Evaluating the effect of using nanofluids on the parabolic trough collector's performance

Solar collectors utilize solar energy, a sustainable and renewable source, to cater to both household and industrial needs. This paper investigated the usage of mono and binary nanoparticles in parabolic trough collectors. This paper used multiwalled carbon nanotube/Fe3O4 nanoparticles as the additives to the collector heat transfer fluid (in Syltherm 800 oil) and also evaluated the performance implications of energy systems in six scenarios. A MATLAB‐based computational model is provided to investigate the influence of employing binary nanoparticles on a solar collector's performance. The influence of nanoparticle modifications and volume percentages on energy, exergy, economic, and environmental aspects is studied. Finally, the impact of nanoparticles on each of the four mentioned areas is examined. At the same total energy rate, in the best case, adding 4% by volume of Fe3O4 (Case 2) to the base fluid increases the valuable energy rate absorbed from 7.32 kW in the base state to 7.50 kW (2.5%). The carbon dioxide produced in the system life cycle by using useful energy is called EnergoEnvironmental, and the carbon dioxide produced in the system life cycle by using useful exergy is called ExergoEnvironmental. At last, the calculation of the parameters EnergoEnviroEconomic and ExergoEnviroEconomic are done, the penalty policy is considered, and the calculations are generalized to solar collector power plants due to the carbon dioxide cost policies.

primary renewable energy sources, they are expected to account for approximately 85% of the newly installed capacity. 6,7As a result, new facilities related to these energy sources will be expanded worldwide. 8mong the various types of renewable energy, many countries have considered solar energy due to its inexhaustibility, sustainability, low greenhouse gas emissions, easy access to reduce fossil fuel consumption, and environmental problems for various applications. 9The use of solar energy, in addition to the stated advantages in terms of greenhouse gas emission and sustainable development, also has an advantage over other types of energy.
Solar power provides water heating for residential and industrial units, 10 electricity generation, 11 and air conditioning. 12In each case, the appropriate technology is used depending on the purpose of the operation.Figure 1 shows the equipment needed to use solar energy for various applications.
Meanwhile, photovoltaic panel systems convert solar energy into electrical energy, and techniques such as linear collectors, Fresnel collectors, and solar towers convert radiant energy into heat energy.Solar collectors have received much attention on a domestic and industrial scale due to their reasonable dimensions and suitable thermal efficiency in recent years. 13,14As depicted in Figure 1, solar collectors are divided into two general categories: centralized and decentralized. 15e output temperature range in decentralized collectors is more than in centralized collectors, so where high temperature is required, concentration collectors such as solar dishes and linear parabolic trough collectors (PTCs) are used. 16,17Due to the significance and advancement of solar collectors in recent years, numerous studies have been conducted on the impact of different parameters, such as geometry, heat transfer fluid, climatic conditions, and so on, on the execution of sun-oriented collectors to optimize their efficiency. 18onsidering the emphasis of the world community on the importance of areas such as sustainable development goals or net zero, the development methods of the above items in the field of renewable energy should be evaluated.One of the tools that can play a significant role in this field is the machine learning method. 19herefore, this research is focused on the recent advances in machine learning applied to heat transfer with nanoparticles in renewable energy systems. 20ne of the most important areas in the analysis of nanofluids is the stability of the composition and the absence of physical and chemical reactions between the nanoparticles.In this regard, Kanti et al. 21investigated the dispersion stability and thermophysical properties of alumina (Al 2 O 3 ), graphene oxide (GO), and their hybrid nanofluids (HNF) in different volume percentages to determine the optimal mixing percentages of nanoparticles with machine learning methods.Said et al. 22 studied the issue of using multiwalled carbon nanotube (MWCNT) nanoparticles to increase and improve thermal performance in solar converters.They studied the MWCNT/water nanofluid with a volume fraction of 0.3% and 0.05% to evaluate the stability and thermophysical properties, and their results show that the use of nanofluid in a volume fraction of 0.3% while maintaining the chemical stability of the composition, heat exchanger efficiency improves up to 5.49% compared to the base fluid.
The use of different nanoparticles in the working fluid to improve the performance of solar collectors is one of the hottest topics in this regard. 235][26] For example, Colangelo et al. investigated the effect of using alumina nanofluid in solar collectors. 27They reported an approximately 8% increase in thermal efficiency by adding a 3% volume fraction of alumina nanoparticles to water. 27n another study, Bellos and Tzivanidis 28 simulated the difference in the effect of using two nanoparticles of CuO and Al 2 O 3 in Syltherm 800 oil in EES software.Their results showed that in the best conditions of using CuO, 1.26% and Al 2 O 3 , 1.13% affect the thermal efficiency of linear parabolic collectors.Kasaeian et al., 29 designing and constructing a linear parabolic collector, investigated how adding different volumetric percentages of nanoparticles to the base fluid enhances efficiency.Recent studies are where the stability of nanoparticle dispersion, thermal performance, and optical properties of an independent nanoparticle is guaranteed.
Due to this issue, the need for studies on the physical and chemical properties of binary nanoparticles to enhance the limit of single-component nanoparticles in linear parabolic collectors and improve the thermal properties of the base fluid was raised.Hybrid nanofluid research has been underway since 2015, and to date, the development of laboratory-scale study and numerical analysis has expanded. 30][33] In this regard, Minbari et al. 34 studied dispersion stability, viscosity, and extinction coefficient of binary Al 2 O 3 -CuO/water.While introducing pH 7.5-8.5 as favorable conditions for Al 2 O 3 -CuO/water binary nanofluid, their results showed that increasing the nanoparticle volume fraction enhances the nanofluid's extinction coefficient and absorption spectrum.In another laboratory study, Dalkılıç et al. 35 found that the thermal conductivity of a binary compound of 0.8% CNT and 0.2% SiO 2 was 26.3% higher than water.As mentioned, limited numerical studies have been performed on the applications of nanoparticles in solar systems. 36,37In one of the numerical studies, Bellos and Tzivanidis 38 investigated the effect of adding two nanoparticles of Al 2 O 3 and TiO 2 separately and in combination with the base fluid of Syltherm 800 on the performance of linear parabolic collectors in EES software.Their results showed that single nanofluids in the best conditions improve the system's performance by 0.7%, while hybrid nanofluids increase efficiency by up to 1.8%.In another study, Al Oran et al. 39 developed a numerical model in MATLAB software to investigate the effect of adding nanoparticles individually and in combination on energy analysis and exergy of solar collectors.Their findings show that Al 2 O 3 and CeO 2 composite nanofluids are more efficient than Al 2 O 3 and CeO 2 -independent nanofluids.The maximum increase in energy efficiency and exergy when using Al 2 O 3 and CeO 2 composite nanofluids were reported to be 1.09% and 1.03%, respectively.Also, hybrid nanofluids are superior to single nanofluids (MONOs) by offering lower pressure drop values, increasing Nusselt number, and consequently, better heat transfer coefficient. 39In a CFD simulation, Ekiciler et al. 40 Investigated the effect of adding different pairs of nanoparticles in different volume percentages to the base fluid of linear parabolic collectors.Their study showed that in all combined teams, according to heat transfer characteristics, the flow is superior to the base fluid (Syltherm 800).
On the other hand, the performance of solar systems can be determined using the four concepts of energy analysis, exergy, economic, and environmental. 41In this field research, Moosavian et al., 18 intending to find the best climatic climate for constructing a solar power plant from linear parabolic collectors in a case study for Iran, developed modeling in MATLAB software.This study analyzed solar collectors' energy, exergy, economics, and environment in different climates.Their results showed that energy efficiency, exergy efficiency, and the annual emission of CO 2 of Shiraz represents the Mediterranean Climate (Csc) are 71.97%,17.01%, and 140 kg of CO 2 per reference collector, 42 and this city is the best place to build a solar power plant.
According to the research done on parabolic collectors in this research, to complete the previous research, 18 the effect of using binary nanofluid on the best climate of the previous research is investigated.Therefore, according to the latest study on the effect of climate change on the performance of parabolic solar collectors in the field of energy, exergy, economic and environmental, in this study, the results obtained for the best case (Shiraz with Csc climate) from the point of view of using nanoparticles is evaluated.
The importance and innovation of the present article can be justified according to the current knowledge in using the concept of improving the thermal performance of the heat transfer fluid.This issue is evaluated by using nanoparticles that are structurally capable of being used in heat transfer fluid without causing chemical reactions.In this regard, while selecting the appropriate nanoparticles in terms of physical and chemical properties, the fair volume percentage for each is analyzed and evaluated to achieve the most optimal conditions.This assessment is calculated by examining the energy efficiency and exergy factors, the unit cost of energy, and the amount of carbon dioxide produced (considering the system life cycle and the cost of carbon dioxide produced based on incentive and punitive policies).The ultimate goal of this study is to determine the most optimal conditions for constructing a solar power plant concerning the four factors of energy, exergy, economic and environmental.The novelty of this research is to investigate the effect of using composite nanoparticles on the 4E performance of the system, which is studied for the first time from this perspective.

| Location specifications
Iran is located between 29°and 41°north latitude and ranks among the best regions in the world for solar energy.According to Figure 2, Iran's solar radiation ranges from 1095 to 2410 kWh per square meter per year, above the global average.Over 280 sunny days are reported per year. 43ccording to Figure 2, it can be seen that Shiraz has the highest average radiation in Iran, which confirms the high potential of this city for the construction of solar power plants.Table 1 presents the parameters related to the analyzed location, including the type of climate, wind speed, ambient temperature, radiation intensity, and sunny hours.
It is necessary to select a parabolic collector with specific dimensions as a numerical modeling reference to study the effect of using nanoparticles on energy, exergy efficiency, and environmental and economic factors.Therefore, in this study, the LS-2 collector was used in the experimental study by Dudley et al. 42 (Sandia National Laboratories) and was chosen as a reference for numerical modeling.Table 2 summarizes the general characteristics of SNL collectors. 18These properties include geometric dimensions and optical parameters of modeling references.

| Properties of nanoparticles
As mentioned earlier, the utilization of nanofluids in solar collectors helps improve their efficiency.However, the stability of dispersion and concentration is a critical aspect when using a nanofluid as a working fluid in solar collectors.This factor directly impacts the maximum efficiency of the system.Since the properties of each type of nanofluid are different, it is necessary to analyze the system's performance according to various conditions and nanofluids to obtain an optimal nanofluid with a suitable volume percentage.
Although the stability of nanoparticles in the base fluid is still an important issue, it has been proven that nanofluids can enhance the performance of solar collectors by improving their thermal conductivity and optical properties.For this reason, as mentioned earlier, it has led researchers to focus on binary nanofluids enhancing solar system performance.
This study uses MWCNT/Fe 3 O 4 binary nanofluid as the collector heat transfer fluid.The reason for choosing MWCNT nanoparticles is high thermal conductivity, and the reason for selecting Fe 3 O 4 nanoparticles is strong infrared absorption and, consequently, increases the system's optical properties.In addition, Fe3O4 nanoparticles can be controlled by changing the strength and direction of the magnetic field due to their magnetic properties.MWCNT nanoparticles are in the form of filaments, and Fe 3 O 4 nanoparticles are spherical, which after combining, are added to Syltherm 800 oil, which has suitable thermal properties and is the base fluid (Figure 3).Also, according to the studies, the combination of these two materials will be in good condition in terms of stability of chemical and physical properties and will not undergo destructive chemical and physical processes in the base heat transfer fluid. 21,22eanwhile, it should be mentioned that turbulent flow constraints and nanoparticle matching constraints are considered in this study.Table 3 presents the thermal properties of the studied nanoparticles.
The solar collector can be considered a control volume whose inputs, that is, energy input energy and solar radiation, enter from its borders, and its output, that is, energy output energy, leaves its walls along with losses.The schematic of the system control volume is shown in Figure 4A, and the schematic of energy absorption by the nanofluid through the absorber tube and cover is presented in Figure 4B.

| Energy analysis
According to the control volume in Figure 4, the energy balance around it can be written according to Equation (1). 18 In this equation, Q ̇s is equal to the rate of solar energy reaching the surface of the collector, Q ̇f in , is equal to the energy rate of the incoming fluid, Q ̇f out , is equal to the energy rate of the outgoing fluid, and Q ̇l is equal to the wasted energy rate of the system.The amount of solar energy reaching the surface of the collector is also calculated from Equation (2). 48 where G is the vertical radiation intensity per surface unit, and A a is the area of the collector.The existence of optical losses causes only a part of the solar energy that reaches the surface of the collector to be transferred to the receiver tube by its mirrors, and its amount can be calculated from Equation (3). 49 T A B L E 1 Characteristics of Shiraz climatic zone. 44 In Equation 3, the parameter η opt represents the ratio of absorbed radiation to the total incoming radiation and it can be calculated from Equation (4). 49 where ρ ref (concentrator reflectance), τ (cover transmittance), α (absorber absorbance), and ϒ (intercept fac- tor) and their values are available in Table 2.The extraction of thermal equations related to solar collectors depends on the types of heat transfer in it.For this purpose, in Figure 5, a schematic of the heat transfer types and the related thermal resistances is presented.
The net energy fraction transferred to the fluid is equal to the difference in energy to the control volume of the outlet and inlet fluids and can be calculated from Equation (5). 50 The value of fluid outlet temperature in Equation ( 5) is unknown, so Equation ( 6) is used instead to calculate useful energy. 49

Q F
In this equation, F R is the heat removal factor, A r is the area of the side surface of the absorbent tube, U L is the collector loss coefficient, and T amb is the ambient temperature.The value of F R can also be calculated according to Equation ( 7). 51 In Equation ( 7), the parameter F′ is equal to the collector efficiency factor and can be calculated according to Equation (8). 51


In Equation ( 8), D r i , and D r o , are equal to the inner and outer diameters of the receiver tube, respectively, and h c f , is the heat transfer coefficient of fluid displacement, and its value is obtained from Equation (9). 52 The value of Nusselt number Nu f for Reynolds below 2300 is obtained from Equation (10). 52 R e P r = 0.023 × , where Pr f is the Prandtl number of the fluid inside the receiver.Heat loss coefficient U L is calculated from Equation (11), assuming the presence of a vacuum in the distance between the receiver tube and cover (glass cover). 49A B L E 2 SNL PTC characteristics.18

Symbol
In Equation (11), A c is the area of the cover, In Equation ( 12), T r is the surface temperature of the absorbent tube, and T c is the temperature of the cover surface, and their values are unknown, so after the initial guess, they are corrected with Equations ( 13) and ( 14). 18 In the next step, the heat transfer coefficient of the displacement between the cover and the environment The Nu air parameter expresses the Nusselt number of air and is obtained from Equation ( 16). 52 R e P r = 0.193 × × air air air 0.618 0.33 (16)   The radiant heat transfer coefficient between the cover and the environment In this equation, the constant σ of Stefan Boltzmann and T sky represents the sky's temperature, which is obtained according to Equation (18). 43T = 0.05532 × sky amb 1.5 (18)   After calculating useful heat according to Equation ( 6), the amount of wasted heat is obtained from Equation (19).
Finally, with the help of the obtained values, the system's energy efficiency is calculated from Equation (20). 53

| Exergy analysis
The exergy analysis of the system around the schematic control volume in Figure 4 is in the form of Equation (21).
The parameters of Ex ̇f in , are equal to the exergy rate of the incoming fluid, Ex ̇s is the exergy rate of solar radiation (exergy flow on the incoming solar irradiation), Ex ̇f out , is the exergy rate of the outgoing fluid, Ex ̇l is wasteful exergy, and Ex ̇des is exergy destruction.The value of Ex ̇sThe exergy rate of solar radiation is calculated from equation. 18


In Equation ( 22), T sun is equal to the temperature of the sun's surface, and its value is estimated to be 5780K.Also, parameter l is the interaction factor calculated from Equation 23. 54


where f i is the view factor describing the geometric relationship between the radiation source and the radiation absorber, and ϵ i is the dilution factors incident on the surface from the source of the view factor.The useful exergy parameter is obtained from the exergy difference between the output and input fluid to the collector and is calculated according to Equation (24). 18


In this equation, P Δ is the value of the pressure drop along the receiver tube obtained according to Equation (25). 55I G U R E 5 Cross-sectional thermal resistance of PTC. 18PTC, parabolic trough collector.
f r is the friction factor coefficient and u f is the speed of the fluid inside the receiver tube, which can be calculated from Equations ( 26) and (27), respectively. 55Re = 1 (0.79 × ln( ) − 1.64) ( ) The collector's lost exergy is also obtained by Equation (28). 54

Ex
Ex Ex ̇= ̇+ l In this equation, Ex ̇l opt , is equal to the optical dissipative exergy and Ex ̇l thermal , is the thermal dissipative exergy, and they are obtained from Equations ( 29) and (30), respectively. 49

Ex
Dissipated exergy expresses the irreversibility that exists in the heat transfer term.Specifically, this parameter expresses the possible work lost when transferring thermal energy from a hot source to a cold source.The amount of destroyed exergy follows Equation (31). 49 In solar collectors, the dissipated exergy contains two main terms.one between the sun and the absorber tube and one between the absorber tube and the heat transfer fluid.The above parameters are given in Equations ( 32) and (33), respectively. 48 Finally, the exergy efficiency is obtained using Equation (34). 55Ex Ex = ̇̇× 100 exergy u s (34)

| Economic analysis
In the economic analysis of solar collectors, the main goal is to calculate the cost of each kilowatt hour of energy produced.This cost is calculated from Equation (35). 56

C
In the relationship above, C I is the initial equipment cost, C O is the maintenance cost and C Ins is the insurance cost, in terms of kWh $ .Equation ( 36) is used to calculate the initial cost of the equipment. 56 In Equation (36), I is the coefficient related to equipment life (L) and interest rate (i) and is obtained from Equation (37). 57 Also, in relation 36C, the initial cost of installing the equipment is in $ and is obtained from Equation (38). 5838)   In this equation, the storage tank, heat transfer fluid, and solar collector costs per unit area which is presented in Table 4. Due to the impossibility of supplying some of the parts and equipment the collector needs inside the country, the figures in Table 4  offered in international online stores, and the shipping and customs fees have been omitted.Also, C pump is the price of the used pump, which is obtained from Equation (39). 58P = 3540* ( )

C C
In Equation ( 39), the price of the pump is a function of the required pressure, which is obtained from relation (40). 50

P
The values related to the lifetime of the solar collector and the interest rate and cost of different components are presented in Table 4. Also, according to the available references, the total cost of maintenance, repairs, and insurance is considered equal to 6% of the start-up cost.
The environmental impacts of energy systems can be assessed in four ways, as shown in Figure 6.In this case, CO 2 emissions are discussed in two cases, and in two cases, there is a penalty cost for this emission.
The available equations for the above four methods are presented in Table 5.
The difference between energy-based and exergybased analyses is only related to helpful energy and useful exergy.The values obtained from exergy-based environmental analyses are generally smaller than those obtained from energy analysis, so energy-based environmental analyses are more cautious.
In these equations, x co2 equals to the amount of carbon dioxide released in kilograms at the considered time.y co2 equals to the amount of carbon dioxide emission of the reference energy system.Its value is equal to 0.00647 kg.Carbon dioxide per kilowatt-hour is obtained by the life cycle assessment (LCA) method. 56 working is the operating time of the system.
LCA, alongside technical and economic assessments, constitutes the components of a comprehensive sustainable assessment.By incorporating environmental effects, this method enables the consideration of not only technical and economic aspects but also environmental impacts.This method performs a general assessment of the product's environmental effects, from extraction to disposal and recycling, leading to the overall pollution index.Figure 7 provides a schematic of the overall LCA cycle.
In Equations ( 40) and ( 41), c ( ) co2 is the price of carbon dioxide, and C ( ) co2 is the environmental cost of carbon dioxide emissions.The resulting parameter is the cost of carbon dioxide emissions generated by a particular system and is considered a method of environmental assessment of energy systems. 56Due to widespread concerns about climate change and global warming, methods, and policies have been proposed to reduce carbon dioxide emissions as much as possible.Environmental-economic methods to make environmental impacts more concrete for a more detailed analysis of the problem by developing incentives or penalties to reduce the environmental impacts of the energy system.Figure 8 provides a schematic of the application of environmental-economic analysis and how it interacts with environmental research.In this study, according to the range of changes in the price of carbon dioxide, which is between $0.013 and $0.016 per kg, the price of $0.0145 per kg is considered the standard price. 64

| Nanofluids equations
This section shows how to calculate the properties of nanofluids.These general equations can be applied to single and composite nanoparticles with suitable modifications.In these equations, the base fluid is denoted by (bf), the nanoparticle by (np), the nanofluid by (nf), and the total volumetric concentration of the nanoparticles in the base fluid by (φ).Indices 1 and 2 are used to separate binary nanoparticles.The governing equations for single and composite nanofluids are presented in Table 6.

| MODELING AND SIMULATION
A numerical model is presented in MATLAB software to investigate the effect of using binary nanofluid on the performance of a solar collector.Then the impact of nanoparticle changes and their volume percentages on energy efficiency, exergy, economic and environmental parameters are investigated.The inputs of this program include climatic and ecological conditions, including ambient temperature, solar radiation intensity, wind speed, sunshine hours, and nanoparticle properties, including thermal properties, type of nanoparticles, and their volume percentage (according to the contents in Tables 2 and 3).The outputs of this program also include the output temperature of the working fluid, energy efficiency and exergy, economic analysis to determine the unit cost of energy produced, and environmental parameters.Figure 9 shows the flowchart of the modeling performed.Before presenting the numerical modeling results, it is worthwhile to prove the accuracy of the modeling performance.For this purpose, Table 7 compares the fluid outlet temperature and thermal efficiency obtained from numerical modeling with the research's experimental results. 42According to Table 7, the average values of thermal efficiency error and outlet temperatures are 2.07% and 0.06%, respectively, which confirms the accuracy of numerical modeling performance.
According to Table 7, the average error value of thermal efficiency and outlet temperature is 2.07% and 0.06%, respectively, which confirms the accuracy of numerical modeling.
Based on the classification in Figure 9, the results of this study are classified into two categories of primary and secondary outcomes.Preliminary results include the effect of using binary nanoparticles on the parameters related to energy analysis and exergy.In this section, different types of energy and exergy are calculated.In the next step, using the auxiliary concepts and the results obtained from the first part, the economic and environmental studies of the reference solar collector in the case of hybrid nanofluids are discussed.The following analyzes the effect of using nanoparticles on each of the above four areas.
In this regard, six scenarios are proposed.These scenarios are presented in Table 8.Table 8 shows that in all scenarios with nanoparticles, a volume of 4% is considered to compare at a certain volume percentage and to determine the optimal procedure under the same conditions.

| System analysis from an energy perspective
By Analyzing the system from the energy point of view, energy efficiency is calculated for all scenarios presented in Table 8.The results are shown in the diagram in Figure 10.In these calculations, it is assumed that the obtained values are the average energy efficiency of the system for the whole year.
According to the results, it is observed that Scenario 2 has the highest average energy efficiency.Therefore, F I G U R E 10 Energy efficiency of scenarios (%).
Figure 11 presents the energy balance for June of each scenario to understand this issue better to determine how to divide each method's energy type.This diagram helps better understand the amount of energy absorption and loss in each case.As a result of establishing the law of energy conservation in the balance sheet, the amounts of dissipative energy and valuable energy are marked on the left side of the axis with a negative sign, and the amount of solar energy input on the right side with a positive sign.
According to Figure 11, it can be concluded that using nanoparticles in different scenarios increases the rate of valuable energy by improving the thermal properties and, thus, better absorption of solar energy than the base state.This is the primary purpose of using nanoparticles in solar systems.At the same total energy rate, in the best case, adding 4% by volume of Fe 3 O 4 (Case 2) to the base fluid increases the valuable energy rate absorbed from 7.32 kW in the base state to 7.50 kW (2.5%).Figure 12 shows the proper energy rate values for this scenario by month.
According to Figure 12, it can be stated that the highest radiation capacity is related to June, which indicates the highest amount of solar energy received in this month.

| System analysis from an exergy perspective
A similar energy analysis process has been adopted to analyze the system exergy.In the first step, the exergy efficiency of the techniques in Figure 13 is presented to find the best scenario from the exergy point of view.
Higher exergy efficiency means more potential use of available solar capacity.
Figure 13 in exergy analysis shows that Scenario 2 had the best performance using the available potential.Therefore, to better understand this issue, Figure 14 examines the different types of exergy related to June for various scenarios in Figure 14.It is necessary to present this diagram to find the effect of using nanoparticles on dividing the total input exergy into different forms of exergy.
In the last step of the exergy analysis, the usefulness of the second scenario is presented as the best scenario from the point of view of exergy every month in Figure 15.
Figure 15 shows a minimal difference in the values of the total exergy rate due to the same geographical and geometric conditions.This difference is related to the exergy of the fluid entering the receiver due to the effect of nanoparticles on the thermal properties.The second scenario has the highest total exergy rate (10.61 kW) and the most useful one (1.62 kW), resulting in the highest exergy efficiency.Table 9 shows the energy efficiency and exergy of all scenarios presented separately by month to compare results monthly for different situations.
The trend of the data presented in Table 9 indicates a similar behavior in the profile of the energy efficiency chart concerning the exergy efficiency.In Figure 16, the second scenario's energy efficiency and exergy diagrams are drawn monthly to explain the issue better.
The same trend between the energy efficiency and exergy profiles is noticeable in Figure 16.This trend is such that energy efficiency and exergy reach their lowest values in June and July.The justification for this can be related to the flow of heat transfer fluid and ambient temperature this month.Although the ambient temperature and the amount of sunlight are at their highest in these months, the amount of energy and energy lost and the exergy destroyed is such that despite the increase in power and total exergy, the energy and exergy efficiencies are still high.They will have a noticeable reduction.The fluid flow issue significantly impacts this, so Figure 17 shows the effects of flow changes on energy efficiency and exergy of the second scenario in June.It can be seen from Figure 17 that the increase in flow, while leading to an increase in energy efficiency, also changes the trend of the graph, converting the minimum region to the maximum area while increasing the values of the exergy efficiency without affecting it.

| System analysis from an economic perspective
The energy unit's production cost is discussed in line with the solar collector system's economic analysis.In this regard, according to the lifespan and interest rate stated in Table 4 and other ancillary conditions such as maintenance costs as well as equipment and staff insurance, by dividing the total cost by the total energy produced by the turbine, the cost of production per unit Energy ($/kWh) is calculated.Figure 18 shows the monthly energy costs for each scenario.
From Figure 18, it can be deduced that considering the exact total cost in all cases and applying the effect of nanoparticle price, the one that contains fewer nanoparticles or produces more usable power, will have a lower unit energy cost.Therefore, the cost of adjusted energy

Month
January February March April May June July August September October November December (unit fuel cost) is the lowest due to the lower mass of nanoparticles and high helpful power.To better compare scenarios and volume percentages related to nanoparticles, Figure 19 shows each plan's average unit cost of energy.As shown in Figure 6, there are four determining parameters for the environmental analysis of the solar collector system.According to Figure 19, it can be shown that the main reason for the lower price of mode 6 (among qthe modes with nanoparticles) is related to the price of nanoparticles used and the power produced in this case.What is important in this situation is whether the increase in the price of the energy unit due to the addition of nanoparticles is justified.In response, it should be said that this issue should be evaluated by considering the impact of these nanoparticles in other analyses to determine whether this increase in energy unit cost is justified by improving the performance of the system from the point of view of other areas.

| System analysis from an environmental perspective
As shown in Figure 6, there are four determining parameters for the environmental analysis of the solar collector system.
Two parameters describe the amount of carbon dioxide produced as a fundamental parameter.Two parameters express the emission cost based on the carbon dioxide equivalent price, which is an environmental evaluation standard.It should be noted that the amount of carbon dioxide produced by renewable energy is much less than by fossil fuels.Renewable energy, therefore, plays an important role in reducing greenhouse gases.A parameter (ENEN) is obtained by calculating the amount of carbon dioxide generated in the system's life cycle (from production to recycling to decomposition) from the available energy.Calculating the amount of carbon dioxide generated in the system's life cycle using available exergy yields a parameter (EXEN).The parameters (ENENEC) and (EXENEC) are obtained by applying the equivalent price of carbon dioxide as an environmental penalty criterion.
According to the table results, it can be seen that the trend of monthly changes in carbon dioxide emissions behaves similarly to the behavior of energy rate and exergy but shows the opposite behavior compared to energy and exergy efficiencies.Since this behavior is similar in all scenarios, Figure 20 shows Scenario 5 as an example of the monthly CO 2 emission curve.According to Table 10 and Figure 20, the amount of carbon dioxide produced from the point of view of energy and exergy in all scenarios in June has the maximum amount due to the effect of the relevant energy rate and useful exergy.The data also show that analysis (ENEN) predicts higher values than analysis (EXEN), and therefore (ENEN) is a more cautious criterion for environmental analysis of the system.
To better compare the (ENEN) and (ENEN) factors, Figure 21 shows the stacked diagrams of the above factors for Scenario 5 in different months of the year.The trend in Figure 21 shows that the ratio of carbon dioxide emitted from the analysis (ENEN) to the amount emitted from the study (EXEN) is about four times.Therefore, the ENEN analysis is more cautious about evaluating and designing the analytical solar power plant.And this is more reliable.Finally, Figure 22 shows the annual release rate of each scenario.
According to Figure 22, the second scenario from the perspective of ENEN analysis and the sixth scenario from the standpoint of EXEN analysis will have the highest pollution level.For greater transparency of environmental analysis, penalty costs are discussed under the ENENEC and EXENEC factors.According to the | 3531 incentive and punishment policy, the ENENEC invoice calculates the estimated cost (according to the incentive and punishment policy) based on energy, and the EXENEC invoice is based on exergy.Therefore, it is appropriate to calculate the acceptable amount due to carbon dioxide emissions annually for the final evaluation of environmental analyses.Figure 23 shows each solar collector's annual cost of carbon dioxide emissions for different scenarios.
As shown in Figure 23, the annual cost of carbon dioxide emissions from a collector in all energy-based scenarios is about $1.8, while the exergy-based price is less than $0.5 per year.This result is evidence of a more cautious energy-based analysis.Despite the small penalty costs for a collector, it will be essential to calculate the parameters (ENENEC) and (EXENEC) if the penalty policy is considered and the calculations are generalized to solar collector power plants.It is clear that the amount of costs incurred is inversely related to the environmental analysis of the system, so the lower the amount of carbon dioxide emissions and the resulting penalty costs, the lower the number of pollutants in the system life cycle.

| CONCLUSION
The present study investigated the behavior of parabolic trough collectors by considering energy, exergy, and environmental indices and economic and environmental characteristics.A study that Developed a numerical model in MATLAB software to investigate the effect of adding nanoparticles individually and in combination on energy analysis and exergy of solar collectors also another numerical model developed that conforms to the empirical studies presented by Dudley et al. 34 (In Sandia National Labs) and the results of validating this mathematical model with a practical model were factchecked.Also, all results obtained for the best case 18 (Shiraz with Csc climate) are evaluated in terms of the use of composite nanoparticles.In this regard, while selecting the appropriate nanoparticles in terms of physical and chemical properties, the fair volume percentage for each is analyzed and evaluated to achieve the most optimal conditions.Moreover, the EnergoEnvironmental (ENEN) and ExergoEnvironmental (EXEN) parameters are introduced and calculated to study the system environmentally.The Energoenviroeconomic (ENENEC) and Exergoenviroeconomic (EXENEC) concepts are used to study the system's behavior in the environmental-economic domain.
The main reason for choosing MWCNT nanoparticles is high thermal conductivity, and the reason for selecting Fe 3 O 4 nanoparticles is strong infrared absorption and, consequently, increases the system's optical properties.2. Exergy analysis, Scenario 2 had the best performance using the available potential because it has the highest total exergy rate (10.61 kW) and the most useful ones (1.62 kW), resulting in the highest exergy efficiency.3. The second scenario from the perspective of ENENEN (EnergoEnviroEconomic) analysis and the sixth scenario from the standpoint of EXENEN (ExergoEnviroEconomic) analysis will have the highest pollution level (the annual cost of carbon dioxide emissions from a collector in all energy-based scenarios is about $1.8, while the exergy-based price is less than $0.5 per year; Figure 23).
Although in this research, an attempt has been made to evaluate all aspects of the effect of nanoparticles in the heat transfer fluid and its effect on the thermal performance of the solar system, due to the importance of choosing nanoparticles, the conditions for conducting further research on the effect of the combination of different types of nanoparticles with different percentages There is.Also, the impact of new methods and technologies, especially the machine learning method, can be used as suggested topics for future research.

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h c c am , is the displacement heat transfer coefficient between the cover and the environment,  h r c am , is the radiation heat transfer coefficient between the cover and the environment,  h r r c , is the radiant heat transfer coefficient between the absorber tube and the cover.The value of the radiant heat transfer coefficient between the absorber tube and the cover,  h r r c , can be calculated from Equation (12).

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h c c am , can be calculated from Equation(15).52 

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I G U R E 7 Life cycle assessment cycle.F I G U R E 8 Interaction between Environmental and EnviroEconomic analysis.

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I G U R E 11 Energy balance of scenarios.F I G U R E 12 Monthly useful energy of best scenario.MOOSAVIAN ET AL.| 3525

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I G U R E 13 Exergy efficiency of scenarios.F I G U R E 14 Exergy balance of scenarios.

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I G U R E 15 Monthly exergy efficiency of different cities. T A B L E 9 Energy and exergy efficiency (%).

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I G U R E 18 Monthly cost of generated electricity.F I G U R E 19 Average cost of generated power of different cities.

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I G U R E 21 Comparison ENEN and EXEN of Case 5. ENEN, EnergoEnvironmental; EXEN, ExergoEnvironmental. F I G U R E 22 Yearly CO 2 emission of scenarios.MOOSAVIAN ET AL.

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I G U R E 23 Yearly EnergoEnviroEconomic and ExergoEnviroEconomic results. -47 are based on the prices T A B L E 4 SNL PTC characteristics.

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Environmental analysis methods.Environmental analysis equations.
T A B L E 6 Mono and binary nanofluid equations.
T A B L E 7 Validation results with SNL tests.Mono and binary nanofluid scenarios.
Monthly changes in energy and exergy efficiency of Case 2.
F I G U R E 17The effect of volume flow rate changes on monthly energy and exergy efficiency trends.
T A B L E 10 1.The use of nanoparticles in different scenarios increases the rate of valuable energy by improving the thermal properties and thus better absorption of solar energy than the base state (adding 4% by volume of Fe 3 O 4 (Case 2) to the base fluid increases the valuable energy rate absorbed from 7.32 kW in the base state to 7.50 kW (2.5%).