Single-phase and two-phase models of a hybrid nanofluid traveling through a non-uniformly heated (PTC) receiver: A comparative study

The current study used single and two-phase modeling to numerically explore three-dimensional the turbulent forced convection of a hybrid nanofluid passing through a non-uniformly heated parabolic trough solar collector (PTC) for increasing heat transfer. The typical heat flux profile on the receiver’s absorber outer wall was addressed by a finite volume method (FVM) and the MCRT method. The results demonstrated that the single and two-phase models produced almost similar hydrodynamic results but dissimilar thermal ones. It was found that the results of mixture model matched the experimental ones. The results also illustrated that the hybrid nanofluid gives the highest thermal performance for a mixture composed of 1.5% copper + 0.5% alumina dispersed in the water.


INTRODUCTION
Recently, nanotechnology has facilitated the development of a new category of fluids known as nanofluids.It was composed of nanoparticles suspended in a fluid base.Nanofluids have intriguing characteristics that could make them suitable for a variety of engineering applications, such as heat transmission enhancement.Among other properties, nanofluids exhibit a significant enhancement in liquid thermal conductivity, liquid viscosity, and heat transfer coefficient.As is commonly known [1], metals in the solid state have higher thermal conductivities than liquids.Copper's thermal conductivity at ambient temperature is 700 times greater than that of water and 3000 times greater than engine oil.Metallic liquids have substantially greater thermal conductivity than nonmetallic liquids.Consequently, fluids containing suspended metal particles are predicted to have a substantially greater thermal conductivity than unadulterated liquids [2].Two forms of nanofluid convective heat transfer modeling exist in general.The first is known as single-phase modeling, in which both the nanoparticles and the base fluid are considered homogeneous and to possess unique properties, taking into account the liquid and solid properties; the second is known as two-phase modeling, in this case the nanoparticles and the base fluid are treated independently.Alternatively, the solar collector, also known as a green heat exchanger device that converts solar energy into thermal energy in solar thermal applications or directly into electrical energy in PV (photovoltaic) applications [3][4][5], is one of the primary components of a solar energy and water heating system.
The parabolic trough solar collector (PTC) is one of the most crucial solar collector types.This variety of solar collector is a linear concentrating solar collector capable of operating between 15 and 400 degrees Celsius.Using the reflective surface of a linear parabolic reflector, it concentrates solar energy into a vacuum-sealed, tubular receiver located along the focal line of the parabola.
In the receiver, an interior absorber tube is enclosed by an exterior glass cover and supporting structures [6][7].This type can be used to generate electricity or operate machinery.Sokhansefatetal [8] investigated the effect of Al 2 O 3 /synthetic oil nanofluid on heat transfer in a PTC tube.It was determined that raising the nanoparticle concentration and operating temperature improved heat transfer.Risi et al. [9] researched the thermal heat improvement for CuO+Ni/nitrogen gas-phase nanofluid in a transparent PTC tube.They demonstrated that upon 0.3% vol., the negative influence of the pressure drop overcame the favorable impact of the thermal characteristics.Moreover, their optimizing method indicated that the maximal solar to thermal efficiency was equivalent to 62.5%.Moghari et al. [10] numerically investigated the laminar forced and natural convection inside a horizontally mounted annulus filled with Al 2 O 3 /water nanofluid by using the two-phase modeling.Both the inside and outside walls maintained a constant thermal flux.In addition, the effects of nanoparticle concentration, Grashof number, and heat flux ratio on the hydrodynamic and thermal properties were illustrated.A hybrid nanofluid, on the other hand, is a highly sophisticated kind of nanofluid that can be described as a mixture of base fluid (such as oil, water, polymer solutions, etc.) and two (or more) different types of composite nanoparticles suspended in a base fluid simultaneously [11].Madhesh et al. [12] investigated experimentally the convective heat transmission and rheological properties of hybrid Cu-TiO 2 nanofluids.Conclusion: the convective heat transfer coefficient was improved by increasing the concentration of hybrid nanofluids and the Reynolds number.Also postulated was a correlation between the Nusselt number and the Reynolds number, the Prandtl number, and the hybrid nanofluid volume concentration.Otanicar et al. [12] investigated experimentally the effect of various nanofluids on the efficiency of micro-solar thermal collectors.Utilizing nanofluids as an absorption medium increased its effectiveness by up to 5 percent, as reported.Benabderrahmane et al. [13] investigated numerically the enhancement of heat transmission within a PTC absorber with longitudinal fins and nanofluids.In their endeavor, Al 2 O 3 , Cu, SiC, and C nanoparticles were utilized.The authors concluded that Cu nanoparticles significantly enhanced thermal transfer compared to other nanoparticles.Mwesigye and Meyer [14] investigated numerically the optimal thermal and thermodynamic performance of PTC receivers using various nanofluid concentration ratios.For silver/ Therminol VP-1, copper/ Therminol VP-1, and Al 2 O 3 / Therminol VP-1 nanofluids, the thermal efficiency of the PTC was enhanced by 13.9%, 12.5%, and 7.2%, respectively.This increase was accomplished by increasing the volume fraction of nanoparticles from 0% to 6%.Coccia et al. [16] investigated experimentally the effect of different water-based nanofluids on PTC performance.With the use of (Fe 2 O 3 , SiO 2 , TiO 2 , ZnO, Al 2 O 3 , and Au) nanoparticles, various concentrations and temperatures were investigated.They concluded that using nanofluids did not significantly enhance the collector's efficacy.Rehan et al. [17] compared the efficacy of low concentration ratio solar PTC using pure water, Al 2 O 3 / water, and Fe 2 O 3 / water nanofluids in a recent experimental investigation.Their comparison employed various concentrations (0.2%, 0.25%, and 0.3%) and volume flow rates (1, 1.5, and 2 L/min).Al 2 O 3 / water and Fe 2 O 3 / water nanofluids increased thermal efficacy by approximately 13% and 11%, respectively, when compared to unadulterated water.Bellos and Tzivanidis [18] analyzed the thermal performance of a PTC operating with mono and hybrid nanofluids.They reported a mean improvement in thermal efficiency of approximately 4.25 percent.Benabderrahmane et al. [19] investigated numerically the three-dimensional turbulent forced convection of Al 2 O 3 nanofluid within a non-uniformly heated PTC receiver with two longitudinal fins.They utilized single two-phase modeling to enhance thermal transfer.They discovered that the combination of nanofluid and two longitudinal fins improved heat transfer within the collector.It is evident from the aforementioned research that the usage of hybrid nanofluids enhanced the thermal efficacy of PTC.However, it is still necessary to examine the impact of various hybrid nanofluid types on the thermal efficacy of PTC.Using both single-phase and twophase models, this study intends to examine the influence of turbulent forced convection on a hybrid nanofluid within a non-uniformly heated solar PTC receiver.

GEOMETRICAL MODEL
Fig. 1 shows the model considered in the current study that consists of a receiver of the PTC.The borosilicate glass and the steel were the materials used for the glass cover.The annular gap between them is treated as a vacuum at low values of the pressure and the ambient temperature.A hybrid nanofluid circulates inside the absorber.Table 1 lists the thermophysical characteristics of the nanofluid, while the dimensions of the receiver are listed in Table 2.

MATHEMATICAL MODEL
The governing equations of the mathematical model read: • Continuity equation: ( • Momentum equation: ( • Energy equation: ( • Discrete Ordinate radiation model equation: • Turbulence model: ( Where

NUMERICAL METHOD
The finite volume method (FVM) is employed to accomplish the numerical simulation.The conventional  The inner radius of the absorber 3.2 cm The outer radius of the Absorber 3.5 cm The inner radius of the glass cover 5.96 cm The outer radius of the glass cover 6.25 cm

Glass envelope material Borosilicate
The transmittance of the glass cover 96%

Coating absorbance 95%
Glass cover emissivity 0.873 turbulence model k-ε was utilized.The pressure-based equation is solved using the pressure-based solver.The pressure and volume fraction are calculated using the PRESTO and QUICK methods.A second-order upwind approach is employed for the other convection-diffusion and radiation equations.A SIMPLE method is employed to address the pressure-velocity coupling.All the equations are solved sequentially and iteratively in order obtain a convergent solution.For all the simulations performed in this analysis, the convergence criteria are considered when the algebraic residuals are less than 10 -4 for DO intensity, 10 -6 for energy and epsilon equations and 10 -3 for other equations.

GRID SENSITIVE STUDY
Table .3shows the evolution of the average Nusselt number as a function of cell number for a range of Reynolds numbers between 10 4 and 10 6 .A structured and refined mesh near the walls was used (Fig. 2).A grid independence analysis is undertaken to limit the impact of the number of grid sizes on the obtained numerical results to justify the numerical findings' accuracy and stability.

BOUNDARY CONDITIONS
In this numerical investigation, the external wall of the absorber tube receives a non-uniform heat flux that was calculated using Monte-Carlo ray approach and a DNI value was assigned to be 1000 W/m2. Figure 3 illustrates the modeling outcomes of the local concentration ratio distribution on the outer absorber surface cross-section.The symmetry boundary condition is applied to annular space inlets and outlets.The envelope of the external glass implements a thermal boundary condition involving convective and radiative heat transfer.Sky temperature and emissivity are evaluated by the correlations given below [20,21]: While the convective heat transmission coefficient is predicted by the subsequent experimental correlation [22]:

MODEL VALIDATION
The Nusselt number and friction coefficient values for a simple tube were compared to those predicted using empirical correlations from the literature to attain confidence  about our numerical results.Gnielinski [23] proposed a correlation for estimating the Nusselt number inside turbulent tubes as a function of Reynolds number and Prandtl number, whereas the friction factor was calculated using Petukhov's correlation [24].The correlations mentioned above are listed below: Ditus-Boelter [25] developed a straightforward for obtaining the Nusselt number using only the Reynolds and Prandtl numbers.This correlation is given by: (12) Where n = 0.4 when the wall temperature exceeds the bulk one, and n = 0.3 in the opposite case.
Blasius [26] recommended a correlation to calculate the friction factor inside smooth pipes under a turbulent flow as follow: (13) ( 14) Figure 4 indicates that the average Nusselt number and the friction factor are consistent, with the greatest variation being less than 8.5% and the minimum deviation being around 0.2%.

Comparison Between Single and Two-Phase Models
The numerical analysis demonstrates that the local Nusselt number yields different values for homogeneous and two-phase models.Nonetheless, the calculations by the two-phase models are more accurate (Figure 5).In contrast, the local Darcy friction factor results are quite comparable (Fig. 6) when the maximum variation is approximately 2.7%.On the basis of Figures 5 and 6, it could be concluded that single and two-phase models generate nearly typical hydrodynamic behavior but dissimilar thermodynamic behavior.Nusselt number values resulted from the simulations were compared against those values determined by the experimental correlations available in the literature for 1% alumina nanoparticles dispersed in water as the base fluid and under turbulent flow conditions in order to determine which model more closely matches the experimental results.In a tube, Xuan and Li [27] studied the nanofluid's flow and convective heat transfer.They proposed a correlation for calculating the average Nusselt number as a function of the Pr, and Pe, in addition the nanoparticle volumetric fraction.These associations are demonstrated by: (15) Where: In addition, Velgapudi et al. [28] suggested a correlation for the turbulent flow as a function of Re and Pr, which were given by: ( 16) Duangthongsuk and Wongwises [29] experimentally explored the coefficient of heat transmission and the friction factor for nanofluids confined inside a horizontally mounted tube.They established the correlation given below to predict the Nusselt number as a function Re and Pr together with the nanoparticle's concentration.(17) As shown in Fig. 7, the mixture model gives values closer to the experimental results, especially with the Nusselt number calculated by the correlation of Xuan and Li [27] where the maximum deviation did not exceed 5%; therefore, from these results, it may be concluded that the two-phase model is the most suitable for nanofluid flows.However, the homogenous model needs further modifications.

Impact of The Hybrid Nanofluid On Heat Transfer And Flow Field
Combining two distinct categories of dispersed nanoparticles in a base fluid is the most important characteristic of hybrid nanofluids.When nanoparticle materials are chosen properly, the positive characteristics of each can be enhanced, and the negative characteristics of a   single material can be compensated for.Alumina, a ceramic material, possesses several advantageous properties, such as chemical inertness, strong corrosion resistance, and high stability.In contrast to metallic nanoparticles, its thermal conductivity is reduced.Nanoparticles of aluminum, zinc, copper, and other metals have a high thermal conductivity.In contrast, metallic nanoparticles have restricted applications in nanofluids due to their stability, reactivity, and high cost.
It is anticipated that the adding metal nanoparticles to a nanofluid composed of Al2O3 nanoparticles will improve the thermophysical characteristics of this composition, based on the properties of metallic and nonmetallic nanoparticles described above.Figure 8 depicts the fluctuation of the Nusselt number as a function of Re for various nanofluid solutions with a 2% volume fraction and 13 nanometer-diameter nanoparticles.
The findings indicate that the 2% (Cu+Al2O3)/water hybrid nanofluid possesses superior heat transmission properties in comparison to 2% copper or 2% alumina dispersed in water.The addition of metallic nanoparticles (Cu) to a nanofluid composed of water and oxide ceramic (Al2O3) is therefore predicted to substantially enhance the mixture's thermophysical properties and heat transfer characteristics.
In contrast, the addition of nanoparticles to water increases the Darcy friction factor, as shown in Fig. 9.This increase is likely due to an increase in HTF thermal conductivity.On the basis of the preceding analysis, it can be concluded that dispersing nanoparticles in water, which is used as the HTF within a PTC absorber, can improve heat transfer while simultaneously increasing the pressure drop within the absorber tube.Therefore, it is essential to calculate the thermal performance criteria (PEC), which could defined as the ratio between the dimensionless Nusselt number and the dimensionless friction factor: (18) Figure 10 shows that the PEC value varies from 1.12 to 2.4, reflecting that the nanofluid offers a better comprehensive heat transfer enhancement than the base fluid.It is noted that the hybrid nanofluid improves the heat transmission greatly.This means that combining two different kinds of nanoparticles positively impacts the heat transfer characteristics.

Temperature Distribution Variation
Figures 11shows the distribution of temperature at the center cross-section of the absorber, the DNI was assigned to be 1000 W/m 2 and the inlet temperature of the HTF was   573 K.It can be seen that the combination of the two different nanoparticles (Al 2 O 3 and Cu) leads to increasing HTF temperature, this augmentation is due to dispersing the metallic particles, which have a higher thermal conductivity.
The temperature contours of the radial direction on the center cross-area of the absorber for the four nanofluids at the identical setting are showed in figure 12; the twophase flow in the presence of Cu particles give remarkably almost identical values less than that obtained in the case of addition of Alumina particles; decreasing the temperature gradient affects an enhancement in the heat transfer coefficient.

CONCLUSION
Three dimensional numerical simulation of the turbulent forced convection of a hybrid nanofluid inside a PTC absorber was explored.The flow field was simulated employing the single and two-phase mixture and VOF models.The obtained findings demonstrate that single and two-phase models predict almost identical hydrodynamic results but dissimilar thermal ones, which means that the single-phase model still needs to be modified.The numerical results show that the hybrid nanofluid greatly augments the heat transfer characteristics, and it is considered better than the classical nanofluid.Moreover, it was found that dispersing nanoparticles in water as a base fluid which is used as HTF inside a PTC absorber, can enhance the heat transfer, while it accompanies by enhancing the pressure drop in the absorber tube.

Figure 2 .
Figure 2. Geometry's mesh used in the study.

Figure 3 .
Figure 3.The local concentration ratio on a cross-section of the outer absorber surface.

Figure 6 .
Figure 6.Local Darcy friction factor for single and twophase models at Re= 36340 and ϕ=0.01.

Figure 7 .
Figure 7. Single and two-phase models Vs. experimental data.

Figure 8 .
Figure 8.The impact of hybrid nanofluid on the heat transmission.

Figure 12 .Figure 11 .
Figure 12.Temperature contours (K) at the middle cross-section of the absorber wall (DNI= 1000 W/m 2 at HTF inlet temperature 573 K)

Table 2 .
The physical parameters of the receiver