is equal to 3.7.

Fig. 10
figure 10

Heat transfer coefficient over test duration

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Figure 11 shows the inside heat transfer coefficient of the fluid such as DI water (0%) and Al2O3/DI water (1.0% volume fraction) nanofluid at the flow rate of 0.01 kg s−1 through the absorber. The same trend is followed for other mass flow rate also. The volume fraction is influenced directly by the heat transfer rate. This heat transfer rate mainly depends on the thermal conductivity of HTF. The heat transfer coefficient is increased from 136.61 to 144.13 W m−2 K−1 for DI water and 145.04 to 153.00 W m−2 K−1 for 1.0% volume fraction of nanofluid. The maximum heat transfer rate is 152.91 W m−2 K−1. The difference between 0 and 1.0% concentration is 8.8 W m−2 K, and the inside heat transfer enhancement is 6.2% as shown in Fig. 12.

Fig. 11
figure 11

Comparison of heat transfer coefficient based on flow rate

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Fig. 12
figure 12

Comparison of heat transfer coefficient over concentration

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The instantaneous collector efficiency for the whole test period from 8.00 am to 4.00 pm is calculated for all volume fractions, and averages of these instantaneous collector efficiencies for each volume fraction are calculated for both the mass flow rates. These efficiency values of nanofluid and DI water are presented in Fig. 13. The attained maximum instantaneous efficiency is 59.13% (m = 0.015 kg s−1) and 59.05% (m = 0.010 kg s−1) for USR copper tube, 55.20% when using water as HTF [34, 35] for the same type receiver. Similar results were attained for alumina-based nanofluid for the mass flow rate of 0.010 kg s−1 where alumina and therminol were used as HTF [36, 37]. The reason for this very slight variation in efficiency is glass shielding of copper tube receiver, the diameter of the receiver and mass flow rate of the HTF. The instantaneous collector efficiency is decided by two main factors such as solar radiation and useful heat gain.

Fig. 13
figure 13

Comparison of ηth with DI water and Al2O3

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The global efficiency equation of the present working model is validated with other researchers as shown in Fig. 14. Here various heat transfer coefficients such as wind loss coefficient, radiation loss coefficient, heat loss coefficient, inside heat transfer coefficient, and overall heat loss coefficient are considered. So, this maximum efficiency point is compared with other efficiency models. The model developed by Marco et al. [15] offered not only maximum energy absorbed but also the quantity of heat loss. The minimum energy was absorbed by Kalogirou et al. model [38]. The absorbed energy is enhanced by 1.51% than Murphy et al. model [39] and 2.95% less than Valanarasu’s model [7]. But in the case of removed energy, the present work exhibits lower heat loss than Valanarasu’s model [7] and higher than Murphy’s model [39]. The current model has good agreement with the previous models developed by Valanarasu and Murphy.

Fig. 14
figure 14

Performance verification of present model

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Conclusions

The thermal performance of alumina/DI water nanofluid at different concentrations and mass flow rates on the concentrated solar concentrator was investigated and compared with DI water. The alumina nanoparticles are mixed with DI water using the magnetic stirrer and then sonicated by an ultrasonic bath for 60 min.

Nanofluid is synthesis at five different concentrations from 0.2 to 1.0% by volume (incremental step 0.2%). The collector efficiency is increased with the increased mass flow rate and concentration of nanoparticles in the base fluid. The increase in the mass flow rate increases thermal efficiency. However, the higher mass flow rate of HTF changes the flow from laminar to turbulent condition.

On an average basis, the maximum collector efficiency for deionized water is 58.45% (m = 0.010 kg s−1), 58.59% (m = 0.015 kg s−1) and 58.58% (m = 0.010 kg s−1), 58.68% (m = 0.015 kg s−1) for nanofluid. At the HTF flow rate of 0.010 kg s−1 and 0.015 kg s−1 mass flow rates, the efficiency enhancements are 1.55% and 1.49% for various nanofluid concentrations.