Numerical Study of Thermal Performance Influence on Design Parameter and Fe 3 O 4 Nanofluid of Flat Plate Direct Absorption Solar Collector

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Introduction
Modern society has been developed based on fossil fuels, and most consumed energy currently derives from fossil fuels. However, global warming is accelerating as a side effect of the long-term consumption of fossil fuels, resulting in global environmental issues such as droughts, floods, and climate change [1]. Using fossil fuels is limited to overcome these problems; therefore, the importance of energy resources is strengthened. However, it results in various issues related to energy resources, such as sovereignty, monopoly, and the supply chain of energy resources. Therefore, reducing fossil fuel consumption and using renewable energy is necessary for a sustainable future and human prosperity [2]. Among various renewable energies, solar radiative energy is attractive as a significant energy source in the future due to green energy and inexhaustible energy reserves flowing into the earth from the sun. To efficiently use solar radiative energy, research on various methods (photovoltaic [3], photothermal [4], photochemistry [5], and photobiology conversion [6]) has been actively performed. Among them, the photothermal method of obtaining thermal energy from solar radiative energy has a high energy conversion efficiency and a low cost. Besides, it can be used in a large-scale facility. Therefore, the photothermal conversion method is currently used generally to use solar radiative energy [7].
The photothermal conversion method is divided into an indirect absorption solar thermal collecting method and a direct absorption solar thermal collecting method [8]. The indirect absorption solar thermal collecting method is that the receiver coating black color thermal absorption obtains the solar radiation, and heat transmission from the heated receiver to the working fluid generates thermal energy [9]. However, this method has a disadvantage: when the surface temperature of the receiver is high, there is significant heat loss to the surrounding, which reduces the efficiency of solar thermal conversion [10]. In comparison, the direct absorption solar thermal collecting method is that the working fluid immediately absorbs solar radiative energy, which is then transformed into thermal energy to create thermal energy. Therefore, the direct absorption solar thermal collecting method has the advantage that heat loss could be minimized, and solar thermal conversion efficiency is high [11]. However, some studies have been carried out through the dispersion of plasmonic [12][13][14][15][16][17], metal oxide [18][19][20][21][22], and nonmetallic NPs (nanoparticles) [23][24][25][26][27][28][29] for the direct absorption solar thermal collecting method because working fluids, such as water, antifreeze, and oil, generally used in the solar collector [30], possess large optical transmittance. The beneficial aspect of using NF for the direct absorption solar thermal collecting method is that it can improve both the heat transfer performance of the working fluid and the optical absorption performance [31,32]. Existing studies reported that solar absorbance over 98% in the optical length under 10 mm could be secured by various types of NPs [33]. Moreover, it is reported that solar radiative energy can be efficiently converted to thermal energy by techniques like modified shape [13,18,19,21], dopping [16,34] of NPs, and hybrid NF [6,[35][36][37] for considering solar spectrum distribution characteristics.
As the potential of NFs to improve optical absorbance was confirmed, studies on the NF-based direct absorption solar collector (DASC) have been performed. Using NFs made of graphite, magnetite, and silver, Gorji and Ranjbar [38] performed an experimental and numerical investigation on the operation of DASC. They reported that the thermal efficiency of the DASC using magnetite NF was higher than graphite and silver NFs, and the thermal efficiency of the DASC using 40 ppm magnetite NF was 57.4% higher than that using water. Siavashi et al. [39] performed a numerical study on the performance of the DASC with/without a metal sheet as the absorber plate using SWCNH (single-walled carbon nanohorn). They confirmed that the efficiency of the DASC using pure water was improved by using a metal sheet, and the efficiency of the DASC was improved in the condition that slow mass flow rate (MFR) ( _ m ≤ 0:5 g/s) when using SWCNH NF with low concentration. Vital et al. [40] numerically investigated the thermal performance of the DASC using TiN, ZrN, HfN, and Au NF. The thermal performance of the DASC using metal nitride NFs such as TiN, ZrN, and HfN is higher than using Ag NF, and it was estimated that metal nitride NFs have a thermal efficiency of more than 80%. Karami [41] studied the thermodynamic 1st and 2nd law efficiencies of residential-type DASC using Fe 3 O 4 /SiO 2 hybrid NF. They reported that the residential type DASC using Fe 3 O 4 /SiO 2 hybrid NF had a maximum thermodynamic 1st and 2nd law efficiencies; these are 21.7% and 66.4% improved than using water, respectively. In addition, Esmaeili et al. [42] compared the performance characteristics of the DAPTSC (direct absorption parabolic trough solar collector) with CuO NF and porous metal foam to absorb solar radiative energy efficiently. They claimed that utilizing CuO NF and porous metal foam increased the-thermal efficiency of the DAPTSC by 26.8% and 23.8%, respectively. However, when considering the thermodynamic 2nd law efficiency, the solar collector can be efficiently operated by using CuO NF compared to using porous metal foam due to high pressure loss by using porous metal foam. Struchalin et al. [43] confirmed that the DASC using MWCNT NF over 0.01 wt% concentration had no mechanical damage for 45 days. However, a small amount of sediment was experimentally found, and the precipitation pattern of NPs in DASC was confirmed through the CFD model. Li et al. [44] numerically examined the effect of design parameters on DASC by reflecting the optical properties of Mxene NFs, and they confirmed that the absorbance efficiency of the DASC using 100 ppm Mxene NF was 77.49%, and it was 55.47% higher than the water. Sreekumar et al. [45] investigated the DASPTSC performance with a hybrid NF and reported that the maximum thermal efficiency and exergy efficiency of the DASPTSC with antimony tin oxide/silver hybrid NF were 63.5% and 5.6% at a MFR of 0.022 kg/s, respectively. Also, Mashhadian et al. [46] reported that when using the Al 2 O 3 /MWCNT hybrid NF, the temperature difference parameter of the DAPTC can be improved by a maximum of 240.7% compared to using water, and the DPASC using the Al 2 O 3 /MWCNT hybrid NF has the potential to reduce CO 2 emission and water consumption by as much as 450.33 kg and 2016.3 m 3 per collector.
The existing literature [40][41][42][43][44][45] showed that by increasing the concentration, the NF-based DASCs' thermal and exergy efficiencies might be increased, and it can be inferred that the DASC thermal performance is influenced by the condition of solar absorption. This is because the DASC performance depends on the optical absorbance of the NF. However, the influence on the thermal performance of the DASC should be investigated considering the design characteristics and operating parameters because it is different according to the design and operating parameters of the DASC, and thermal performance may be downgraded by heat loss facilitated through the NF with the excessive optical absorbance. Therefore, for the optimal design of the DASC, it is essential to investigate the parameter affecting the performance of the DASC because the performance of the DASC is complicatedly related to the design of the DASC (the radiation characteristics of the receiver and height of the DASC) and operating conditions (the concentration of the NF, the MFR, and the inlet temperature).
Studies on improving the optical absorbance of the NF have been actively performed. However, as an application study, the investigation of the effect on design parameters and operating characteristics in the DASC needs to be revised, and it was conducted that almost all studies were basic numerical research based on 2D geometry. Therefore, various designs and operating parameters should be investigated to understand the performance characteristics and design an optimal DASC. However, it is still difficult to understand the relationship among design variables, operation conditions, and the thermal performance of the DASC. To deeply understand the relationship between the thermal performance of the DASC, it needs to comprehensively 2 International Journal of Energy Research analyze variables related to the thermal performance. In this study, the DASC thermal performances affecting various designs and operating parameters (the concentration, MFR, height of the DASC, and radiation characteristics of the receiver), and the relationship among parameters were numerically investigated. First, the CFD simulation model of the FPDASC (flat plate direct absorption solar collector) was designed based on the optical model of Fe 3 O 4 NF verified through experimental results because Fe 3 O 4 NF has good light absorption, is cheaper than plasmonic NF, and has improved convective heat transfer performance when exposed to magnetic fields [47]. Furthermore, the thermohydrodynamic characteristics of the FPDASC and the relationship between the thermal and exergy efficiencies affecting the design and operating parameters were numerically analyzed. Through this study, it can contribute to the optimal design of the DASC and expand the application area of the DASC in thermal energy production based on solar thermal energy.

Numerical Model and Methods
2.1. Description of FPDASC. Figure 1 shows the description of the CFD model of the FPDASC used in this study. In the FPDASC, the solar radiative energy absorption perfor-mance (SEAP) determines the FPDASC thermal performance. As depicted in Figure 1(a), the working fluid absorbs the solar radiative energy that falls on the top side of the FPDASC, and the receiver is located at the bottom side. The working fluid and absorbed thermal energy are transferred to the working fluid through the FPDASC. Heat loss occurs to the surroundings due to the high temperature of the FPDASC. Through these processes, the FPDASC produces thermal energy. In Figure 1(a), H is the height of the FPDASC in this study. The simulation model was designed by referring to the geometry of the FPDASC used in studies by Delfani et al. [48] and Karami et al. [49]. Figure 1(b) shows the geometry of the FPDASC. The FPDASC consists of glass entering the solar radiative energy, the frame for the role of both the flow structure and the receiver to collect the solar radiative energy, the insulation for suppression of the heat loss to surrounding, and the working fluid that absorbs the solar radiative energy and converts it to thermal energy. The frame and glass materials are aluminum and sodium borosilicate. The Fe 3 O 4 NF was used as the working fluid because the Fe 3 O 4 NF has superior optical absorbance in visible and near-infrared bands among NFs based on the metal oxide [38]. Moreover, comparing the optical model of Fe 3 O 4 NF of this study and existing studies [11,50] is possible.   Tables 1 and 2 show the specification and simulation conditions of the FPDASC. The simulation was conducted under conditions that solar irradiance is 1000 W/m 2 , the concentration of the Fe 3 O 4 NF is 0-0.1 wt%, the MFR is 0.005-0.02 kg/s, and the inlet temperature is 35-50°C.

Numerical Model of FPDASC.
To investigate the thermohydrodynamic characteristics of the FPDASC using the Fe 3 O 4 NF, the simulation was carried out using Fluent 2021 R2 as a commercial CFD program [51]. Fluent can derive accurate thermal and flow simulation results, and multiphysics analysis is possible. Therefore, generally, it is widely used in various fields related to thermal and fluid flow. The solid and fluid zone meshes of the FPDASC were designed using hexahedron and prism mesh, as shown in Figure 2. In the numerical model, the flow of the FPDASC was assumed to be a laminar flow of incompressible fluid under a steady state. For a numerical model of the FPDASC, governing equations such as continuity, momentum, and energy equations were used [51]. Also, it was assumed that h cv (convective heat transfer coefficient) at the outside of the FPDASC is 10 W/(m 2 •°C) to consider the heat loss around the FPDASC [40,44]. Table 3 shows the boundary condition of the numerical model.
The thermal performance of the FPDASC is influenced by the solar absorption performance of the Fe 3 O 4 NF. The nongray discrete ordinates (DO) model is free from optical thickness limitations and can consider the optical characteristics of spectrum bands [52]. Therefore, the nongray DO model as the radiative transfer model was used to reflect the optical absorption characteristics of the Fe 3 O 4 NF. The radiative transfer equation (RTE) can be expressed as

Inlet and outlet region
Glass and fluid zone of DASC  The glass of the FPDASC was in semitransparent wall condition because the solar radiative energy passed through the glass of the FPDASC. The energy source of the solar radiative energy entering the FPDASC is designed by Equation (2) as Planck's blackbody relation.
In Equation (2), T sol (the solar temperature) is 5800 K and Ω s (the solid angle of the sun as seen from the earth) is 6:8 × 10 −5 . Also, S att is the attenuation constant.
For pressure velocity coupling processing, the SIMPLE (the semi-implicit method for pressure-linked equations consistent) algorithm was utilized to solve the momentum and energy equations. In this numerical model of the FPDASC, the RTE and energy equation are calculated one by one, assuming prevailing values for other variables. Due to sequential calculation, the DO model and energy equation were solved using the 2nd upwind spatial discretization technique. To improve the accuracy of the DO model, division with 6 × 6 and pixels with 3 × 3 were set. When the energy equation was calculated 30 times, the DO model was calculated only once. The residual criteria for continuity, momentum, energy, and the DO equation were defined as less than 10 -4 , 10 -4 , 10 -7 , and 10 -6 , respectively.

Optical and Thermal Properties of Fe 3 O 4 NF.
The relation between the base fluid and NPs defines the optical characteristics of the NF. In case that the concentration of the NF corresponds independent scattering regime, the absorption, scattering, and extinction coefficients of the NF can be defined based on the Rayleigh scattering approximation, which estimates the light absorption properties of liquid and particle mixtures based on the Rayleigh scattering. In the case that the concentration of the NF corresponds independent scattering regime, the absorption, scattering, and extinction coefficient of the NF can be defined based on the Rayleigh scattering approximation. Gorji and Ranjbar [38] mentioned that the optical characteristics of the NF correspond to the independent scattering regime in the case that the f v of the NF is under 0.006. The maximum concentration of Fe 3 O 4 NF used in this study was 0.1 wt% (f v = 1:96 × 10 −4 ), and it meets the criteria of the indepen-dent scattering regime. Therefore, the optical properties of Fe 3 O 4 NF were designed based on Rayleigh scattering approximation [40,53].
The extinction coefficient of the NF is defined as the sum of the extinction coefficients on the base fluid and NPs, and it can be expressed as [38,39] The absorption coefficient of the base fluid is defined as The scattering effect can be negligible, and only optical absorption can be considered in the case of the base fluid with high optical transmittances, such as the water, the antifreeze, and the oil. Therefore, it can be ignored as K s,bf ≈ 0. [54].
The extinction coefficient of the NP is expressed by In Equation (5), Q e,np is the extinction efficiency of the NP. The Q e,np can be expressed as the sum of Q a,np (the absorption efficiency) and Q s,np (the scattering efficiency). The Q a,np and Q s,np are expressed as In Equations (6) and (7), λ is the wavelength. m is the relative complex refractive index of NF and it is expressed as m = ðn np + κ np iÞ/n bf . n np and n bf are the refractive index of the NP and the base fluid, respectively. κ np is the absorption index of NP. x is the particle size diameter.
The thermal properties, such as the density, specific heat, thermal conductivity, and viscosity, are depended on the concentration of the NF. The ρ nf (the density of the Fe 3 O 4 NF), c p,np (the specific heat of the Fe 3 O 4 NF), k nf (thermal conductivity of the Fe 3 O 4 NF), and μ nf (the viscosity) are defined as [40,55] 5 International Journal of Energy Research

Analysis Method of Optical Characteristics and Thermal
Performance. The optical transmittance of the NF is calculated by the Beer-Lambert law, and it is expressed by [50] T where the TðλÞ nf is the transmittance of the NF at the wavelength, the K e,nf is the extinction coefficient of the NF at the wavelength, and the L op is the optical length which is the length of the light through the solution.
In this study, the scattering effect is insignificant because the NF concentration is comparatively low. Therefore, the scattering effect is disregarded [38][39][40]. The SEAP of the NF should be considered in the solar spectrum because the energy level of the solar radiative energy and the optical absorption of the NF are different according to the wavelength. The solar weight absorption coefficient quantitatively evaluates the SEAP in consideration of the optical absorption and the solar radiative energy according to the wavelength. The solar weight absorption coefficient can be estimated through The thermal efficiency of the FPDASC is defined as the ratio of the solar radiative energy entering the FPDASC to the useful thermal energy obtained by the FPDASC. The useful thermal energy obtained by the FPDASC and the thermal efficiency of the FPDASC are expressed as Equations (14) and (15), respectively.
In Equation (15), ðT in − T amb Þ/I is the normalized temperature difference (NTD) considering the temperature of the FPDASC and the irradiance condition. The thermal efficiency curve can be obtained by statistical curve fitting using the least squares method based on the Hottel-Whillier equation [56]. When the NTD is 0, thermal efficiency is the maximum thermal efficiency.
The exergy efficiency of the FPDASC is expressed by where T amb , T sol , _ Q sol , and _ Ex dest are the ambient temperature of the FPDASC, surface temperature of the solar, absorbed solar radiative energy at the FPDASC, and exergy destruction of the FPDASC, respectively. Also, _ Q sol is IðταÞ A I . In this study, the T sol is assumed as 5800 K.
The exergy destruction is expressed by The entropy generation by the heat transfer and the pressure loss of the working fluid in the FPDASC are expressed as Equations (18) and (19), respectively.
The Bejan number means the ratio of the entropy generation by the heat transfer to the total entropy generation, and that is expressed as

Validation of FPDASC CFD Model
To assess the accuracy of the CFD analysis model of the FPDASC, verification on the optical absorbance model of Fe 3 O 4 NF through the comparison with the experimental result, the mesh independence test, and the comparison of the CFD analysis model of the FPDASC through the existing study were carried out. Figure 3(a) shows the comparison of results between the optical absorption model and measured optical transmittances of the Fe 3 O 4 NFs. The transmittances of the Fe 3 O 4 NFs were measured by a UV-Vis spectrophotometer (U-2900, Hitachi, Japan). As a result, it was confirmed that the optical absorbance model of the Fe 3 O 4 NF had errors within ±10% compared to the measured data. Figure 3(b) displays the mesh independence test result. When the element number is more than 154,348 (under the mesh size of 2 mm), the useful heat and the pressure loss are 114.9 W and 2.77 Pa, respectively. Errors in these values have less than two decimal places, and it is confirmed that the error depending on the element number is insignificant. In addition, Figure 3(c) shows a comparison between the simulation model results and the study of Delfani et al. [48], who studied similar FPDASC. In the study of Delfani et al. [48], the thermal efficiency of the FPDASC using the base fluid is η = 0:502 − 20:18NTD.  Overall, increasing the concentration of the NF increases the SWAP, but the improvement decreases progressively as the concentration increases. This phenomenon becomes more evident as the optical length of the NF increases. It is because the amount of solar energy absorbed per penetration depth increases due to the increase in the number of NPs, but there is also an increase in reflection due to scattering as the concentration of the NF increases. Figure 5 displays the thermal efficiency curve of the Fe 3 O 4 NF at various concentrations when the height of the Fe 3 O 4 NF is 10 mm and the MFR is 0.01 kg/s. The increase of the NTD reduces the thermal efficiency of the FPDASC, and it is raised by the concentration of the Fe 3 O 4 NF. Table 4 shows the parameters of the thermal efficiency curve of the FPDASC using various Fe 3 O 4 NF concertation. The maximum efficiency of the FPDASC increases from 0.4843 to 0.773 with increasing the Fe 3 O 4 NF concentration from 0 wt% to 0.1 wt%. Since the NTD increases as increasing the inlet temperature of the FPDASC, the surrounding heat loss rises as increasing the NTD. Thus, the thermal efficiency of the FPDASC decreases. However, as the concentration of Fe 3 O 4 NF increases, the FPDASC's ability to absorb solar radiative energy increases, resulting in an increase in the FPDASC's thermal efficiency and operational range. When the thermal efficiency of the FPDASC approaches zero, the NTD increases from 0.0236 to 0.0377 as the Fe 3 O 4 NF concentration increases from 0 to 0.1 wt%. It is confirmed that the increase of the Fe 3 O 4 NF concentration expands the FPDASC operating range.

Result and Discussion
In the FPDASC, the irreversibility of the FPDASC increases due to increased thermal energy production of the FPDASC increases as raising the Fe 3 O 4 NF concentration. Figure 6 shows the entropy generation according to the Fe 3 O 4 NF concentration. The increase of the entropy generation results from improved solar absorption performance by increased concentration of the Fe 3 O 4 NF. The entropy generation in even a low concentration of 0.025 wt% Fe 3 O 4 NF is 1.356-1.379 times enhanced than the water due to improved solar absorption performance. Besides, by raising the concentration of the Fe 3 O 4 NF until 0.1 wt%, the entropy generation increases to 0.645-0.652 W/K, which is 1.513 times higher than the water. Although the entropy generation increases with increasing the Fe 3 O 4 NF concentration because the solar absorption performance nonlinearly increases, the improvement effect on the entropy generation by increasing the Fe 3 O 4 NF concentration is decreased as Fe 3 O 4 NF concentration has a limit. In the FPDASC, with raising the NTD, the irreversibility of heat energy generation decreases, but the irreversibility of heat loss decreases. In the case of the water, the entropy generation is minimum at 0.01 ((m 2 •°C))/W and is 0.433.   Figure 7 illustrates the temperature contour of the water, 0.05 wt% Fe 3 O 4 NF and 0.1 wt% Fe 3 O 4 NF. In the case of the FPDASC, the solar radiative energy is absorbed and a comparatively high temperature forms at the bottom (the receiver). Therefore, it can be confirmed that thermal energy is produced through the heat transfer between the working fluid and the receiver. When using the Fe 3 O 4 NF, unlike water, the major media for collecting the solar radiative energy is changed from the receiver to the Fe 3 O 4 NF. Therefore, the temperature distribution pattern is different. In the 0.05 wt% and 0.1 wt% Fe 3 O 4 NF, the temperature is relatively high at the top of the FPDASC because solar radiative energy is primarily absorbed from the top of the FPDASC. As increasing the concentration, it can be confirmed that the outlet temperature of the FPDASC is nonuniform by the unmixed temperature between the top and bottom. Even though the SEAP can be improved by increasing the concentration of the Fe 3 O 4 NF, when the concentration is increased over 0.1 wt%, the solar radiative energy absorption is more concentrated at the top of the FPDASC, and the heat loss to the surrounding is expected to increase. To suppress thermal stratification of the FPDASC due to the increase in the concentration of the Fe 3 O 4 NF, it is necessary to add mixing structures like wave surface and fin that disturb the flow of the fluid inside the fluid FPDASC. It was confirmed through the numerical study by Hosseinnezhad et al. [55] that introducing the DASC on the wave surface induces vortex flow at the top and bottom of the DASC, improves heat transfer, and disturbs temperature stratification. Because the thermal stratification in the FPDASC can be suppressed, while the pressure loss can increase when the working fluid has enough optical absorption, the height of the FPDASC should be minimized. Figure 8 shows the FPDASC inlet and outlet temperature difference according to the MFR of the Fe 3 O 4 NF. The temperature difference between the inlet and the outlet are reduced as the MFR increases. In the case of water, when the NTD is 0.05 ((m 2 •°C))/W, the temperature difference between the inlet and outlet is reduced from 4.96°C to 1.45°C. Increased MFR of the working fluid increases the  heat capacity of the FPDASC, contributing to a decrease in the temperature difference between the inlet and outlet. When using the 0.1 wt% Fe 3 O 4 NF as the working fluid, the temperature difference between the inlet and the outlet decreases from 8.48°C to 2.36°C with an increasing MFR from 0.005 to 0.02 kg/s. However, the application of Fe 3 O 4 NF increases the inlet and outlet temperature difference at the same MFR compared to water due to the enhanced solar radiative energy absorption capacity as the concentration of Fe 3 O 4 NF. It is confirmed that the outlet temperature can be 62%-71% higher produced using the 0.1 wt% Fe 3 O 4 NF than water. The thermal efficiency of the FPDASC is significantly affected by increased MFR of the Fe 3 O 4 NF because the average temperature is reduced, and the heat transfer is improved by increasing the velocity of the Fe 3 O 4 NF in the FPDASC. Figure 9 displays the variation of maximum thermal efficiency according to the MFR of the Fe 3 O 4 NF. When using water, the maximum thermal efficiency increases from 0.442 to 0.509 as the MFR increases from 0.005 to 0.02 kg/s. The maximum efficiency improves with the increased Fe 3 O 4 NF concentration due to enhanced SEAP by increasing the Fe 3 O 4 NPs. The maximum efficiency of the 0.1 wt% Fe 3 O 4 NF increased from 0.707 to 0.811 according to increasing the MFR from 0.005 to 0.02 kg/s, which is 26.5%-30.2% improved compared to using water. In addition, when the _ m increases from 0.005 to 0.02 kg/s, the improvement in the thermal efficiency of the FPDASC is 6.88% and 10.4% at the water and 0.1 wt% Fe 3 O 4 NF, respectively. The thermal efficiency is more significantly improved by using the Fe 3 O 4 NF than water. In the improvement of thermal properties, the concentration of 0.1 wt% belongs to a low concentration, and the improvement of the thermal properties is slight. In contrast, the light transmittance improvement effect is remarkable. Therefore, the thermal efficiency improvement effected by increasing the Fe 3 O 4 NF concentration is derived from the enhanced SEAP by raising the concentration of the Fe 3 O 4 NF. Besides, the thermal capacity of the FPDASC and convective heat transfer increase due to the increased MRF. Therefore, the thermal efficiency of the FPDASC is improved by reducing heat loss to the surroundings with increasing MRF. Figure 10 shows

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International Journal of Energy Research and the MFR in the FPDASC decreases the Bejan number, but the irreversibility by the pressure loss is very insignificant. Based on the obtained result, it is judged that the influence of the pressure loss can be negligent in the performance of the FPDASC designed in this study.

Influence of Geometry and Receiver
Material on the Thermal Performance of the FPDASC. Figure 11 shows the variation of the maximum thermal efficiency of Fe 3 O 4 NF depending on the height of the FPDASC. The increase in the height of the FPDASC brings to the rise in the maximum thermal efficiency. As increasing the height of the FPDASC from 10 to 25 mm in the case of using water, the maximum thermal efficiency rises from 0.4843 to 0.543. When using the Fe 3 O 4 NF, the maximum thermal efficiency increases by increasing the height of the FPDASC. Still, the improvement effect on increasing the height of the FPDASC is reduced by increasing the concentration of the Fe 3 O 4 NF, and the critical point on maximum thermal efficiency enhancement by raising the height of the FPDASC appears over the concentration of 0.05 wt%. When using 0.05 wt% Fe 3 O 4 NF in the FPDASC, the critical height of the FPDASC is 20 mm, and its maximum thermal efficiency is 0.766. Whereas, in the case of using 0.1 wt% Fe 3 O 4 NF, the required critical height of the FPDASC decreases to 15 mm, but the maximum efficiency slightly increases by 0.777. Increasing the height of the FPDASC means the increase of the optical length acquiring solar radiative energy. Therefore, as shown in Figure 4, the thermal efficiency can be improved by raising the height of the FPDASC because the increase of the optical length increases the solar weight absorption coefficient of the Fe 3 O 4 NF. With the increase in the concentration of the Fe 3 O 4 NF until 0.1 wt%, the solar weight absorption coefficient increases, while the effect on the improvement of optical absorption by the optical length is insignificant. Additionally, increasing the height of the FPDASC increases the optical length and the solar weight absorption coefficient. At the same time, it contributes to increasing the convective heat loss area. Therefore, as the     13 International Journal of Energy Research Figure 12 shows the temperature contour at the A-A' section when using water and 0.1 wt% Fe 3 O 4 NF according to the various heights of the FPDASC. When using the water, the temperature at the receiver at the bottom of the FPDASC is relatively high. Moreover, it is confirmed that the temperature of the glass at the top of the FPDASC increases as the height of the FPDASC from 10 to 25 mm. Whereas, when using the 0.1 wt% Fe 3 O 4 NF, the solar radiative energy is primarily absorbed at the top of the FPDASC, and this phenomenon is enhanced according to increasing the height of the FPDASC from 10 to 25 mm. This phenomenon increases nonuniform temperature distribution in the FPDASC, which increases the heat loss to the surroundings and reduces thermal efficiency. Based on the simulation result, the increase in the height of the FPDASC brings an increase in the flow nonuniformity of the working fluid in the FPDASC.   14 International Journal of Energy Research Figure 13 shows the velocity contour and vector according to the height at y/H = 0:5 in the FPDASC. As the height of the FPDASC increases from 10 to 25 mm, it is confirmed that the velocity at the center of the FPDASC is slow due to the increased cross-section area, and the dead zone, where the working fluid is stagnant, is enlarged. Therefore, due to the slow velocity and the enlarged dead zone in the FPDASC by raising the height, the convective heat transfer decreases and heat loss increases. These flow patterns increase the difference in residence time according to the fluid pathline and deteriorate the temperature nonuniformity of the FPDASC. To prevent the nonuniform temperature, additional struc-tures (guide vanes, manifolds) that guide the flow of the working fluid are needed.
The thermal efficiency of the FPDASC is different by the solar radiative energy absorption characteristics of the Fe 3 O 4 NF and the receiver. Figure 14 shows the thermal efficiency of the FPDASC with different receiver emissivities. As the emissivity of the FPDASC approaches zero, the reflection occurs in the receiver. In contrast, as it approaches one, the solar radiative energy is actively absorbed in the receiver, similar to the black body.

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International Journal of Energy Research water, the maximum efficiency increases from 0.4843 to 0.702, according to increasing the emissivity of the receiver from 0.2 to 0.8. The SEAP is improved by increasing the emissivity of the receiver because the solar radiative energy is mainly absorbed in the surface of the receiver by the high light transmittance of the water. Whereas, when using 0.1 wt% Fe 3 O 4 NF, maximum efficiencies of the FPDASC with the receiver emissivity of 0.2 and 0.8 are similar, ranging from 0.772 to 0.774. When using 0.1 wt% Fe 3 O 4 NF, the operation range of the FPDASC is extended according to the decrease of the receiver emissivity from 0.8 to 0.2. At 0.1 wt% Fe 3 O 4 NF, the SEAP of the receiver does not affect the thermal performance of the FPDASC because the solar radiative energy is almost absorbed in 0.1 wt% Fe 3 O 4 NF near the top of the FPDASC. However, as the emissivity of the receiver rises, the radiative heat loss also rises; therefore, the operating range of the FPDASC is reduced. The increase in the emissivity of the receiver can absorb nonabsorbed solarenergy at the working fluid. In contrast, the convective and radiative heat losses are increased by the heated receiver. When the optical absorbance of the working fluid is low, such as water, the solar energy in the visible band is pene-trated through the working fluid. Therefore, penetrated solar energy through the working fluid is absorbed by the receiver, and absorbed solar energy increases according to the increase of emissivity. Whereas, when the concentration of the Fe 3 O 4 NF increases, the absorbed solar energy increases, and the penetrated length is short. It is resulted in heating the local region of the working fluid. Because the solar energy reaching the receiver decreases rapidly as the concentration of the Fe 3 O 4 NF, increasing the emissivity of the receiver has little effect on the solar energy absorption, while the radiative heat loss increases due to increasing emissivity. Therefore, to improve the thermal efficiency of the FPDASC through enhanced optical absorption of the NF, the receiver should be made of materials with low emissivity. Figure 15 shows the variations of thermal and exergy efficiencies according to the conditions of the working fluid and the design parameter of the FPDASC. In the concentration variation of Fe 3 O 4 NF, as shown in Figure 15(a), the thermal and exergy efficiencies when using  . Therefore, the irreversibility increases by improved production of the useful heat owing to increased concentration of the Fe 3 O 4 NF. In comparison, it is confirmed that increasing the MFR increases the thermal efficiency but decreases the exergy efficiency in the FPDASC. As shown in Figure 15(b), when using water, the maximum exergy efficiency decreases from 0.0234 to 0.0213 as the MFR increases from 0.005 to 0.02 kg/s. When using 0.1 wt% Fe 3

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International Journal of Energy Research from 0.0346 to 0.0293 under the same MFR change. Because the entropy generation is not affected by the increased pressure loss, the decrease of the exergy efficiency by _ m results from the thermal environmental condition of the FPDASC. The production of useful heat in the FPDASC is increased by increasing the MFR; however, it decreases the average temperature of the FPDASC, resulting in reduced entropy generation.
The thermal and exergy efficiencies are improved by the increase of height in the FPDASC when using water, as shown in Figure 15(c). The maximum exergy efficiency increases from 0.022 to 0.0235 as the height of the FPDASC rises from 10 to 25 mm. This is because the increase in the optimal height of the FPDASC due to the high light transmittance of water increases the optical length that can absorb solar radiative energy, thereby increasing the useful heat energy production of the FPDASC. Using 0.1 wt% Fe 3 O 4 NF, the thermal efficiency reaches the peak at the height of 15 mm, but the exergy efficiency decreases from 0.031 to 0.026 as the height of the FPDASC increases from 10 to 25 mm. Since the 0.1 wt% Fe 3 O 4 NF has a high SEAP, the SEAP is not affected by increasing the height of the FPDASC. Instead, the thermal and exergy efficiencies are reduced due to increased heat loss area and temperature stratification in the FPDASC.
The thermal and exergy efficiencies are influenced by the optical characteristic of the receiver and the working fluid. As shown in Figure 15(d), since the water has a low SEAP, the solar radiative energy absorption increases due to the increase of the receiver's emissivity in the FPDASC, resulting in improved thermal and exergy efficiencies. When using water in the FPDASC, the maximum exergy efficiency is increased from 0.022 to 0.0304 as the emissivity of the receiver increases from 0.2 to 0.8. Nevertheless, when using water, the thermal and exergy efficiencies of the FPDASC with the emissivity of the receiver with 0.8 are lower than using 0.1 wt% Fe 3 O 4 NF. In the case of using 0.1 wt% Fe 3 O 4 NF in the FPDASC, the high emissivity of the receiver decreases the thermal and exergy efficiencies. When using the 0.1 wt% Fe 3 O 4 NF, as the emissivity of the receiver increases from 0.2 to 0.8, the maximum exergy efficiency decreases from 0.031 to 0.0291. When the emissivity of the receiver is high, the solar radiative energy absorption process of the FPDASC is similar to the direct absorption solar thermal collecting method. At the receiver, solar radiative energy is converted into thermal energy in the case of using water in the FPDASC. Therefore, the thermal and exergy efficiencies are improved by using the receiver with high emissivity. However, when using the 0.1 wt% Fe 3 O 4 NF, the SEAP of the FPDASC is not affected by the high emissivity of the receiver but increases heat loss. Therefore, in the FPDASC, it is possible to efficiently produce thermal energy by reducing heat loss and increasing SEAP when the working fluid's optical absorbance is high and the receiver's emissivity is low.

Conclusion
The effects on the thermal and exergy efficiencies of the FPDASC were numerically carried out, considering the characteristics of the Fe 3 O 4 NF as the working fluid of the FPDASC and various design parameters. Increasing the Fe 3 O 4 NF concentration raises the thermal and exergy efficiencies. As the Fe 3 O 4 NF concentration increases from 0 to 0.1 wt%, the maximum thermal efficiency increases from 0.484 to 0.773. The maximum exergy efficiency rises from 0.027 to 0.031 when the height of the FPDASC is 10 mm and the MFR is 0.01 kg/s. Increasing the MFR of the 0.1 wt% Fe 3 O 4 NF from 0.005 to 0.02 kg/s increases the thermal efficiency from 0.707 to 0.811. An increase in MFR increases the pressure loss of the FPDASC, but it is not significant because the Bejan number approaches near 1.
The thermal and exergy efficiencies are affected by increasing the height of the FPDASC and the optical characteristics of the working fluid. As the optical absorbance increases due to the increased concentration of Fe 3 O 4 NF, the improvement in thermal and exergy efficiencies by increasing the height of the FPDASC becomes insignificant. However, thermal and exergy efficiencies are decreased due to the expanded convective heat loss area. In addition, thermal stratification occurs in the FPDASC due to improved optical absorbance of the Fe 3 O 4 NF. It has resulted from excessive optical absorbance of the working fluid and nonuniform flow velocity. Therefore, the optical absorption of the working fluid is higher, and the channel height of the FPDASC should be shorter. Also, flow fluid structure is needed to uniform flow velocity in the FPDASC.
The thermal and exergy efficiencies are affected by the emissivity of the receiver. In the case of water, because the receiver absorbs the nonabsorbed solar energy of water, the emissivity of the receiver should be high. However, in the case of excellent optical absorption of the working fluid, such as 0.1 wt% Fe 3 O 4 NF, the emissivity of the receiver should be low to reduce the radiative heat loss of the FPDASC.