Thermal evaluation of geometrical innovations in concentric and eccentric evacuated single and double solar collectors

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Lino, Janayna Rocha Silva, Claudia Rosa do Espirito Santo Nóbrega, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3345207/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 19 Jan, 2024 Read the published version in Journal of the Brazilian Society of Mechanical Sciences and Engineering → Version 1 posted 4 You are reading this latest preprint version Abstract In this study, an experimental and numerical investigation of eight geometrical configurations of evacuated tube solar collectors was conducted. The configurations were tested simultaneously in outdoor installation under the same test conditions. The parameters such as collector eccentricity, solar concentration, vacuum, collector absorber, and cover tube materials were investigated. The numerical model developed in MATLAB was validated with experimental results. The results show that the eccentricity and the absorptivity of the material of the absorber are the parameters that have the highest influence on the collector performance. The use of reflective film in the eccentric solar collectors’ configurations can increase efficiency by 33%. The vacuum presented an efficiency increase variation between 1% and 4% in the eccentric tube collectors. For the concentric collectors configurations, the use of the vacuum between the tubes can reach an increase of 9% in its performance. The eccentricity of the collector using reflective film and vacuum allows an effective solar concentration in the collector absorber presenting a 26% higher efficiency when compared with the concentric collector. Evacuated tube solar collector eccentric absorber low concentration solar collector reflective film modeling of eccentric collector Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 1. Introduction In the last decades, the use of traditional energy sources has been replacedcontinuously by sustainable energy due to global warming, depletionof fossil fuels, and diversification of energy matrices. In this way, solar energy has been attracting a lot of attention and stands as a promising source, which can be and has been applied for several applications as: agriculture, heat production, seawater distillation, electricity generation, and many others [ 1 ]. Due to their economic and technical viability and high performance, thermal solar collectors are extensively used. One of the most common and promising thermal collectors is the evacuated tube solar collectors (ETC) [ 1 , 2 ]. These collectors can be applied as sources for organic Rankine cycle (ORC), absorption systems, hydrogen production, freeze recovery, thermoelectric generation, and others. Yaïci et al. [ 3 ] conducted an investigation of a solar-driven ORC system that works with fluid mixtures and used micro-cogeneration. They chose an evacuated tube flat plate solar collector to feed the system, due to its efficiency and delivered temperature. Parabolic trough collectors (PTC) are also diversely used for ORC applications [ 4 ]. Meraj et al. [ 5 ] performed an analysis as a case study in New Delhi. The results showed that there was no need to design the thermal and photovoltaic system for high capacities of the absorption system, and that the concentration ratio plays the main hole. Pandya et al. [ 6 ] tested several solar collectors to determine the optimum heat source for an absorption cooling system. The authors tested the flat-plate solar collector (FPC), ETC, PTC, and compound parabolic collector (CPC). Results showed that ETC demands the lowest area, and FPC the lowest cost. Jiang et al. [ 7 ] made a numerical and experimental investigation on thermal and optical aspects on triangular solar air collectors. They evaluated three models: using insulation material, transparent cover plate and double transparent cover plate. The one using transparent cover plate has the highest optical efficiency and the different models are adaptable for different weather conditions. Karabuga et al. [ 8 ] conducted a thermodynamic analysis using ETC to power an ORC system, which produces electrical energy and generates hydrogen. The energy and exergy efficiencies of the whole system were about 51% and 16%, respectively. Imponenti et al.[ 9 ] used parabolic trough collectors to supply and control a freeze recovery. The results showed PTC plants are an opportunity for capital and operational cost-savings in these systems. Al-Tahaineh and AlEssa [ 10 ] used the evacuated tube solar collector to heat a cold zone in a thermoelectric generator (TEG). The results indicated that TEG applications have a promising potential for solar energy. The ETC outlet hot water temperature is one of the most significant parameters in the TEGs performance. The most diverse commercial thermal solar collector used is the evacuated tube (ETC) [ 11 ]. Two main techniques are used to enhance the efficiency of ETC: geometrical modifications and the use of nanofluids and PCMs. Henein and Abdel-Rehim [ 12 ] investigated the performance of a heat pipe ETC using MgO/MWCNT nanofluid. The hybrid use of 50% MgO and 50% MWCNT presents the best performance for all tested flow rates. Alrowaili et al. [ 13 ] conducted an investigation of a CuO-Cu/water nanofluid coupling ETC and an energy storage system. The ETC presented high efficiency using hybrid nanofluid 2.5g CuO + 1.5g Cu in different flow rates. Ismail et al. [ 14 ] made a numerical comparative study about the use of circular and rectangular absorbers for ETC using Al 2 O 3 /water as a nanofluid. The best ETC configuration is using a circular absorber and the maximum improvement in the ETC efficiency using nanofluid was about 9%. Eltaweel et al. [ 15 ] investigated the use of MWCNT/water as a nanofluid for ETC and FPC using various flow rates. The maximum energy efficiency found for the ETC was 55% at 0.02kg/s and with 0.05 wt%. According to the results, the enhancement in efficiency can reduce the collector area. Tabarhoseini and Sheikholeslami [ 16 ] investigated the entropy generation inside an ETC using CuO/water nanofluid. They concluded that the entropy generation using just water is higher than using nanofluid, the heat transfer entropy generation was reduced by about 6% using 5% CuO. Yeh et al. [ 17 ] tested a double spiral coil heat exchanger with phase change material (PCM) in a parabolic trough collector. The results show that maintaining the temperature difference between the working fluid and PCM it is possible to increase the duration of available hot water for domestic applications. The optimal configuration was found for 2.6 times longer discharging process and outlet temperature of 55°C. Proposing a geometrical modification, Teles et al. [ 18 ], modelled numerically an eccentric solar collector with a small concentration. A maximum of 73% efficiency was obtained using this model modification. Seddaoui et al. [ 19 ] combined the configuration of FPC and ETC to create a new design of vacuum flat plate collectors. This model was tested experimentally and simulated numerically. The results showed that for high absorber emissivity values the new model was more efficient than the ETC, although for low absorber emissivity the ETC was more efficient. Almitani et al. [ 20 ] tested several geometries of a twisted turbulator effect inside a parabolic solar collector. They also tested nanofluids using MWCNT and MgO nanoparticles in different concentration ratios. The results showed that the use of the turbulator improved the efficiency of the collector and increased the Reynolds number from 10,000 to 25,000. Roshith and Varghese [ 21 ] made a numerical investigation of different tube geometry for a glass ETC. A high collector length-to-diameter ratio, inclination angle, and circumferential heat input lead to a high natural circulation flow rate. The effects of vacuum and solar film in a low-concentration eccentric collector were investigated [ 22 ]. The eccentric collector with both reflective film and vacuum reached a maximum efficiency of 89% and a minimum of 42%. Ismail et al. [ 23 ] evaluated experimentally the performance of a low-concentration concentric solar collector that works with the direct flow. The highest thermal efficiency reported was 68% for the model with concentration and vacuum. So far, the research was dedicated to improving the performance of solar collectors by using thermal (use of nanofluids and PCM) and geometrical innovations. The literature review shows a research gap related to analyzing and comparing several geometrical innovations in concentric and eccentric evacuated tube solar collectors using different parameters. Based on this premise, this paper aims to carry out comparative analyses of evacuated tube solar collectors with different geometric configurations. This paper presents the simultaneous outdoor experimental tests on eight solar collector configurations; eccentric, concentric with and without reflective film, and with and without vacuum in the annular space to identify the collector configuration that produces the best thermal performance. Further numerical simulations were conducted on the best solar collector configuration to investigate the most adequate materials for both the cover tube and the collector absorber. The contribution of this study includes individual outdoor testing of the eccentric collector, simultaneous outdoor testing of both concentric and eccentric solar collectors’ configurations and validation of the developed numerical code with experimental results. 2. Evacuated tubes collector models formulation Eight models of evacuated tubes collector are studied in this paper (Figs. 1 and 2 ). Three important parameters are investigated: eccentricity between the cover and the absorber tube, the reflective film outside the bottom part of the cover tube and vacuum in the gap between the cover and absorber tube. The models are: C-WR-WV- concentric with a reflective film and with vacuum; C-WR-WTV- concentric with a reflective film and without vacuum; C-WTR-WV-concentric without reflective film and with vacuum; C-WTR-WTV- concentric without reflective film and without vacuum; E-WR-WV- eccentric with a reflective film and with vacuum; E-WR-WTV- eccentric with a reflective film and without vacuum; E-WTR-WV- eccentric without reflective film and with vacuum; E-WTR-WTV- eccentric without reflective film and without vacuum. The glass cover of the absorber receives solar irradiation that is transmitted through the glass. The solar irradiation is reflected by the reflective film, with 0.78 reflectivity, positioned in the external cover bottom part and concentrated on the absorber. The copper absorber, through which the working fluid (water) flows inside, receives concentrated solar irradiation and heats the flowing water (Fig. 3 ). The collector models have the same general dimensions and are shown in Table 1 . Table 1 General dimensions of solar collectors models. \({R}_{c,ext}\) (m) \({R}_{c,int}\) (m) \({R}_{a,ext}\) (m) \({R}_{a,int}\) (m) \({L}_{c}\) (m) 0.05 0.0485 0.01425 0.01325 1 To determine the eccentricity (focus point of reflection) in the eccentric models (E-WR-WV, E-WR-WTV, E-WTR-WV and E-WTR-WTV) the same formulation and models developed by Teles and Ismail [ 22 ] were used. While the concentration in the value of 3.46 was obtained based on Duffie and Beckman [ 24 ]. To describe the thermal-fluid phenomena that occur in the solar collectors the conservation equations of mass, momentum, and energy were used in the formulation of the thermal model. To use those equations, we considered that during a solar hour the collector operates in the steady-state regime, the thermal/physical properties are constant, all the surfaces reflect and emit diffusively and there is no heat transfer in the angular direction. Under these conditions, the equations can be written in the form: Mass: $$\rho \left(\frac{\partial u}{\partial x}+\frac{\partial v}{\partial r}\right)=0$$ 1 Momentum: $$\rho \left(u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial r}\right)=-\frac{\partial P}{\partial x}+{\mu }_{}\left(\frac{{\partial }^{2}u}{\partial {x}^{2}}+\frac{1\partial }{r\partial r}\left(r\frac{\partial u}{\partial r}\right)\right)$$ 2 $$\rho \left(u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial r}\right)=-\frac{\partial P}{\partial r}+{\mu }_{}\left(\frac{{\partial }^{2}v}{\partial {x}^{2}}-\frac{v}{r²}+\frac{1\partial }{r\partial r}\left(r\frac{\partial v}{\partial r}\right)\right)$$ 3 Energy: $$\rho \left(u\frac{\partial T}{\partial x}+v\frac{\partial T}{\partial r}\right)=\frac{{k}_{}}{{c}_{p}}\left(\frac{\partial ²T}{\partial x²}+\frac{1\partial }{r\partial r}\left(r\frac{\partial T}{\partial r}\right)\right)+\frac{S}{{c}_{p}}$$ 4 The boundary conditions of each part of the solar collectors presented in Figs. 1 and 2 are defined below: $${\dot{q}}_{c-abs,cover}=I{\alpha }_{glass}$$ 5 $${\dot{q}}_{conv,c-env}={h}_{conv,c-env}\left({T}_{env}-{T}_{out cover}\right)$$ 6 $${\dot{q}}_{rad,c-sky}=\epsilon \sigma \left({T}_{sky}^{4}-{T}_{out cover}^{4}\right)$$ 7 $${\dot{q}}_{conv,a-c}={h}_{conv,}\left({T}_{absorber}-{T}_{inside cover}\right)$$ 8 $${\dot{q}}_{rad,a-c}={F}_{c-a}\epsilon \sigma \left({T}_{absorber}^{4}-{T}_{inside cover}^{4}\right)$$ 9 The coefficients of convection heat transfer outside and inside the cover were obtained from the relations developed by Karlekar and Desmond [ 25 ] and Raithby and Hollands [ 26 ], respectively. The sky temperature was estimated by the correlation developed by Swinbank [ 27 ]. The detailed formulation was based on the study by Teles and Ismail [ 22 ]. To solve the equations the finite volume method was used. The SIMPLE algorithm and the power-law scheme were used to couple the momentum equations, and the TDMA was used to solve the discretized equations [ 28 ]. A random field is considered to start the interactive process and the process is finished when the stipulated convergence is reached (Eq. 10 ). The parameter can be the variables u, v, T and P of the conservation equations and n is the index of the iteration order. $$\sum _{i,j}\left|\frac{{ϕ }_{ij}^{n}-{ϕ }_{ij}^{n+1}}{{ϕ }_{ij}^{n}}\right|\le {10 }^{-6}$$ 10 The home build code was constructed in MATLAB and the numerical code used is similar to that used by Teles and Ismail [ 22 ].Grid tests were conducted for the cover and absorber domain. The most relevant test was the one related to the results. Table 2 presents the results of the grid tests and the corresponding deviation in the collector efficiency. The grids used for the cover were 20x5 and that for the absorber was 20x16 is used. Table 2 Results of grid tests with reference to the collector efficiency Cover Grid Absorber Grid deviation 5x5 5x8 13% 10x5 10x8 12% 20x5 20x16 1% 40x10 40x32 1% 3. Experimental rig, materials, procedure and uncertainty The experimental tests were conducted in outdoor conditions in the city of Campinas-Brazil (22°49'08.0"S 47°03'58.5"W) during the summer and autumn seasons. The circuit incorporates one collector tube of the configurations described in Figs. 1 and 2 , a controlled cold-water tank, globe valves at the entry and exit of the collector, a vacuum pump (VULKAS 12 CFM), and the measuring instrumentation. The instrumentation was composed of a measuring wind cup anemometer for measuring wind speed, a stopwatch, calibrated thermocouples Type-T and field logger system, a radiometer, a vacuum pump, and a pressure sensor for vacuum measurements. Since these are shown in Fig. 5 . The measuring cup and stopwatch were used to measure the collector mass flow. The mass flow measurements were conducted three times at the beginning of the experiment and an average of the results was used in the calculations. The thermocouples type-T were calibrated in the range from 0°C to 60°C, using a reference thermometer, and positioned in several parts of the collector. Two thermocouples were used to measure the inlet and outlet water ( \(\pm 0.24^\circ\) C). The field logger (NOVUS) was used to perform and save temperature data on a laptop. The MES-100 radiometer ( \(\pm 34 W/m²\) ) and Instrutherm cup anemometer (uncertain: \(\pm 2\%+0.2 m/s\) ) were used to measure the solar irradiation and wind speed. The vacuum sensor (Pirani PR-10K gauge headand Pirani 501) is used to measure the vacuum in the annular space of the collector, which is insulated with the aid of a silicone sealant. The average vacuum was \({4.10}^{-1}mbar\) . To maintain this degree of vacuum, the pump was kept working during the tests. The tests were carried out from 8:30 am to 3:00 pm, and the measurements of solar irradiation and wind speed were done in intervals of 30 minutes since they depend on the weather conditions. These long intervals were used to ensure that the measures did not take into account variations of solar radiation occurring by clouds. In this way, the measures are made for stable weather conditions. The radiometer was positioned parallel to the collector during the measurements of solar irradiation. Already the temperatures were measured at intervals of 30 seconds. As the experimental circuit (Fig. 4 ) does not have any solar tracking system, care was taken to position the solar collector facing the geographic north (80°), so that it would be guaranteed that throughout the day there would be incidence of sunlight on the collectors. The experimental tests were done in two groups; the first group was conducted on a single flow circuit with one collector at the time as shown in Fig. 6 , while in the second group two collectors were tested simultaneously under the same conditions as shown in Fig. 7 . The tests for the first group were conducted for the flow rate of 0.0081 kg/s. For the second group the tests were conducted according to Table 2 . Table 2 Experimental date of each configuration test in Campinas-Brazil under different conditions. Configuration Experiment date Flow rate (kg/s) C-WR-WV 02/21/2021 0.0081 C-WR-WTV 11/29/2020 0.0081 C-WTR-WV 04/02/2021 0.0081 C-WTR-WTV 03/12/2021 0.0081 E-WR-WV 30/04/2021 0.0081 E-WR-WTV 04/11/2021 0.0081 E-WTR-WV 05/16/2021 0.0081 E-WTR-WTV 05/24/2021 0.0081 C-WR-WV and E-WR-WV 08/23/2022 0.0054 C-WR-WTV and E-WR-WTV 09/02/2022 0.0068 C-WTR-WV and E-WTR-WV 09/08/2022 0.0062 C-WTR-WTV and E-WTR-WTV 09/23/2022 0.0080 To have a fair analysis, the efficiency is defined depending on the concentration level, which means that when there is no solar concentration C is equal to 1. $$\eta =\frac{\dot{m}cp∆ T}{IC{A}_{absorber}}$$ 11 3.1 Uncertainty To calculate the uncertainty of the results found in the experiments, the method proposed by Holman [ 29 ] was used. Each measurement has an uncertainty, and the uncertainty in the calculated result, as the efficiency in this study, is affected by the uncertainties in the primary measurements. The calculated result \(R\) is a given function of the independent variables \({ x}_{1}\) , \({x}_{2}\) ,…, \({x}_{n}\) ; so \(R=R({x}_{1},{x}_{2},\dots , {x}_{n})\) . Making \({w}_{R}\) be the uncertainty in the calculated result and \({w}_{1}\) , \({w}_{2}\) ,…, \({w}_{n}\) the uncertainties of the independent variables, \({w}_{R}\) is given by: $${w}_{R}={\left[{\left(\frac{\partial R}{\partial {x}_{1}}{w}_{1}\right)}^{2}+{\left(\frac{\partial R}{\partial {x}_{2}}{w}_{2}\right)}^{2}+\dots +{\left(\frac{\partial R}{\partial {x}_{n}}{w}_{n}\right)}^{2}\right]}^{1/2}$$ 11 To determine the uncertainty of the efficiency the solar irradiance, mass flow, and the fluid difference of temperature (Tout-Tin) were used in Eq. 11 and the uncertainty in the calculated efficiency is: $${w}_{\eta }={\left[{\left(\frac{\partial \eta }{\partial ∆ T}{w}_{∆ T}\right)}^{2}+{\left(\frac{\partial \eta }{\partial \dot{m}}{w}_{\dot{m}}\right)}^{2}+{\left(\frac{\partial \eta }{\partial I}{w}_{I}\right)}^{2}\right]}^{1/2}=\pm 6.54\%$$ 12 3.2 Model verification The model verification was performed for the cases: C-WTR-WV, C-WTR-WTV, E-WR-WV, E-WR-WTV, E-WTR-WV, and E-WTR-WTV. The comparison was made for the outer temperature of the water in the collectors for the highest solar radiation during the day of the experiment (0.0081 kg/s). The deviation between experimental and numerical was 1.9% for C-WTR-WV, 1.88% for C-WTR-WTV, 0.86% for E-WR-WV, 0.94% for E-WR-WTV, 2.2% for E-WTR-WV, and 1.67% for E-WTR-WTV (Fig. 8 ). This shows the good agreement between the numerical model and experiments. 4. Results and discussion 4.1 Experimental results First, the experimental results comparing the performance of all the tested models are presented and discussed. Identified the collector configuration with the best thermal performance, additional simulations were performed to identify the best material for the absorber tube and the transparent cover. The solar radiation, ambient temperature, wind, and inlet water temperature measured during the single collector experiments are shown in Fig. 9 for each collector configuration. Figure 10 shows the maximum efficiency reached during the day for the eight studied solar collector configurations. The highest efficiencies of 84% and 83% were achieved by the collector configurations E-WR-WV and E-WR-WTV, respectively. The cases C-WR-WTV, C-WTR-WTV, and E-WTR-WTV presented lower efficiencies of 48%, 49% and 47%, respectively. From this, it is possible to conclude that, the effect of the reflective film is significant for the collector that has the absorber positioned eccentrically in relation to the cover tube. The vacuum effects in the concentric collector can achieve a 9% improvement in efficiency, and the reflective film can achieve a 33% improvement in the case of the eccentric collector. The energy absorbed by the solar collector depends directly on solar irradiation (G). In order to compare the configurations of the solar collectors, the parameter (Tout-Tin)/G that relates the difference between inlet and outlet temperature and the solar irradiation was used. Figure 11 shows the parameters for the different configurations during the daily experiment. Considering this, the best configurations response of the collector were for E-WR-WV and E-WR-WTV (Eccentric collectors with reflective film). This shows the effectiveness of the use of reflective film in eccentric collectors. An intermediate level of response was found by configuration C-WR-WV. Configurations E-WTR-WV, C-WTR-WV and C-WTR-CWTV had a similar low response and presented a uniform curve during the day. This behavior is justified by the absence of solar concentration in the configurations and low vacuum effects. For configuration C-WR-WTV, the response was as low as the others during 11–13 hours and even lower for the other hours. In this experiment, one can observe that the weather conditions show high inlet water temperature this combined with the absence of a vacuum in the system caused an increase in the heat losses. Figure 12 shows the comparison of the daily efficiency for the configurations with reflective film. For the configurations with eccentricity (E-WR-WV and E-WR-WTV) both equipped with reflective films but one with vacuum and the other without, the collector performance during the day is very similar showing the dominant effect due to eccentricity and the reflective film (Fig. 12 a). For the concentric configurations (C-WR-WV and C-WR-WVT) without eccentricity or reflective film, the daily efficiency is relatively low in comparison with eccentricity and reflective film case due to less thermal losses because of the vacuum effect and the highly concentrated radiation due to the eccentricity and reflective film. One can also see the significant improvement due to the vacuum effect (Fig. 12 b). Figure 13 a shows the experimental conditions during the tests on the configurations C-WTR-WTV and E-WTR-WTV both without vacuum but with reflective film. Figure 13 b shows the variation of the efficiency and fluid temperature at entry and exit of the concentric and eccentric configuration C-WTR-WTV and E-WTR-WTVboth without vacuum and without reflective film under the same working conditions. The results show little difference in the thermal efficiency (1.72% average) and inlet and outlet temperature difference (0.06°C average) indicating the marginal effect of the geometry of the configurations. Figure 14 a shows the experimental conditions during the tests on the configurations C-WR-WTV and E-WR-WTV both without vacuum but with reflective film. Figure 14 b shows the variation of the efficiency and fluid temperatures during the tests of Fig. 14 a. As one can see the effects of the eccentricity and reflective film are significant showing higher efficiency by about 30%. Figure 15 a shows the experimental conditions during the tests on the configurations C-WTR-WV and E-WTR-WV both without reflective film but with a vacuum. Figure 15 b shows the variation of the efficiency and fluid temperatures during the tests corresponding to Fig. 15 a. The results show close efficiency and outlet fluid temperature with an efficiency difference of about 1%. This result confirms that the dominant effect is due to the eccentricity and reflective film. Figure 16 a presents the simultaneous test data of the collector configurations C-WR-WV and E-WR-WV with both vacuum and eccentricity and reflective film. As can be seen the solar collector configuration with vacuum, eccentricity, and solar film shows superior performance and higher efficiency of about 26% on average. These results conform to the significant effects produced by the eccentricity and reflective film on the efficiency and outlet working fluid temperature. 4.2 Numerical predictions The experimental tests showed that the collector configuration E-WR-WV that has eccentricity, reflective film, and vacuum in the annular space presented the best thermal performance in comparison to the other collector configurations. Considering these aspects, further numerical tests were conducted to investigate possible materials for manufacturing the absorber of the collector and the external cover. Some of the absorber materials investigated in this section have absorption levels of absorption coatings widely used in the collector’s industry. The simulations were conducted for solar radiation of G = 800W/m², Ambient temperature = 28°C, Inlet water temperature = 28°C, and External convection coefficient = 14W/m².°C. Seven different materials were used for the absorber (copper tarnished, copper polished, aluminum, steel black, steel grey, galvanized iron, and stainless steel), glass, and makrolon for the external cover. Figure 17 shows the variation of the efficiency with the type of cover material used. The correlation between the absorptivity of the absorber material and the efficiency is clear, higher absorber absorptivity leads to higher efficiency. With reference to the cover material, the results indicated that glass is the best material for the cover tube. Further simulations were conducted for the same collector configuration, E-WR-WV, with an absorber tube length of 18 m for copper tarnished, copper polished, aluminium, steel black, steel grey, galvanized iron, and stainless steel as absorber materials. The weather conditions such as solar radiation, ambient temperature, and wind speed are presented in Fig. 18 . Figures 19 and 20 show the variation in the daily efficiency and outlet temperature. Figure 19 shows that the best absorber material is steel black chrome, which shows a maximum collector efficiency of 82% and a minimum of 77%. The absorber tube of copper tarnished shows a minimum collector efficiency of 62% and a maximum of 66%. The worst absorber tube material is copper light red, which reached a maximum efficiency of 24%. Figure 19 shows the daily outlet temperature variations for the different simulated absorber materials. The maximum outlet temperature of steel black chrome = 85°C, copper tarnished = 73°C, copper light red = 41°C, steel grey = 54°C, aluminium matt silver = 43°C, galvanized iron = 85°C, and stainless steel = 57°C. Since the results from Figs. 19 and 20 were simulated for the same weather conditions and collector configuration, the different results are directly related to the absorptivity of the absorber material shown in Fig. 17 . 5. Conclusions In this study, eight collectors’ configurations of concentric and eccentric tube solar collectors, with and without reflective film and with and without vacuum were investigated both experimentally and numerically. The experimental results showed the significant effect of the reflective film on the efficiency of eccentric tube solar collectors’ configurations. The comparison between the eccentric tube solar collectors’ configurations with and without reflective film showed an increase of about 33% due to the incorporation of the reflective film. The vacuum did not show a significant influence on the results of the eccentric tube collectors, presenting an efficiency increase variation between 1% and 4% for cases with and without reflective film, respectively. While the reflective film increased significantly the performance of the eccentric tube solar collectors, the vacuum had a higher increase in the performance of the concentric tube collectors. For concentric tubes configurations, the increase in efficiency caused by the vacuum reached 9%. The configuration that showed the best result was that with the eccentric collector configuration with both reflective film vacuum. When analyzing different materials for the absorber and the tube cover, it was observed that the steel black chrome showed the best results due to its high absorptivity which directly influences the efficiency. For the cover tube, glass proved to be the best option. Declarations CRediT authorship contribution statement Mavd P. R. Teles: Conceptualization, Methodology, Writing - original draft, Writing - review & editing, Investigation. Janayna Rocha Silva: Writing - original draft, Methodology. Fatima A. M. Lino : Writing - original draft, Writing - review & editing, Methodology. Claudia Rosa do Espirito Santo Nóbrega: Writing - original draft, Writing - review & editing, Methodology. Kamal A. R. Ismail: Conceptualization, Methodology, Writing - review & editing, Funding acquisition. Declaration of Competing Interest The authors declare they have no competing financial interests or personal relationships that might influence the present research. Acknowledgments The authors acknowledge the BIOFABRIS Laboratory from the Faculty of Chemical Engineering- at the University of Campinas for providing the 3D-printed tube seals off the collector versions. FunderInformation The authors wish to thank the support from Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (Fapema) for the Ph.D. grant [Grant number BD-08373/17]. References Kumar A, Said Z, Bellos E (2021) An up-to-date review on evacuated tube solar collectors. J Therm Anal Calorim 145:2873–2889. https://doi.org/10.1007/s10973-020-09953-9 Olfian H, Ajarostaghi SSM, Ebrahimnataj M (2020) Development on evacuated tube solar collectors: A review of the last decade results of using nanofluids. 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J Energy Resour Technol Trans ASME 142. https://doi.org/10.1115/1.4047303/1083969 Al-Tahaineh H, AlEssa AHM (2022) A hybrid TEG/evacuated tube solar collectors for electric power generation and space heating. J Eng Appl Sci 69:1–15. https://doi.org/10.1186/s44147-021-00065-1 Kumar A, Tiwari AK, Said Z (2021) A comprehensive review analysis on advances of evacuated tube solar collector using nanofluids and PCM. Sustain Energy Technol Assessments 47:101417. https://doi.org/10.1016/j.seta.2021.101417 Henein SM, Abdel-Rehim AA (2022) The performance response of a heat pipe evacuated tube solar collector using MgO/MWCNT hybrid nanofluid as a working fluid. Case Stud Therm Eng 33:101957. https://doi.org/10.1016/j.csite.2022.101957 Alrowaili ZA, Ezzeldien M, Shaaalan NM et al (2022) Investigation of the effect of hybrid CuO-Cu / water nanofluid on the solar thermal energy storage system. J Energy Storage 50:104675. https://doi.org/10.1016/j.est.2022.104675 Ismail KAR, Teles MPR, Lino FAM (2021) Comparative analysis of eccentric evacuated tube solar collector with circular and rectangular absorber working with nanofluid. Clean Eng Technol 3:100105. https://doi.org/10.1016/j.clet.2021.100105 Eltaweel M, Abdel-Rehim AA, Attia AAA (2021) A comparison between flat-plate and evacuated tube solar collectors in terms of energy and exergy analysis by using nanofluid. Appl Therm Eng 186:116516. https://doi.org/10.1016/j.applthermaleng.2020.116516 Tabarhoseini SM, Sheikholeslami M (2022) Entropy generation and thermal analysis of nanofluid flow inside the evacuated tube solar collector. Sci Rep 12:1–16. https://doi.org/10.1038/s41598-022-05263-2 Yeh CY, Boonk KJF, Sadeghi G et al (2022) Experimental and numerical analysis of thermal performance of shape stabilized PCM in a solar thermal collector. Case Stud Therm Eng 30:101706. https://doi.org/10.1016/j.csite.2021.101706 Teles M, de PR, Ismail KAR, Arabkoohsar A (2019) A new version of a low concentration evacuated tube solar collector: Optical and thermal investigation. Sol Energy 180:324–339. https://doi.org/10.1016/j.solener.2019.01.039 Seddaoui A, Dar Ramdane MZ, Noureddine R (2022) Performance investigation of a new designed vacuum flat plate solar water collector: A comparative theoretical study. Sol Energy 231:936–948. https://doi.org/10.1016/j.solener.2021.12.038 Almitani KH, Alzaed A, Alahmadi A et al (2022) The influence of the geometric shape of the symmetrical twisted turbulator on the performance of parabolic solar collector having hybrid nanofluid: Numerical approach using two-phase model. Sustain Energy Technol Assessments 51:101882. https://doi.org/10.1016/j.seta.2021.101882 Roshith K, Varghese J (2022) A numerical investigation into the flow development and heat transfer characteristics for different tube geometry configurations in a water in glass evacuated tube solar water heater. J Sol Energy Eng. https://doi.org/10.1115/1.4054471 Teles MPR, Ismail KAR (2022) Experimental and Numerical Assessments of the Effects of Vacuum and Solar Film on the Performance of a Low Concentration Eccentric Solar Collector. J Energy Resour Technol 144. https://doi.org/10.1115/1.4052982 Ismail KAR, Teles MPR, Lino FAM (2022) Modeling and experimental evaluation of the effects of reflective film and vacuum on the performance of concentric double tube direct flow solar collector. J Energy Resour Technol 1–13. https://doi.org/10.1115/1.4054532 Duffie JA, Beckman WA (2013) Solar engineering of thermal processes, 4th edn. John Wiley & Sons, Hoboken Karlekar BV, Desmond RM (1977) Engineering heat transfer, 1st edn. West Publishing Company, Saint Paul Raithby G, Hollands K (1975) A General Method of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection Problems. Advences Heat Transf 11:265–315. https://doi.org/https://doi.org/10.1016/S0065-2717(08)70076-5 Swinbank WC (1963) Long-wave radiation from clear skies. Q J R Meteorol Soc 89:339–348. https://doi.org/10.1002/QJ.49708938105 Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Pub. Corp., USA Holman JP (2012) Experimental Methods for Engineers, 8th edn. McGraw-Hill, New York Cite Share Download PDF Status: Published Journal Publication published 19 Jan, 2024 Read the published version in Journal of the Brazilian Society of Mechanical Sciences and Engineering → Version 1 posted Reviewers agreed at journal 15 Sep, 2023 Reviewers invited by journal 15 Sep, 2023 Editor assigned by journal 13 Sep, 2023 First submitted to journal 11 Sep, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-3345207","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":233595836,"identity":"076ae67e-59d5-4209-8e0e-19b5da567f63","order_by":0,"name":"Mavd Paula Teles","email":"","orcid":"","institution":"UNICAMP: Universidade Estadual de Campinas","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Mavd","middleName":"Paula","lastName":"Teles","suffix":""},{"id":233595837,"identity":"bee0c576-7ea9-4903-bc1f-c6541677d118","order_by":1,"name":"Fatima A.M. Lino","email":"","orcid":"","institution":"UNICAMP: Universidade Estadual de Campinas","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Fatima","middleName":"A.M.","lastName":"Lino","suffix":""},{"id":233595838,"identity":"04f4f565-554e-44b9-8000-ba4f75dfa9ca","order_by":2,"name":"Janayna Rocha Silva","email":"","orcid":"","institution":"UNICAMP: Universidade Estadual de Campinas","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Janayna","middleName":"Rocha","lastName":"Silva","suffix":""},{"id":233595839,"identity":"decb0178-3ce0-484c-96e3-749e0df3c050","order_by":3,"name":"Claudia Rosa do Espirito Santo Nóbrega","email":"data:image/png;base64,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","orcid":"https://orcid.org/0000-0003-3897-7012","institution":"State University Maranhao: Universidade Estadual do Maranhao","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Claudia","middleName":"Rosa do Espirito Santo","lastName":"Nóbrega","suffix":""},{"id":233595840,"identity":"f3dc506d-21a5-488f-90af-9410c5e10caf","order_by":4,"name":"Kamal A.R. Ismail","email":"","orcid":"","institution":"UNICAMP: Universidade Estadual de Campinas","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Kamal","middleName":"A.R.","lastName":"Ismail","suffix":""}],"badges":[],"createdAt":"2023-09-11 13:56:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3345207/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3345207/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40430-023-04665-1","type":"published","date":"2024-01-19T15:01:32+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":43505322,"identity":"c9806fcf-b0f8-4908-a972-cbe4621b189a","added_by":"auto","created_at":"2023-09-21 20:52:43","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":78225,"visible":true,"origin":"","legend":"\u003cp\u003eCross section of the eccentric evacuated tubes collector models.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/fc391a13bb8a088bf0a43110.png"},{"id":43505331,"identity":"bf647e9a-56b9-4526-93d0-32f0edc5404c","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":80613,"visible":true,"origin":"","legend":"\u003cp\u003eCross section of the concentric evacuated tubes collector models.\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/e6146313d5c016f9a396e9e8.png"},{"id":43505769,"identity":"3d18487e-c372-4c9c-bde6-77cf23c17e98","added_by":"auto","created_at":"2023-09-21 21:00:43","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":79005,"visible":true,"origin":"","legend":"\u003cp\u003eConfiguration of the collectors’ models.\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/ab334869dacdd9965daaf6b4.png"},{"id":43505324,"identity":"09e94f50-db5e-403f-bef0-553df7b6a740","added_by":"auto","created_at":"2023-09-21 20:52:43","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":97736,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental Layout.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/d9ff639e39d676a7a2b41f79.jpg"},{"id":43505771,"identity":"0b22c737-2d06-4f60-a65f-6e7dc1ba5ad6","added_by":"auto","created_at":"2023-09-21 21:00:43","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":457965,"visible":true,"origin":"","legend":"\u003cp\u003eMeasurements Instrumentations.\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/60a198f3cae0fa1118016200.png"},{"id":43505837,"identity":"ef452775-ac70-4938-9f33-0abbb2e13001","added_by":"auto","created_at":"2023-09-21 21:08:43","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":522254,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental single collector test circuit.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/6b2af26aadbd59979b3171e9.png"},{"id":43505838,"identity":"6ffd0748-6998-4232-977a-aa23580d124d","added_by":"auto","created_at":"2023-09-21 21:08:44","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":73060,"visible":true,"origin":"","legend":"\u003cp\u003eExperimental double collector test circuit.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/6360641cb9446cc517b80d81.jpg"},{"id":43505327,"identity":"ba0b6610-56a8-4125-862c-15944839b29f","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":154142,"visible":true,"origin":"","legend":"\u003cp\u003eVerification of models between numerical and experimental results.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/c574f47fdfc2c0aeb1546d3d.png"},{"id":43505774,"identity":"5cff3d84-5b22-4004-8a39-f0d7b4c60558","added_by":"auto","created_at":"2023-09-21 21:00:44","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":398038,"visible":true,"origin":"","legend":"\u003cp\u003eExperiment conditions during the day: (a) Solar radiation, (b) Ambient temperature, (c) Wind, and (d) Inlet water temperature.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/18ce7a65fd108b1ab1bb9a14.png"},{"id":43505772,"identity":"24e14bba-2790-4dd0-8503-4f745035b7af","added_by":"auto","created_at":"2023-09-21 21:00:44","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":27085,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum efficiency of the different configurations of solar collectors.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/96e09ea2d167e9aa2d636f38.png"},{"id":43505328,"identity":"9c86face-a1a1-445c-92ca-56ef66b226e7","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":25260,"visible":true,"origin":"","legend":"\u003cp\u003e(Tout-Tin)/G for different configurations of solar collectors.\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/b0ad6c4623d1e18d760342f4.png"},{"id":43505336,"identity":"3d4b59b8-a61d-4a89-a6a4-f57c62a258e1","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":96204,"visible":true,"origin":"","legend":"\u003cp\u003eEfficiency for different configurations of solar collectors during the day, (a) eccentric collector and (b) concentric collector.\u003c/p\u003e","description":"","filename":"12.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/4708a68298d913c246a02c87.png"},{"id":43505779,"identity":"6ac3050c-76fe-4d32-a0ad-7005bac49cf5","added_by":"auto","created_at":"2023-09-21 21:00:44","extension":"png","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":137602,"visible":true,"origin":"","legend":"\u003cp\u003eExperiment results of the solar collectors C-WTR-WTV and E-WTR-WTV during the day: (a) experiment conditions and (b) collector efficiency.\u003c/p\u003e","description":"","filename":"13.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/ab9c6a284f52c27e0517b362.png"},{"id":43505340,"identity":"f2bc5359-35ec-4810-b037-93a37ad10872","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":162309,"visible":true,"origin":"","legend":"\u003cp\u003eExperiment results of the solar collectors C-WR-WTV and E-WR-WTV during the day: (a) experiment conditions and (b) collector efficiency.\u003c/p\u003e","description":"","filename":"14.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/a3e423a4fd66a2aa0c8b5c49.png"},{"id":43505335,"identity":"933e9e28-3460-4ce2-92e6-4231f5ebc735","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":135917,"visible":true,"origin":"","legend":"\u003cp\u003eExperiment results of the solar collectors C-WTR-WV and E-WTR-WV during the day: (a) experiment conditions and (b) collector efficiency.\u003c/p\u003e","description":"","filename":"15.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/555aee146c27675c95de9852.png"},{"id":43505777,"identity":"eac87485-5d40-487a-b7ee-7ba137beba00","added_by":"auto","created_at":"2023-09-21 21:00:44","extension":"png","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":137481,"visible":true,"origin":"","legend":"\u003cp\u003eExperiment results of the solar collectors C-WR-WV and E-WR-WV during the day: (a) experiment conditions and (b) collector efficiency.\u003c/p\u003e","description":"","filename":"16.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/1d3c9c8c7f8cb87bbba70ec8.png"},{"id":43506295,"identity":"87139d53-12a5-4054-8b0f-b350b16153a2","added_by":"auto","created_at":"2023-09-21 21:16:44","extension":"png","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":96030,"visible":true,"origin":"","legend":"\u003cp\u003eMaximum efficiency using different materials of cover and absorber.\u003c/p\u003e","description":"","filename":"17.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/26593336709ffbefea82f7a4.png"},{"id":43505841,"identity":"22499163-65ef-45cc-9cf5-d77b2d619487","added_by":"auto","created_at":"2023-09-21 21:08:44","extension":"png","order_by":18,"title":"Figure 18","display":"","copyAsset":false,"role":"figure","size":151158,"visible":true,"origin":"","legend":"\u003cp\u003eDaily ambient conditions of simulation.\u003c/p\u003e","description":"","filename":"18.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/b6f495c1f4d979b3c04ff49c.png"},{"id":43505341,"identity":"34533306-4702-44af-b27c-40d8c2c2524d","added_by":"auto","created_at":"2023-09-21 20:52:44","extension":"png","order_by":19,"title":"Figure 19","display":"","copyAsset":false,"role":"figure","size":115409,"visible":true,"origin":"","legend":"\u003cp\u003eDaily efficiency using different materials.\u003c/p\u003e","description":"","filename":"19.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/89a0b747fa864af2c55224e2.png"},{"id":43505839,"identity":"07a7d66a-abb0-4ed6-b0be-73bb30a53f0b","added_by":"auto","created_at":"2023-09-21 21:08:44","extension":"png","order_by":20,"title":"Figure 20","display":"","copyAsset":false,"role":"figure","size":140915,"visible":true,"origin":"","legend":"\u003cp\u003eDaily outlet temperature using different materials.\u003c/p\u003e","description":"","filename":"20.png","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/dbcf5c1fd34ba67a9ad627e5.png"},{"id":49979095,"identity":"79c65d5b-ed39-4d47-a74a-00763a3dde67","added_by":"auto","created_at":"2024-01-22 15:10:52","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":3074511,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3345207/v1/f87f8a91-31ac-463a-935e-4476e4d251d7.pdf"}],"financialInterests":"","formattedTitle":"Thermal evaluation of geometrical innovations in concentric and eccentric evacuated single and double solar collectors","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eIn the last decades, the use of traditional energy sources has been replacedcontinuously by sustainable energy due to global warming, depletionof fossil fuels, and diversification of energy matrices. In this way, solar energy has been attracting a lot of attention and stands as a promising source, which can be and has been applied for several applications as: agriculture, heat production, seawater distillation, electricity generation, and many others [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDue to their economic and technical viability and high performance, thermal solar collectors are extensively used. One of the most common and promising thermal collectors is the evacuated tube solar collectors (ETC) [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]. These collectors can be applied as sources for organic Rankine cycle (ORC), absorption systems, hydrogen production, freeze recovery, thermoelectric generation, and others. Ya\u0026iuml;ci et al. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e] conducted an investigation of a solar-driven ORC system that works with fluid mixtures and used micro-cogeneration. They chose an evacuated tube flat plate solar collector to feed the system, due to its efficiency and delivered temperature. Parabolic trough collectors (PTC) are also diversely used for ORC applications [\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]. Meraj et al. [\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e] performed an analysis as a case study in New Delhi. The results showed that there was no need to design the thermal and photovoltaic system for high capacities of the absorption system, and that the concentration ratio plays the main hole.\u003c/p\u003e \u003cp\u003ePandya et al. [\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e] tested several solar collectors to determine the optimum heat source for an absorption cooling system. The authors tested the flat-plate solar collector (FPC), ETC, PTC, and compound parabolic collector (CPC). Results showed that ETC demands the lowest area, and FPC the lowest cost. Jiang et al. [\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e] made a numerical and experimental investigation on thermal and optical aspects on triangular solar air collectors. They evaluated three models: using insulation material, transparent cover plate and double transparent cover plate. The one using transparent cover plate has the highest optical efficiency and the different models are adaptable for different weather conditions. Karabuga et al. [\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e] conducted a thermodynamic analysis using ETC to power an ORC system, which produces electrical energy and generates hydrogen. The energy and exergy efficiencies of the whole system were about 51% and 16%, respectively. Imponenti et al.[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e] used parabolic trough collectors to supply and control a freeze recovery. The results showed PTC plants are an opportunity for capital and operational cost-savings in these systems. Al-Tahaineh and AlEssa [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e] used the evacuated tube solar collector to heat a cold zone in a thermoelectric generator (TEG). The results indicated that TEG applications have a promising potential for solar energy. The ETC outlet hot water temperature is one of the most significant parameters in the TEGs performance.\u003c/p\u003e \u003cp\u003eThe most diverse commercial thermal solar collector used is the evacuated tube (ETC) [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Two main techniques are used to enhance the efficiency of ETC: geometrical modifications and the use of nanofluids and PCMs. Henein and Abdel-Rehim [\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e] investigated the performance of a heat pipe ETC using MgO/MWCNT nanofluid. The hybrid use of 50% MgO and 50% MWCNT presents the best performance for all tested flow rates. Alrowaili et al. [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] conducted an investigation of a CuO-Cu/water nanofluid coupling ETC and an energy storage system. The ETC presented high efficiency using hybrid nanofluid 2.5g CuO\u0026thinsp;+\u0026thinsp;1.5g Cu in different flow rates. Ismail et al. [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e] made a numerical comparative study about the use of circular and rectangular absorbers for ETC using Al\u003csub\u003e2\u003c/sub\u003eO\u003csub\u003e3\u003c/sub\u003e/water as a nanofluid. The best ETC configuration is using a circular absorber and the maximum improvement in the ETC efficiency using nanofluid was about 9%.\u003c/p\u003e \u003cp\u003eEltaweel et al. [\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] investigated the use of MWCNT/water as a nanofluid for ETC and FPC using various flow rates. The maximum energy efficiency found for the ETC was 55% at 0.02kg/s and with 0.05 wt%. According to the results, the enhancement in efficiency can reduce the collector area. Tabarhoseini and Sheikholeslami [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e] investigated the entropy generation inside an ETC using CuO/water nanofluid. They concluded that the entropy generation using just water is higher than using nanofluid, the heat transfer entropy generation was reduced by about 6% using 5% CuO. Yeh et al. [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e] tested a double spiral coil heat exchanger with phase change material (PCM) in a parabolic trough collector. The results show that maintaining the temperature difference between the working fluid and PCM it is possible to increase the duration of available hot water for domestic applications. The optimal configuration was found for 2.6 times longer discharging process and outlet temperature of 55\u0026deg;C.\u003c/p\u003e \u003cp\u003eProposing a geometrical modification, Teles et al. [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e], modelled numerically an eccentric solar collector with a small concentration. A maximum of 73% efficiency was obtained using this model modification. Seddaoui et al. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] combined the configuration of FPC and ETC to create a new design of vacuum flat plate collectors. This model was tested experimentally and simulated numerically. The results showed that for high absorber emissivity values the new model was more efficient than the ETC, although for low absorber emissivity the ETC was more efficient. Almitani et al. [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e] tested several geometries of a twisted turbulator effect inside a parabolic solar collector. They also tested nanofluids using MWCNT and MgO nanoparticles in different concentration ratios. The results showed that the use of the turbulator improved the efficiency of the collector and increased the Reynolds number from 10,000 to 25,000. Roshith and Varghese [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] made a numerical investigation of different tube geometry for a glass ETC. A high collector length-to-diameter ratio, inclination angle, and circumferential heat input lead to a high natural circulation flow rate. The effects of vacuum and solar film in a low-concentration eccentric collector were investigated [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]. The eccentric collector with both reflective film and vacuum reached a maximum efficiency of 89% and a minimum of 42%. Ismail et al. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] evaluated experimentally the performance of a low-concentration concentric solar collector that works with the direct flow. The highest thermal efficiency reported was 68% for the model with concentration and vacuum.\u003c/p\u003e \u003cp\u003eSo far, the research was dedicated to improving the performance of solar collectors by using thermal (use of nanofluids and PCM) and geometrical innovations. The literature review shows a research gap related to analyzing and comparing several geometrical innovations in concentric and eccentric evacuated tube solar collectors using different parameters. Based on this premise, this paper aims to carry out comparative analyses of evacuated tube solar collectors with different geometric configurations.\u003c/p\u003e \u003cp\u003eThis paper presents the simultaneous outdoor experimental tests on eight solar collector configurations; eccentric, concentric with and without reflective film, and with and without vacuum in the annular space to identify the collector configuration that produces the best thermal performance. Further numerical simulations were conducted on the best solar collector configuration to investigate the most adequate materials for both the cover tube and the collector absorber.\u003c/p\u003e \u003cp\u003eThe contribution of this study includes individual outdoor testing of the eccentric collector, simultaneous outdoor testing of both concentric and eccentric solar collectors\u0026rsquo; configurations and validation of the developed numerical code with experimental results.\u003c/p\u003e"},{"header":"2. Evacuated tubes collector models formulation","content":"\u003cp\u003eEight models of evacuated tubes collector are studied in this paper (Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Three important parameters are investigated: eccentricity between the cover and the absorber tube, the reflective film outside the bottom part of the cover tube and vacuum in the gap between the cover and absorber tube. The models are:\u003c/p\u003e \u003cp\u003e \u003cul\u003e \u003cli\u003e \u003cp\u003eC-WR-WV- concentric with a reflective film and with vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eC-WR-WTV- concentric with a reflective film and without vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eC-WTR-WV-concentric without reflective film and with vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eC-WTR-WTV- concentric without reflective film and without vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eE-WR-WV- eccentric with a reflective film and with vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eE-WR-WTV- eccentric with a reflective film and without vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eE-WTR-WV- eccentric without reflective film and with vacuum;\u003c/p\u003e \u003c/li\u003e \u003cli\u003e \u003cp\u003eE-WTR-WTV- eccentric without reflective film and without vacuum.\u003c/p\u003e \u003c/li\u003e \u003c/ul\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe glass cover of the absorber receives solar irradiation that is transmitted through the glass. The solar irradiation is reflected by the reflective film, with 0.78 reflectivity, positioned in the external cover bottom part and concentrated on the absorber. The copper absorber, through which the working fluid (water) flows inside, receives concentrated solar irradiation and heats the flowing water (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe collector models have the same general dimensions and are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eGeneral dimensions of solar collectors models.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{c,ext}\\)\u003c/span\u003e\u003c/span\u003e (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{c,int}\\)\u003c/span\u003e\u003c/span\u003e (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{a,ext}\\)\u003c/span\u003e\u003c/span\u003e (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({R}_{a,int}\\)\u003c/span\u003e\u003c/span\u003e (m)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({L}_{c}\\)\u003c/span\u003e\u003c/span\u003e (m)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.0485\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.01425\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.01325\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo determine the eccentricity (focus point of reflection) in the eccentric models (E-WR-WV, E-WR-WTV, E-WTR-WV and E-WTR-WTV) the same formulation and models developed by Teles and Ismail [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e] were used. While the concentration in the value of 3.46 was obtained based on Duffie and Beckman [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo describe the thermal-fluid phenomena that occur in the solar collectors the conservation equations of mass, momentum, and energy were used in the formulation of the thermal model. To use those equations, we considered that during a solar hour the collector operates in the steady-state regime, the thermal/physical properties are constant, all the surfaces reflect and emit diffusively and there is no heat transfer in the angular direction. Under these conditions, the equations can be written in the form:\u003c/p\u003e \u003cp\u003eMass:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\rho \\left(\\frac{\\partial u}{\\partial x}+\\frac{\\partial v}{\\partial r}\\right)=0$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eMomentum:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\rho \\left(u\\frac{\\partial u}{\\partial x}+v\\frac{\\partial u}{\\partial r}\\right)=-\\frac{\\partial P}{\\partial x}+{\\mu }_{}\\left(\\frac{{\\partial }^{2}u}{\\partial {x}^{2}}+\\frac{1\\partial }{r\\partial r}\\left(r\\frac{\\partial u}{\\partial r}\\right)\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\rho \\left(u\\frac{\\partial v}{\\partial x}+v\\frac{\\partial v}{\\partial r}\\right)=-\\frac{\\partial P}{\\partial r}+{\\mu }_{}\\left(\\frac{{\\partial }^{2}v}{\\partial {x}^{2}}-\\frac{v}{r\u0026sup2;}+\\frac{1\\partial }{r\\partial r}\\left(r\\frac{\\partial v}{\\partial r}\\right)\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eEnergy:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\rho \\left(u\\frac{\\partial T}{\\partial x}+v\\frac{\\partial T}{\\partial r}\\right)=\\frac{{k}_{}}{{c}_{p}}\\left(\\frac{\\partial \u0026sup2;T}{\\partial x\u0026sup2;}+\\frac{1\\partial }{r\\partial r}\\left(r\\frac{\\partial T}{\\partial r}\\right)\\right)+\\frac{S}{{c}_{p}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe boundary conditions of each part of the solar collectors presented in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e are defined below:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$${\\dot{q}}_{c-abs,cover}=I{\\alpha }_{glass}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$${\\dot{q}}_{conv,c-env}={h}_{conv,c-env}\\left({T}_{env}-{T}_{out cover}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$${\\dot{q}}_{rad,c-sky}=\\epsilon \\sigma \\left({T}_{sky}^{4}-{T}_{out cover}^{4}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$${\\dot{q}}_{conv,a-c}={h}_{conv,}\\left({T}_{absorber}-{T}_{inside cover}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${\\dot{q}}_{rad,a-c}={F}_{c-a}\\epsilon \\sigma \\left({T}_{absorber}^{4}-{T}_{inside cover}^{4}\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe coefficients of convection heat transfer outside and inside the cover were obtained from the relations developed by Karlekar and Desmond [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] and Raithby and Hollands [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e], respectively. The sky temperature was estimated by the correlation developed by Swinbank [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e]. The detailed formulation was based on the study by Teles and Ismail [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eTo solve the equations the finite volume method was used. The SIMPLE algorithm and the power-law scheme were used to couple the momentum equations, and the TDMA was used to solve the discretized equations [\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e]. A random field is considered to start the interactive process and the process is finished when the stipulated convergence is reached (Eq.\u0026nbsp;\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e). The parameter\u003cspan class=\"InlineEquation\"\u003e\u003c/span\u003ecan be the variables u, v, T and P of the conservation equations and n is the index of the iteration order.\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\sum _{i,j}\\left|\\frac{{ϕ }_{ij}^{n}-{ϕ }_{ij}^{n+1}}{{ϕ }_{ij}^{n}}\\right|\\le {10 }^{-6}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe home build code was constructed in MATLAB and the numerical code used is similar to that used by Teles and Ismail [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e].Grid tests were conducted for the cover and absorber domain. The most relevant test was the one related to the results. Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e presents the results of the grid tests and the corresponding deviation in the collector efficiency. The grids used for the cover were 20x5 and that for the absorber was 20x16 is used.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eResults of grid tests with reference to the collector efficiency\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCover Grid\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAbsorber Grid\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003edeviation\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5x5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5x8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10x5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10x8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e12%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20x5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20x16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e40x10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40x32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1%\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"3. Experimental rig, materials, procedure and uncertainty","content":"\u003cp\u003eThe experimental tests were conducted in outdoor conditions in the city of Campinas-Brazil (22\u0026deg;49'08.0\"S 47\u0026deg;03'58.5\"W) during the summer and autumn seasons. The circuit incorporates one collector tube of the configurations described in Figs.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e and \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, a controlled cold-water tank, globe valves at the entry and exit of the collector, a vacuum pump (VULKAS 12 CFM), and the measuring instrumentation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe instrumentation was composed of a measuring wind cup anemometer for measuring wind speed, a stopwatch, calibrated thermocouples Type-T and field logger system, a radiometer, a vacuum pump, and a pressure sensor for vacuum measurements. Since these are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe measuring cup and stopwatch were used to measure the collector mass flow. The mass flow measurements were conducted three times at the beginning of the experiment and an average of the results was used in the calculations. The thermocouples type-T were calibrated in the range from 0\u0026deg;C to 60\u0026deg;C, using a reference thermometer, and positioned in several parts of the collector. Two thermocouples were used to measure the inlet and outlet water (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm 0.24^\\circ\\)\u003c/span\u003e\u003c/span\u003eC). The field logger (NOVUS) was used to perform and save temperature data on a laptop. The MES-100 radiometer (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm 34 W/m\u0026sup2;\\)\u003c/span\u003e\u003c/span\u003e) and Instrutherm cup anemometer (uncertain:\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\pm 2\\%+0.2 m/s\\)\u003c/span\u003e\u003c/span\u003e) were used to measure the solar irradiation and wind speed. The vacuum sensor (Pirani PR-10K gauge headand Pirani 501) is used to measure the vacuum in the annular space of the collector, which is insulated with the aid of a silicone sealant. The average vacuum was \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({4.10}^{-1}mbar\\)\u003c/span\u003e\u003c/span\u003e. To maintain this degree of vacuum, the pump was kept working during the tests.\u003c/p\u003e \u003cp\u003eThe tests were carried out from 8:30 am to 3:00 pm, and the measurements of solar irradiation and wind speed were done in intervals of 30 minutes since they depend on the weather conditions. These long intervals were used to ensure that the measures did not take into account variations of solar radiation occurring by clouds. In this way, the measures are made for stable weather conditions. The radiometer was positioned parallel to the collector during the measurements of solar irradiation. Already the temperatures were measured at intervals of 30 seconds. As the experimental circuit (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) does not have any solar tracking system, care was taken to position the solar collector facing the geographic north (80\u0026deg;), so that it would be guaranteed that throughout the day there would be incidence of sunlight on the collectors.\u003c/p\u003e \u003cp\u003eThe experimental tests were done in two groups; the first group was conducted on a single flow circuit with one collector at the time as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, while in the second group two collectors were tested simultaneously under the same conditions as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. The tests for the first group were conducted for the flow rate of 0.0081 kg/s. For the second group the tests were conducted according to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eExperimental date of each configuration test in Campinas-Brazil under different conditions.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"3\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eConfiguration\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eExperiment date\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFlow rate (kg/s)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WR-WV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e02/21/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WR-WTV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11/29/2020\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WTR-WV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e04/02/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WTR-WTV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e03/12/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE-WR-WV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e30/04/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE-WR-WTV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e04/11/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE-WTR-WV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e05/16/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE-WTR-WTV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e05/24/2021\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0081\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WR-WV and E-WR-WV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e08/23/2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0054\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WR-WTV and E-WR-WTV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e09/02/2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0068\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WTR-WV and E-WTR-WV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e09/08/2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0062\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eC-WTR-WTV and E-WTR-WTV\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e09/23/2022\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.0080\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo have a fair analysis, the efficiency is defined depending on the concentration level, which means that when there is no solar concentration C is equal to 1.\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\eta =\\frac{\\dot{m}cp∆ T}{IC{A}_{absorber}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Uncertainty\u003c/h2\u003e \u003cp\u003eTo calculate the uncertainty of the results found in the experiments, the method proposed by Holman [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] was used. Each measurement has an uncertainty, and the uncertainty in the calculated result, as the efficiency in this study, is affected by the uncertainties in the primary measurements. The calculated result \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(R\\)\u003c/span\u003e\u003c/span\u003e is a given function of the independent variables\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({ x}_{1}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{2}\\)\u003c/span\u003e\u003c/span\u003e,\u0026hellip;, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{n}\\)\u003c/span\u003e\u003c/span\u003e; so \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(R=R({x}_{1},{x}_{2},\\dots , {x}_{n})\\)\u003c/span\u003e\u003c/span\u003e. Making \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{R}\\)\u003c/span\u003e\u003c/span\u003ebe the uncertainty in the calculated result and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{1}\\)\u003c/span\u003e\u003c/span\u003e,\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{2}\\)\u003c/span\u003e\u003c/span\u003e,\u0026hellip;, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{n}\\)\u003c/span\u003e\u003c/span\u003ethe uncertainties of the independent variables, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{R}\\)\u003c/span\u003e\u003c/span\u003e is given by:\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$${w}_{R}={\\left[{\\left(\\frac{\\partial R}{\\partial {x}_{1}}{w}_{1}\\right)}^{2}+{\\left(\\frac{\\partial R}{\\partial {x}_{2}}{w}_{2}\\right)}^{2}+\\dots +{\\left(\\frac{\\partial R}{\\partial {x}_{n}}{w}_{n}\\right)}^{2}\\right]}^{1/2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eTo determine the uncertainty of the efficiency the solar irradiance, mass flow, and the fluid difference of temperature (Tout-Tin) were used in Eq.\u0026nbsp;\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e11\u003c/span\u003e and the uncertainty in the calculated efficiency is:\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$${w}_{\\eta }={\\left[{\\left(\\frac{\\partial \\eta }{\\partial ∆ T}{w}_{∆ T}\\right)}^{2}+{\\left(\\frac{\\partial \\eta }{\\partial \\dot{m}}{w}_{\\dot{m}}\\right)}^{2}+{\\left(\\frac{\\partial \\eta }{\\partial I}{w}_{I}\\right)}^{2}\\right]}^{1/2}=\\pm 6.54\\%$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Model verification\u003c/h2\u003e \u003cp\u003eThe model verification was performed for the cases: C-WTR-WV, C-WTR-WTV, E-WR-WV, E-WR-WTV, E-WTR-WV, and E-WTR-WTV. The comparison was made for the outer temperature of the water in the collectors for the highest solar radiation during the day of the experiment (0.0081 kg/s). The deviation between experimental and numerical was 1.9% for C-WTR-WV, 1.88% for C-WTR-WTV, 0.86% for E-WR-WV, 0.94% for E-WR-WTV, 2.2% for E-WTR-WV, and 1.67% for E-WTR-WTV (Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e). This shows the good agreement between the numerical model and experiments.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results and discussion","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Experimental results\u003c/h2\u003e \u003cp\u003eFirst, the experimental results comparing the performance of all the tested models are presented and discussed. Identified the collector configuration with the best thermal performance, additional simulations were performed to identify the best material for the absorber tube and the transparent cover.\u003c/p\u003e \u003cp\u003eThe solar radiation, ambient temperature, wind, and inlet water temperature measured during the single collector experiments are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e for each collector configuration.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e shows the maximum efficiency reached during the day for the eight studied solar collector configurations. The highest efficiencies of 84% and 83% were achieved by the collector configurations E-WR-WV and E-WR-WTV, respectively. The cases C-WR-WTV, C-WTR-WTV, and E-WTR-WTV presented lower efficiencies of 48%, 49% and 47%, respectively. From this, it is possible to conclude that, the effect of the reflective film is significant for the collector that has the absorber positioned eccentrically in relation to the cover tube. The vacuum effects in the concentric collector can achieve a 9% improvement in efficiency, and the reflective film can achieve a 33% improvement in the case of the eccentric collector.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe energy absorbed by the solar collector depends directly on solar irradiation (G). In order to compare the configurations of the solar collectors, the parameter (Tout-Tin)/G that relates the difference between inlet and outlet temperature and the solar irradiation was used.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e shows the parameters for the different configurations during the daily experiment. Considering this, the best configurations response of the collector were for E-WR-WV and E-WR-WTV (Eccentric collectors with reflective film). This shows the effectiveness of the use of reflective film in eccentric collectors. An intermediate level of response was found by configuration C-WR-WV. Configurations E-WTR-WV, C-WTR-WV and C-WTR-CWTV had a similar low response and presented a uniform curve during the day. This behavior is justified by the absence of solar concentration in the configurations and low vacuum effects. For configuration C-WR-WTV, the response was as low as the others during 11\u0026ndash;13 hours and even lower for the other hours. In this experiment, one can observe that the weather conditions show high inlet water temperature this combined with the absence of a vacuum in the system caused an increase in the heat losses.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows the comparison of the daily efficiency for the configurations with reflective film. For the configurations with eccentricity (E-WR-WV and E-WR-WTV) both equipped with reflective films but one with vacuum and the other without, the collector performance during the day is very similar showing the dominant effect due to eccentricity and the reflective film (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003ea).\u003c/p\u003e \u003cp\u003eFor the concentric configurations (C-WR-WV and C-WR-WVT) without eccentricity or reflective film, the daily efficiency is relatively low in comparison with eccentricity and reflective film case due to less thermal losses because of the vacuum effect and the highly concentrated radiation due to the eccentricity and reflective film. One can also see the significant improvement due to the vacuum effect (Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003eb).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003ea shows the experimental conditions during the tests on the configurations C-WTR-WTV and E-WTR-WTV both without vacuum but with reflective film. Figure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003eb shows the variation of the efficiency and fluid temperature at entry and exit of the concentric and eccentric configuration C-WTR-WTV and E-WTR-WTVboth without vacuum and without reflective film under the same working conditions. The results show little difference in the thermal efficiency (1.72% average) and inlet and outlet temperature difference (0.06\u0026deg;C average) indicating the marginal effect of the geometry of the configurations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003ea shows the experimental conditions during the tests on the configurations C-WR-WTV and E-WR-WTV both without vacuum but with reflective film. Figure\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003eb shows the variation of the efficiency and fluid temperatures during the tests of Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003ea. As one can see the effects of the eccentricity and reflective film are significant showing higher efficiency by about 30%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003ea shows the experimental conditions during the tests on the configurations C-WTR-WV and E-WTR-WV both without reflective film but with a vacuum. Figure\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003eb shows the variation of the efficiency and fluid temperatures during the tests corresponding to Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003ea. The results show close efficiency and outlet fluid temperature with an efficiency difference of about 1%. This result confirms that the dominant effect is due to the eccentricity and reflective film.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003ea presents the simultaneous test data of the collector configurations C-WR-WV and E-WR-WV with both vacuum and eccentricity and reflective film. As can be seen the solar collector configuration with vacuum, eccentricity, and solar film shows superior performance and higher efficiency of about 26% on average. These results conform to the significant effects produced by the eccentricity and reflective film on the efficiency and outlet working fluid temperature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Numerical predictions\u003c/h2\u003e \u003cp\u003eThe experimental tests showed that the collector configuration E-WR-WV that has eccentricity, reflective film, and vacuum in the annular space presented the best thermal performance in comparison to the other collector configurations. Considering these aspects, further numerical tests were conducted to investigate possible materials for manufacturing the absorber of the collector and the external cover. Some of the absorber materials investigated in this section have absorption levels of absorption coatings widely used in the collector\u0026rsquo;s industry.\u003c/p\u003e \u003cp\u003eThe simulations were conducted for solar radiation of G\u0026thinsp;=\u0026thinsp;800W/m\u0026sup2;, Ambient temperature\u0026thinsp;=\u0026thinsp;28\u0026deg;C, Inlet water temperature\u0026thinsp;=\u0026thinsp;28\u0026deg;C, and External convection coefficient\u0026thinsp;=\u0026thinsp;14W/m\u0026sup2;.\u0026deg;C. Seven different materials were used for the absorber (copper tarnished, copper polished, aluminum, steel black, steel grey, galvanized iron, and stainless steel), glass, and makrolon for the external cover.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e shows the variation of the efficiency with the type of cover material used. The correlation between the absorptivity of the absorber material and the efficiency is clear, higher absorber absorptivity leads to higher efficiency. With reference to the cover material, the results indicated that glass is the best material for the cover tube.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFurther simulations were conducted for the same collector configuration, E-WR-WV, with an absorber tube length of 18 m for copper tarnished, copper polished, aluminium, steel black, steel grey, galvanized iron, and stainless steel as absorber materials. The weather conditions such as solar radiation, ambient temperature, and wind speed are presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig18\" class=\"InternalRef\"\u003e18\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigures \u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e and \u003cspan refid=\"Fig20\" class=\"InternalRef\"\u003e20\u003c/span\u003e show the variation in the daily efficiency and outlet temperature. Figure\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e shows that the best absorber material is steel black chrome, which shows a maximum collector efficiency of 82% and a minimum of 77%. The absorber tube of copper tarnished shows a minimum collector efficiency of 62% and a maximum of 66%. The worst absorber tube material is copper light red, which reached a maximum efficiency of 24%.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e shows the daily outlet temperature variations for the different simulated absorber materials. The maximum outlet temperature of steel black chrome\u0026thinsp;=\u0026thinsp;85\u0026deg;C, copper tarnished\u0026thinsp;=\u0026thinsp;73\u0026deg;C, copper light red\u0026thinsp;=\u0026thinsp;41\u0026deg;C, steel grey\u0026thinsp;=\u0026thinsp;54\u0026deg;C, aluminium matt silver\u0026thinsp;=\u0026thinsp;43\u0026deg;C, galvanized iron\u0026thinsp;=\u0026thinsp;85\u0026deg;C, and stainless steel\u0026thinsp;=\u0026thinsp;57\u0026deg;C.\u003c/p\u003e \u003cp\u003eSince the results from Figs.\u0026nbsp;\u003cspan refid=\"Fig19\" class=\"InternalRef\"\u003e19\u003c/span\u003e and \u003cspan refid=\"Fig20\" class=\"InternalRef\"\u003e20\u003c/span\u003e were simulated for the same weather conditions and collector configuration, the different results are directly related to the absorptivity of the absorber material shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5. Conclusions","content":"\u003cp\u003eIn this study, eight collectors\u0026rsquo; configurations of concentric and eccentric tube solar collectors, with and without reflective film and with and without vacuum were investigated both experimentally and numerically.\u003c/p\u003e \u003cp\u003eThe experimental results showed the significant effect of the reflective film on the efficiency of eccentric tube solar collectors\u0026rsquo; configurations. The comparison between the eccentric tube solar collectors\u0026rsquo; configurations with and without reflective film showed an increase of about 33% due to the incorporation of the reflective film. The vacuum did not show a significant influence on the results of the eccentric tube collectors, presenting an efficiency increase variation between 1% and 4% for cases with and without reflective film, respectively.\u003c/p\u003e \u003cp\u003eWhile the reflective film increased significantly the performance of the eccentric tube solar collectors, the vacuum had a higher increase in the performance of the concentric tube collectors. For concentric tubes configurations, the increase in efficiency caused by the vacuum reached 9%.\u003c/p\u003e \u003cp\u003eThe configuration that showed the best result was that with the eccentric collector configuration with both reflective film vacuum. When analyzing different materials for the absorber and the tube cover, it was observed that the steel black chrome showed the best results due to its high absorptivity which directly influences the efficiency. For the cover tube, glass proved to be the best option.\u003c/p\u003e "},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCRediT authorship contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMavd P. R. Teles:\u003c/strong\u003e Conceptualization, Methodology, Writing - original draft, Writing - review \u0026amp; editing, Investigation. \u003cstrong\u003eJanayna Rocha Silva:\u003c/strong\u003e Writing - original draft, Methodology. \u003cstrong\u003eFatima A. M. Lino\u003c/strong\u003e\u003cstrong\u003e:\u003c/strong\u003e Writing - original draft, Writing - review \u0026amp; editing, Methodology. \u003cstrong\u003eClaudia Rosa do Espirito Santo N\u0026oacute;brega:\u003c/strong\u003e Writing - original draft, Writing - review \u0026amp; editing, Methodology. \u003cstrong\u003eKamal A. R. Ismail: \u003c/strong\u003eConceptualization, Methodology, Writing - review \u0026amp; editing, Funding acquisition.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare they have no competing financial interests or personal relationships that might influence the present research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors acknowledge the BIOFABRIS Laboratory from the Faculty of Chemical Engineering- at the University of Campinas for providing the 3D-printed tube seals off the collector versions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunderInformation\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors wish to thank the support from Funda\u0026ccedil;\u0026atilde;o de Amparo \u0026agrave; Pesquisa e ao Desenvolvimento Cient\u0026iacute;fico e Tecnol\u0026oacute;gico do Maranh\u0026atilde;o (Fapema) for the Ph.D. grant [Grant number BD-08373/17].\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eKumar A, Said Z, Bellos E (2021) An up-to-date review on evacuated tube solar collectors. 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McGraw-Hill, New York\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Evacuated tube solar collector, eccentric absorber, low concentration solar collector, reflective film, modeling of eccentric collector","lastPublishedDoi":"10.21203/rs.3.rs-3345207/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3345207/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this study, an experimental and numerical investigation of eight geometrical configurations of evacuated tube solar collectors was conducted. The configurations were tested simultaneously in outdoor installation under the same test conditions. The parameters such as collector eccentricity, solar concentration, vacuum, collector absorber, and cover tube materials were investigated. The numerical model developed in MATLAB was validated with experimental results. The results show that the eccentricity and the absorptivity of the material of the absorber are the parameters that have the highest influence on the collector performance. The use of reflective film in the eccentric solar collectors\u0026rsquo; configurations can increase efficiency by 33%. The vacuum presented an efficiency increase variation between 1% and 4% in the eccentric tube collectors. For the concentric collectors configurations, the use of the vacuum between the tubes can reach an increase of 9% in its performance. The eccentricity of the collector using reflective film and vacuum allows an effective solar concentration in the collector absorber presenting a 26% higher efficiency when compared with the concentric collector.\u003c/p\u003e","manuscriptTitle":"Thermal evaluation of geometrical innovations in concentric and eccentric evacuated single and double solar collectors","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-09-21 20:52:38","doi":"10.21203/rs.3.rs-3345207/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"reviewerAgreed","content":"","date":"2023-09-15T07:30:11+00:00","index":0,"fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-09-15T06:10:05+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-09-13T14:56:55+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","date":"2023-09-11T09:56:07+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"bmse","sideBox":"Learn more about [Journal of the Brazilian Society of Mechanical Sciences and Engineering](http://link.springer.com/journal/40430)","snPcode":"40430","submissionUrl":"https://www.editorialmanager.com/bmse/default2.aspx","title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"c8f26fcd-c27e-45f8-9118-0152a1f78732","owner":[],"postedDate":"September 21st, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2024-01-22T15:08:53+00:00","versionOfRecord":{"articleIdentity":"rs-3345207","link":"https://doi.org/10.1007/s40430-023-04665-1","journal":{"identity":"journal-of-the-brazilian-society-of-mechanical-sciences-and-engineering","isVorOnly":false,"title":"Journal of the Brazilian Society of Mechanical Sciences and Engineering"},"publishedOn":"2024-01-19 15:01:32","publishedOnDateReadable":"January 19th, 2024"},"versionCreatedAt":"2023-09-21 20:52:38","video":"","vorDoi":"10.1007/s40430-023-04665-1","vorDoiUrl":"https://doi.org/10.1007/s40430-023-04665-1","workflowStages":[]},"version":"v1","identity":"rs-3345207","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3345207","identity":"rs-3345207","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}