CFD modeling of a triple‐walled direct absorption evacuated tube solar collector based on hybrid nanofluid/microencapsulated PCM

Nowadays, direct absorption solar collectors are a new concept of solar collectors which have attracted special attention. The type of heat transfer fluid (HTF) has a significant influence on the efficiency of this kind of collector. Therefore, in this study, a wide range of working fluids including mono nanofluid ( Al 2 O 3 ${\text{Al}}_{2}{{\rm{O}}}_{3}$ and CuO), binary nanofluid, and especially the incorporation of a new hybrid combination of nanofluid and microencapsulated phase change material (MPCM), are used as the working fluids of a triple‐walled direct absorption evacuated tube solar collector. The computational fluid dynamics (CFD) method is used for simulating the collector and investigating the effect of different parameters including volume fraction, base fluid, mass flow rate, and type of absorber tube structure (double‐ and triple‐walled) on collector thermal performance. Results show that binary nanofluids of 0.06% Al 2 O 3 ${\text{Al}}_{2}{{\rm{O}}}_{3}$ /0.002% CuO/water and 0.06% Al 2 O 3 ${\text{Al}}_{2}{{\rm{O}}}_{3}$ /0.002% CuO/ethylene glycol (EG) have the largest working fluid temperature differentials equal to 48.31 and 66.5 K, respectively. It was inferred that, at the mass flow rate of 2.7  kg / h $\mathrm{kg}/{\rm{h}}$ , the efficiency is obtained to be 60.29% employing binary/EG nanofluid, which is 8.68% and 15.31% higher than CuO/EG and Al 2 O 3 ${\text{Al}}_{2}{{\rm{O}}}_{3}$ /EG nanofluids, respectively. Inserting the hybrid CuO nanofluid/MPCM leads to an improvement of 1.14% and 1.22% in the efficiency of triple‐ and double‐walled collectors, respectively, with respect to the individual usage of the nanofluid. The thermal efficiency of the double‐walled structure is higher than triple‐walled considering all HTFs.


| INTRODUCTION
The world has experienced an energy resource shortage following the 1970s energy crises. 1 Due to a rise in population, the demand for energy among humans is increasing.Studies indicate that as a result of this trend, by 2025, oil consumption will have risen to more than 120 million barrels per day. 2 Due to the fact that fossil fuels have many environmental disadvantages, including increased greenhouse gases, global warming, and air pollution, the world is evolving toward utilizing clean, and renewable energy sources.Solar energy is particularly well suited to replace nonrenewable sources of energy like fossil fuels due to its widespread availability and more equitable distribution throughout the environment.
Among solar energy systems, solar thermal collectors are heat exchangers that can satisfy a portion of the world energy demands; however, they still require improvement and refinement. 3,4These collectors are classified as stationary and tracking.Stationary collectors were divided into three types: (1) flat-plate solar collector (FPSC), (2) evacuated tube solar collectors (ETSC), and (3) parabolic trough solar collector (PTSC).Due to the fact that ETSCs have lower heat loss to the ambient as a result of the vacuum insulation, they have higher working temperatures thermal efficiency in comparison with FPSCs.Therefore, they noticed a lot of attention based on their low cost in the market. 5A PTSC is a concentrating collector which concentrates sunlight by parabolic reflector to generate thermal energy above 300°C and power. 6ne of the most recent types of solar collectors is a direct absorption solar collector (DASC), also known as volumetric absorption collector, absorb solar energy directly by the fluid volume. 7Adding nanoparticles to the fluid modifies its optical (absorption and scattering) characteristics, and enhances the efficiency of the DASC. 8Therefore, it is possible to extend this concept to the different geometries of solar collectors to develop the thermal efficiency of them.
Since Tyagi et al. 9 used aluminum nanofluid to evaluate the performance of the DASC, different nanofluids based on carbon-based, metallic, metal oxide, and so forth, nanoparticles were selected and used as the working fluid of the DASC. 10 A review paper was done by Sainz-Mañas et al. 11 based on the application of the nanofluids in the DASCs in low-and medium-temperature.In addition, Moghaieb et al. 12 reviewed the recent development of the nanofluid-based DASCs.They have concluded that significant changes in absorbance properties appeared at low nanoparticle concentrations, and these nanoparticles had a remarkable effect on improving the thermal potential of the DASCs.In DASCs, the thermal efficiency of the system is extremely reliable on the optical absorption of the heat transfer fluids (HTFs).Accordingly, forming novel HTFs with perfect extinction coefficient is needed to have a higher thermal efficiency for the DASCs. 13Karami et al. 14 found that both energy and exergy efficiencies of a DASC with V-shaped rib roughness are optimum by using graphene oxide (GO) nanofluid with a volume fraction of 500 ppm.An experimental investigation was carried out by Hooshmand et al. 15 and they have showed the efficiency increase of a porous-foam-based DASC using SiC/water nanofluid as working fluid with respect to the water-based conventional DASC.According to findings of Kasaeian et al., 16 using multiwalled carbon nanotube (MWCNT); Fe 3 O 4 ferrofluid MWCNT nanofluid in the vacuum-glass absorber tube of the direct absorption parabolic trough solar collector (DAPTC) resulted in a greater temperature and efficiency.They also concluded that 0.5% MWCNT nanofluid is the best volume fraction which has a thermal efficiency of 82.3%.Heyhat et al. 17 enhanced the thermal efficiency of the DAPTC by inserting CuO/water nanofluid and metal foam.According to their results, the highest temperature gradients for nanofluid, metal foam, and their combination are 10.7°C, 8.8°C, and 16.6°C, respectively.Also, the effectiveness of metal foam and nanofluid as solar absorbers has been confirmed.In addition, Simonetti et al. 18 considered the effect of using single-wall carbon nanohorn (SWCNH)/EG nanofluid on the performance of the direct absorption evacuated tube solar collector (DAETC) equipped with a compound parabolic concentrator (CPC).It is observed that by increasing the concentration of nanofluid, the collector efficiency was improved for both simple and CPC-equipped tubes.Struchalin et al. 19 studied the performance of the tabular DASC incorporating MWCNT/water-ethanol numerically and experimentally.They found that the optimum value of the nanofluid concentration is equal to 0.01%, and the structure of the absorber is highly affected by this parameter.Moreover, Joseph and Thomas 20 used ultrahigh stable carbon quantum dot (C-dot) nanofluid as working fluid of a DAPTC and reported that the highest efficiency is 73.41% at Reynolds number of 2952, compared to 15.79% for water.
By the late 2010s, hybrid nanofluids emerged as a promising solution potential, particularly for thermal applications.Hybrid nanofluids are a combination of two (binary) or more distinct kinds of nanoparticles dispersed in a base fluid. 21This class of nanofluids demonstrated superior thermal conductivity qualities when compared to mono nanofluids. 22,23Hybrid nanofluids are also widely used as the working fluids of DASCs. 24Numerical simulation of a DAPTC using hybrid CuO-MWCNT/ water, MWCNT/water, and CuO/water nanofluids revealed that 40.44, 39.01, and 30.8GJ embodied energy and 59.03, 56.95, and 44.96 KL embodied water are saved, respectively. 25Li et al. 26 conducted an experimental investigation to evaluate the solar-thermal conversion performance of EG-based SiC-MWCNTs nanofluids for DASC.Their results indicated that the maximum conversion efficiency using 1 wt% hybrid nanofluid is 48.7% higher than that of pure EG.A hybrid nanofluid based on plasmonic gold nanoparticles in Azadirachta indica leaves extract was used by Gupta et al. 27 as the working fluid of DASC.Based on the results of outdoor performance tests, they found that the maximum photothermal efficiency using a hybrid nanofluid is about 12% higher than that using water.
Incorporating phase change material (PCM) into solar thermal applications is an efficient method which positively affects the performance of these systems. 28CMs are capable of storing and releasing enormous latent heat during phase change at a given temperature range; therefore, adding PCMs to the HTF, improve significantly their specific heat.In some research, PCM emulsions have been used as the working fluid of DASC.29 Wang et al. 30 discovered that the addition of graphite nanoparticles to the paraffin/water emulsion caused a higher thermal conductivity with respect to paraffin/water emulsion without graphite nanoparticles.Zhang et al. 31 used Ti O 4 7 nanoparticles to modify the microencapsulated phase change material (MPCM) shell.The resulting microencapsulated slurry retained the majority of PCM enthalpy, improved its stability, and demonstrated great thermal energy storage.Li et al. 32 synthesized the MPCM with octadecane as the core material and titania (TiO 2 ) as the shell material by the sol-gel method.They indicated that the photo-thermal conversion efficiency improved to 86.0% using hybrid MPCM/CNT suspensions instead of pure water.Burgos et al. 33 investigated on the performance of a hybrid (0.01 wt%) carbon/(5 wt%) paraffin wax RT44HC/water emulsion.They concluded that the capacity of the thermal energy has increased 16% with respect to paraffin/water.Karami et al. 34 investigated the thermal performance of a double-wall DAETC using MPCM and CuO nanofluid and reported that the efficacy of the collector increase by 4.53% and the heat loss lowers by 5.84%. Acording to various researchers, hybrid nanofluid/MPCM as an HTF enhances the thermal conductivity, heat transfer performance, and efficacy of the system in a variety of cases.[35][36][37] Based on the literature review, there are limited works which investigated the triple-walled structure of the absorber tube of DAETCs. Inaddition, there has been no study on the thermal performance of the triple-walled DAETC using hybrid nanofluid/MPCM as the working fluid.Therefore, in the present work, the thermal performance of a triple-walled DAETC is investigated using hybrid CuO nanofluid-MPCM (hydrocarbon n-eicosane@TiO 2 ).Also, different HTFs are considered to comprehensively evaluate the performance of this kind of DASCs.Furthermore, the effect of operating parameters including the type of base fluid, nanofluid volume fractions, and mass flow rate is evaluated developing a three-diemensional (3-D) model of the tripe-walled DAETC.A comparison between double-walled and triple-walled structures of the DAETC is also accomplished to analyze the best performance.

| DAETC GEOMETRY AND WORKING FLUIDS
The triple-walled DAETC, made of borosilicate glass, is shown in Figure 1.As can be seen, the working fluid moves in an annular section and the vacuum is located in the outer wall as a thermal insulation.Furthermore, it is considered that air exists within the inner wall.Because | 2299 the inner fluid surface is thought to be adiabatic, the triple-walled structure disregards the heat transfer among the air-filled inner tube and fluid. 18The tube length is 1.8 m and the inside and outside diameters of the internal, central, and external walls are, respectively, 20. 6  and CuO dispersing in the base fluid; although, hybrid nanofluid/ MPCM is the compound of CuO nanofluid and microencapsulated PCM together.Point out that water and ethylene glycol (EG), which are solar common fluids, are selected as a base fluid of these kind of HTFs.EG is added to water to prevent the water from freezing at low temperatures.It should be noted that these base fluids have a low absorption coefficient, therefore adding nanoparticles into them improves their optical properties. 34Based on the high scattering property of Al O 2 3 and the superior absorption property of CuO, these nanoparticles are the appropriate choices for solar systems.In addition, if these two nanoparticles are dispersed in the base fluid, a binary nanofluid with excellent optical properties could result (Extinction coefficient = Scattering coefficient + Absorption coefficient). 38All HTFs are summarized and labeled in Table 1.
As mentioned, the chosen PCM is the hydrocarbon neicosane, while the MPCM shell material is TiO 2 .Table 2 lists the MPCM properties.Concerning the volume fraction of the solid phase, the effective thermophysical characteristics of the microencapsulated PCM are computed through the subsequent formulas 39 : The effective density, thermal conductivity, viscosity, and specific heat capacity of the microencapsulated PCM slurry are represented ρ eff , k eff , μ eff , and c p.eff .Displayed by the subscripts "p" and "f" are the PCM particles and working fluid, respectively, while the solid volume fraction is represented by the α p .In this paper, ρ f , k f , and c p.f are taken 998.2 kg/m 3 , 0.6 W/mK, and 4182 J/kg K for water and 1111 kg/m 3 , 0.253 W/mK, and 2415 J/kg K for EG.
The critical point is the specific heat capacity of the PCM, which is related to its latent heat during the transition of the phase.There are five different models for defining the specific temperature of a PCM, with slight differences between them. 41The commonly used middle triangle model is chosen for this research. 31This model also includes the following equations 39 : where "l" and "s" denote the liquid and solid phases of the MPCM, respectively, and H ∆ stands for latent heat.∆ are the lower and upper limits of the MPCM, respectively.It should be noted that the T ∆ corresponds to 1 K for the microencapsulated PCM slurry.

| Governing equations and boundary conditions
The Navier-Stokes equations, which include the continuity, momentum, and energy equations for the fluid domain, are given as follows 4 : where V ⃗ f is the fluid velocity, P is the pressure, μ is the viscosity, k is the thermal conductivity, and q s is the volumetric energy source term.
To determine the energy source term, the radiative transfer equation (RTE) is employed.The scattering and emission coefficients are ignored to simplify the RTE.The following equation is the volumetric energy source term considering the Beer-Lambert law 42 : where I 0 represents the sun irradiation, which is 1000 W/m 2 .The length of the light path in the collector and the extinction coefficient of the nanofluid are denoted by l and K λ e , respectively.It is essential to emphasize that the experimental findings of Menbari et al. 38,43 are the source of the optical characteristics of nanofluids (Figure 2).
F I G U R E 2 Extinction coefficients of nanoparticles. 38,43AHINI ET AL.

| 2301
To solve the governing equations, the following assumptions are considered: 1.A laminar incompressible steady-state fluid domain is assumed, and the working fluid, whether it contains nanoparticles or not, is Newtonian. 44. Nanofluids are expected to have the same thermophysical characteristics as the base fluids due to their small volume fraction. 18,453. Throughout the phase change, the optical characteristics remain unchanged. 39e MPCM slurry numerical simulation is made simpler using the single-phase model according to its small size, which is assumed to distribute uniformly throughout the fluid. 44It should be noted that the MPCM with a concentration of less than 25% can be considered a Newtonian fluid. 46,47In addition to the single-phase solution, a two-phase solution can be simulated to examine the performance of the microencapsulated PCM slurry.In the two-phase model, governing equations are more complex and require more solving time for simulation. 4Based on our previous research, 34 singlephase model and mixture models have close results; due to this fact, the single-phase model has been adopted in the present work to reduce the solution time.
Furthermore, the following are the corresponding boundary conditions that are considered: The inlet mass flow rate of the working fluid is represented as ṁi n .The inlet (T in ), ambient (T amb ), and sky (T sky ) temperatures are equal to The inlet mass flow rate and temperature are considered for the inlet conditions of the tube.The pressure outlet is assumed as the system outlet.In addition, the tube wall is confined to the no-slip condition.The upward and downward surfaces of the tube are considered a wall.To calculate the amount of the energy source term, an expression method is utilized in the ANSYS-FLUENT.A detailed view of the boundary conditions is shown in Figure 3.
In the present study, the collector is divided into two sections of upward and downward surfaces.To compute F I G U R E 3 Boundary condition of the direct absorption evacuated tube solar collector.
the overall heat transfer coefficient, an electric analogy model is implemented for those sections, which is shown in Figure 4. Besides, the temperature of the upward and downward of the collector are assumed to be T T = upward sky , T T = downward amb , respectively.According to the first law of thermodynamics, the following formula is used to calculate the collector efficiency 18 : The average outlet temperature, inlet temperature, mass flow rate, specific heat capacity, irradiance, and collector net surface are represented by T ¯out , T in , ṁ, c p , I 0 , and A, respectively.

| Numerical study and validation
The governing equations are solved using the ANSYS-FLUENT 2021 R2 as a computational fluid dynamics software, which includes the continuity, momentum, and energy equations.A discretization of the governing equations is carried out using the SIMPLE algorithm.Residual convergence values are assumed to 10 −5 , 10 −5 , and 10 −8 for the mass, momentum, and energy conservation, respectively.The grids for the numerical domain are created using ANSYS-workbench 2021 R2.The triple-walled solar collector is simulated using the symmetry method.This method applies more elements, and the computational time becomes less.The unstructured 3-D mesh is constructed for the computational domain, and different grid numbers are assessed to achieve results independent of the mesh.A boundary layer mesh is employed near the tube's interior surface to improve the precision of the numerical simulation.The grid independence analysis utilizing binary nanofluid (W3) at the collector's outlet temperature profile is depicted in Figure 5.It is worth noting that the fluid flows in an annular path, and the figure shows the profile at the outlet fluid temperature.Therefore, a section of the figure that has a gap is related to the air space at the outlet.According to this figure, the temperature profile of working F I G U R E 4 Thermal network design of the system.
F I G U R E 5 Grid independency analysis for binary nanofluid (W3).fluid for 1000, 1300, and 1600 thousand elements are nearly the same.As a result, 1.3 million elements are selected for the rest of the calculation of the study.The computational mesh for the collector is shown in Figure 6, which was chosen after the mesh analysis.
The efficiency of the DAETC is compared to the results of Simonetti et al. 18 to confirm the simulation results.They employed EG as the base fluid to investigate the influence of SWCNH concentration on double-walled and triplewalled DASC efficiency.As seen in Figure 7, the percentage inaccuracy is under 3%, indicating that the present study is in agreement with the results of Simonetti et al. 18 Furthermore, the experimental work of Chen et al. 48is conducted to valid the MPCM slurry simulation findings.Chen et al. 48studied the potential of microencapsulated phase change slurry to pass through a circular stainless steel tube with constant heat flux.Wall thickness, diameter, and length of the examined circular stainless-steel tube (Cri8Ni9Ti) are 1460, 4, and 1 mm, respectively.1-Bromohexadecane (C 16 H 33 Br) is the suggested PCM used in the MPCM slurry, with a concentration of 15.8% and a particle diameter of 8.2 μm. Figure 8 depicts the change in fluid temperature inside the tube after the microencapsulated PCM slurry has been exposed to various heat fluxes.As can be seen, the results of the present work correspond well with the MPCM slurry modeling results of Chen et al. 48I G U R E 6 The computational mesh for the collector using 1,300,000 grids.
F I G U R E 7 Comparison with Simonetti et al. 18 for validation of the direct absorption evacuated tube solar collector.
In this section, a comparison between the structure of the absorber tube (double-and triple-walled) is examined based on thermal performance.A variety of different HTFs are utilized to investigate the efficacy of the DAETC.In addition, the effect of several factors including base fluid type, volume fractions, and mass flow rate on the system performance is explored, comprehensively.An analysis of the usage of hybrid nanofluid/MPCM on the triple-walled and double-walled collectors and its improvements in the systems are both evaluated.

| Performance comparison of double-and triple-walled DAETC
Two different structures (double-walled and triplewalled) of the DAETC are investigated in terms of thermal efficiency, and the impact of nanofluids on the performance of each is evaluated.In Figure 9, the temperature contour plots of the triple-walled and double-walled absorbers are obtained by applying W1 nanofluid at the same flow rate.As it is known, the temperature contour plot in the double-walled is more uniform and regular than in the triple-walled collector.In the triple-walled model, the maximum temperature is Comparison with Chen et al. 48or validation of the microencapsulated phase change material slurry (MPCM).
F I G U R E 9 Temperature contour plots of (A) triple-walled and (B) double-walled collector using W1 nanofluid.

SHAHINI ET AL.
| 2305 more concentrated on the upper surface of the collector, although the double-walled model has a more proportional distribution of temperature.It can be concluded that the structure of the vacuum section in the doublewalled has more effectiveness in terms of temperature distribution with respect to the triple one.In addition, the cylinder structure of the absorber in the double collector spreads the absorbed heat better than the annular structure of the triple-walled of the DAETC.
Figure 10 presents an overall comparison of the average and maximum temperatures of the nanofluids in both structures.According to this figure, as the nanofluid volume fraction increases, an enhancement in working fluid temperature occurs; but the difference in outlet temperature distribution of double-walled and triplewalled is that, in the latter, the temperature distribution is more sensitive to the nanofluid volume fraction, and the temperature difference is much higher than double.Note that a double-walled collector has an average temperature larger than triple-walled across all nanofluid volume fractions.The apparent difference between the triple-walled collector and the double-walled collector is that, except for W1 and W2, the maximum surface temperature in the triple-walled is higher than in the double-walled.This is because the path of light through the working fluid is shorter in the triple-walled structure, and the energy trapped by the nanofluid is more significant.As a result, by applying the same amount of nanofluid, its maximum surface temperature is higher compared to double-walled structure.Also, the average temperature and maximum temperature in the doublewalled structure are much closer than in the triplewalled model.In cases W1 and W2, the volume fraction is lower than in other cases; therefore, it is found that the low volume fraction application results in a greater maximum temperature and a better dispersion in the double-walled collector than in the triple-walled one.
Figure 11 shows the efficiency and the amount of heat loss of the double-walled and triple-walled collectors for different volume fractions of water-based nanofluids.The efficiency of the double-walled collector for W1, W2, W3, W4, W5, and W6 are 69.69%,70.38%, 71.44%, 71.26%, 71.48%, and 71.52%, respectively.Based on the findings, the binary nanofluid has the largest thermal efficiency among all different nanofluids.It is found that the double-walled collector has a higher thermal efficiency than the triple-walled collector.This phenomenon can be attributed to the cylinder structure of the double collector which distributes the heat more uniformly, and its average temperature is higher than the triple collector.Besides, considering that the T ave is an essential parame- ter in the output efficiency, the thermal efficiency elevates due to the higher T ave .This matter is also the reason for the greater heat losses of the double-walled collector compared to the triple-walled one.Indeed, the average temperature not only affects efficiency but also has an influence on thermal loss.
Figure 12 shows the surface temperature distribution of double-walled and triple-walled collectors for waterbased nanofluids (W1, W12, and W3).According to this figure, the T max of the double-walled for W1, W12, and W3 nanofluids are 328.16,329.34, and 332.72 K, respectively.The T max of the triple-walled collector for W1, W12, and W3 nanofluids are 325.88,328.65, and 337.48 K, respectively.The point about the variation of the temperature on the surface of the triple-walled solar collector is that the temperature rises with a more uniform slope than in the double-walled collector.This is one of the advantages of using a triple-walled collector over a double-walled one.
In this section, the effect of the volume fraction on the triple-walled collector is investigated.Figure 13 shows the temperature contour plots of W1 and W4 nanofluids.It is essential to point out that the uniform temperature distribution is observed at a low-volume fraction with respect to the high-volume fraction of nanofluid.Additionally, the top surface of the collector has the maximum temperature, which rises with enhancing volume fraction, and the distribution region of its maximum temperature decreases by increasing it.As it is known, the temperature growth occurred by rising the volume fraction of nanofluid from 0.04% to 0.06%.The outlet temperature difference has grown from 32.89 to 41.91 K.The reason for this matter is that elevating the volume fraction of the nanofluid results in a higher extinction coefficient of the working fluid.Therefore, the heat that is absorbed by the HTF has risen, and consequently, the outlet temperature improves, as well.

| Effect of mono and binary nanofluids
Figure 14 shows the average temperature and outlet temperature difference of the W1, W2, W3, W4, W5, and W6 nanofluids, respectively.As shown, the temperature increment in the binary state is more significant than the separate use of nanofluids.The T ave and T ∆ at the outlet of the triple collector for the W3 nanofluid (W1 + W2) equal 316.81 and 44.48 K, respectively.While for W6 (W4 + W5) nanofluid equal 317.67 and 48.31 K, respectively.The efficiency for W1, W2, W3, W4, W5, and W6 is 51.58%, 54.56%, 63.35%, 60.97%, 64.03%, and 65.63%, respectively.Based on the figure, it is clear that the volume fraction has a large impact on the collector's thermal performance.As determined from the previous section, the outlet temperature in the binary model has the highest value.It is worth noting that the extinction coefficient of the binary nanofluid is around corresponding to the summation extinction coefficient of its individual components. 34dditionally, in this case, the collector efficiency outperforms the individual use of each nanofluid.
In this section, the impact of considering EG as a base fluid is studied in a triple-walled solar collector.Figure 16 shows the contour plot of the outlet temperature of the triple-walled collector for G1, G2, and G3 nanofluids, respectively.It is quite obvious that the temperature enhancement of the EG-based fluid is more noticeable than in the water-based one.Considering binary nanofluids (G3) instead of individual usage of Al O 2 3 nanofluids (G1) and CuO nanofluid (G2), the average temperature rose by 2.72% and 1.53%, respectively.Figure 17 represents the overall information of the outlet temperature difference and average temperature for all of the EG-based nanofluids.It is evident that the average temperature of EG-based nanofluids grows between 2% and 4% compared to the waterbased nanofluids, which have a major effect on the effectiveness of the collector.
The efficiency of the triple-walled collector for different EG-based nanofluids is presented in Figure 18.Based on this figure, improving the volume fraction of binary nanofluids results in a 4.6% improvement in efficiency.In comparison, the efficiency enhancement of CuO and Al O 2 3 nanofluids equals 10.56% and 5.48%, respectively.
F I G U R E 17 Average temperature and temperature difference of the triple-walled collector using ethylene glycol-based nanofluids at the outlet.The influence of mass flow rate on the thermal performance of a triple-walled solar collector is examined in this section.Figure 19  maximum temperature is at the upper surface of the collector.
Figure 20 depicts the influence of changing the mass flow rate the maximum surface temperature of the triple-walled collector while using G1, G2, and G3 nanofluids.By changing the mass flow rate of the working fluid from 0.9 to 2.7 kg/h considering G3 nanofluid, the temperature decreases from 352.45 to 317.76 K. Temperature drops of the G2 and G1 are predicted to be 28.45 and 23.83 K, respectively.As shown, the effect of the mass flow rate on the surface temperature is not negligible, but its impact low as the mass flow increases.
Figure 21 illustrates the efficiency and heat loss of the triple-walled collector based on different mass flow rates.As was determined from the previous section, a higher mass flow rate leads to a decrease in working fluid outlet temperature.The reason is that with the increase in the velocity of the working fluid, the time of absorption of solar energy by nanofluid decreases; as a result, it reduces the outlet temperature of the collector.This parameter also has a major effect on the collector efficiency.On the one hand, the increment of the velocity reduces the outlet temperature, on the other hand, decreases the heat loss to the environment.Thus, it is inferred that the enhancement of the mass flow rate  elevates the collector efficiency.According to this figure, the binary nanofluid has the maximum thermal efficiency at all different mass flow inlets.This is because the highest outlet appears in this case and naturally has the highest efficiency.Also, the best thermal efficiencies obtained for G1, G2, and G3 are 44.98%,51.6%, and 60.29%, respectively, which occurred at the mass flow of 2.7 kg/h.

| Effect of hybrid nanofluid/MPCM
The performance of a triple-walled collector is thoroughly explored in this section in regard to utilizing hybrid nanofluid/MPCM.It is worth emphasizing that the melting temperature of the MPCM is critical; because it must be in the range that the solar collector has reached that temperature.If the desired temperature does not occur in the solar collector, the application of MPCM has no impact on the outcomes.The considered volume fraction (α p ) for MPCM is 5%.The baseline working fluid to compare the impact of microencapsulated PCM on the collector is W2 nanofluid.
Effective properties of the MPCM are ρ = 995( ) eff kg m 3 , μ = 0.00114( ) eff kg ms , k = 0.6( ) eff W mK , and c = 4077( ) p.eff J kgK , which are calculated by considering the volume fraction of the PCM based on Equations (1-4). 44Figure 22 shows the results of the hybrid W2 nanofluid/MPCM application.The heat transfer between the working fluid layers is improved by adding MPCM to the W2 nanofluid, and the absorbed heat is used to melt the PCM.Therefore, the temperature of the fluid decreases compared to the state of using W2 nanofluid.The maximum collector surface temperature using W2 nanofluid is K, while for the hybrid nanofluid/MPCM is 337.58K.In fact, the temperature is dropped by 0.8 K using hybrid W2 nanofluid/MPCM with respect to individual usage of W2 nanofluid.
Table 3 reports the simulation results performed for hybrid W2/MPCM and W2.According to this table, the efficiency of the system considering hybrid and W2 nanofluid is 65.17%, and 64.03%, respectively.As shown, the efficiency is increased by adding microencapsulated PCM to the W2 nanofluid.The reason for this phenomenon is that, by incorporating microencapsulated PCM to the base fluid, the absorbed heat of the DAETC has improved due to the latent heat of the PCM.The specific heat capacity is reliable on the latent heat of the PCM according to Equations (5-7).Since, throughout the time of the transition, the specific heat capacity of the working fluid is elevated, which causes the efficiency enhancement, according to Equation (16).Therefore, the addition of hybrid nanofluid/MPCM to the system increased the efficiency by 1.14%.
Moreover, the insertion of hybrid nanofluid/MPCM on the double-walled collector is studied and compared with the triple-walled.Based on Figure 23, by using hybrid nanofluid/MPCM, the efficiency enhancement of the double-walled regarding W2 nanofluid is 1.22%.According to the previous section, the heat loss of the triple is higher than the double collector, and due to this fact, the double collector is better than the triple in terms of efficacy.It can be inferred that regarding hybrid nanofluid/MPCM, the same result is happened, as well.
Figure 24 shows the temperature distribution on the surface of the triple-walled in the states of incorporating W2 nanofluid and the hybrid nanofluid/MPCM (W2 + MPCM).The temperature on the surface is about constant throughout the range in which the MPCM changes phases.In another words, between 0.5, and 0.6 m of the collector surface, the process of the transition of the microencapsulated PCM occurs.When the melting of the MPCM completes, both cases receive solar energy as sensible heat which causes their temperature trend to be almost identical.

| CONCLUSION
In this study, the DAETC thermal performance was numerically investigated introducing a new hybrid working fluid consisting of nanofluid and MPCM.The collector efficacy using various HTF including Al O 2 3 , CuO, and binary (Al O 2 3 + CuO) water-and EG-based nanofluids was evaluated.Also, a variety of parameters, such as the volume fraction of nanofluids, base fluid types, mass flow rate of the working fluid, and the two distinct double-and triple-walled absorber tube constructions were contributed.The results of the study can be drawn as follows: 1. Considering the different volume fractions of nanofluids revealed that this parameter drastically impacts the outlet temperature and collector efficiency.Enhancement of the volume fraction of the Al O 2 3 /water, CuO/water, binary/water, Al O 2 3 /EG, CuO/EG, and binary/EG raised the efficacy of the triple-walled DAETC collector by 9.39%, 9.47%, 2.28%, 5.48%, 10.56%, and 4.61%, respectively.2. The highest working fluid temperature differentials were determined to be 48.31 and 66.5 K, which were attributed to binary 0.06% Al O 2 3 /0.002%CuO/water and binary 0.06% Al O 2 3 /0.002%CuO/EG, respectively.The collector efficiency of the binary nanofluid has the maximum value compared to its ingredients.In addition, the findings demonstrated that the average temperature of EG-based nanofluids increases between 2% and 4% compared to water-based nanofluids.
3. Increasing the flow rate from 0.9 to 2.7 kg/h resulted in a temperature drop of 34.69, 28.45, and 23.83 K for binary 0.04% Al O 2 3 /0.001%CuO/EG, 0.001% CuO/EG, and 0.04% Al O 2 3 /EG nanofluids, respectively.Mass flow rate significantly impacts surface temperature, although the reduction trend decreased by enhancement of it.At ṁ= 2.7kg/h, the best thermal efficiencies achieved for 0.04% Al O 2 3 /EG, 0.001% CuO/EG, and binary 0.04% Al O 2 3 /0.001%CuO/EG nanofluids are 44.98%,51.6%, and 60.29%, respectively.4. Comparing double and triple structures showed that the cylindrical absorber form of the double-walled disperses heat more effectively than the annular form of the triple-walled one, and it also has a higher average temperature.Thus, the triple-walled collector is not as thermally efficient as the double-walled collector.5.It was discovered that in both designs, binary nanofluid had the maximum efficiency.By using binary 0.04% Al O 2 3 /0.001%CuO/water and binary 0.06% Al O 2 3 /0.002%CuO/water, the efficiency of double-walled is 71.44% and 71.52%, respectively, which are 8.1% and 5.9% higher than triple-walled.6.The W2 nanofluid was considered as the baseline working fluid to compare the influence of hybrid nanofluid/MPCM on the collectors.By using hybrid combination of nanofluid and MPCM in both structures, it was found that the three-walled and double-walled collector efficiency increased by 1.14% and 1.22%, respectively.The reason is that MPCM decreased the outlet temperate; however, it improved the efficiency according to latent heat, which affected the specific heat capacity of the working fluid.

F I G U R E 1
Detailed schematic of the triple-walled direct absorption evacuated tube solar collector.SHAHINI ET AL.

10 F
Comparison between T ave and T max of the triple-walled and double-walled collectors.F I G U R E 11 Efficiency and heat loss of double-walled and triple-walled direct absorption evacuated tube solar collector using different water-based nanofluids.I G U E 12 Surface temperature distribution of (A) double-walled and (B) triple-walled collector using W1, W2, and W3 nanofluids.

F 2309 Figure 15
Figure15depicts the efficiency of the triple-walled collector utilizing water-based nanofluids.The efficiency for W1, W2, W3, W4, W5, and W6 is 51.58%, 54.56%, 63.35%, 60.97%, 64.03%, and 65.63%, respectively.Based on the figure, it is clear that the volume fraction has a large impact on the collector's thermal performance.As determined from the previous section, the outlet temperature in the binary model has the highest value.It is worth noting that the extinction coefficient of the binary nanofluid is around corresponding to the summation extinction coefficient of its individual components.34Additionally, in this case, the collector efficiency outperforms the individual use of each nanofluid.In this section, the impact of considering EG as a base fluid is studied in a triple-walled solar collector.Figure16shows the contour plot of the outlet temperature of the triple-walled collector for G1, G2, and G3 nanofluids, respectively.It is quite obvious that the temperature

F
I G U R E 18 Direct absorption evacuated tube solar collector efficiency using different ethylene glycol-based nanofluids.F I G U R E 19 Temperature contour plots at the collector outlet using (A) G1, (B) G2, and (C) G3 nanofluid.
shows the outlet temperature contour plots for Al O 2 3 , CuO, and binary nanofluid considering EG as a base fluid (G1, G2, and G3) at different mass flow rates.Increasing the mass flow rate has caused a temperature drop, as evidenced by the results.Moreover, enhancing this parameter prevents heat distribution from being evenly dispersed among all layers of the working fluid; as a result, the F I G U R E 19 (Continued) I G R E 20 Variation of the maximum surface temperature of the collector based on different mass flow rates.

F
I G U R E 21 Efficiency and heat loss of the direct absorption evacuated tube solar collector versus different mass flow rate.F I G U R E 22 Temperature contour plots of triple-walled outlet employing (A) W2 nanofluid, (B) W2 + microencapsulated phase change material.T A B L E 3 Maximum temperature and efficiency of triple-walled DAETC incorporating W2 and hybrid W2/MPCM.

F
I G U R E 23 Comparison between double-walled and triple-walled collectors using W2 nanofluid and W2 + microencapsulated phase change material.F I G U E 24 Surface temperature distribution using W2 nanofluid and hybrid W2 + microencapsulated phase change material.