NUMERICAL HEAT TRANSFER ENHANCEMENT OF SOLAR RECEIVER TUBE OF PARABOLIC TROUGH COLLECTOR USING FIBERFRAX 140 COATED WITH AL 2 O 3

Parabolic trough collectors (PTCs) play a vital role in solar-thermal energy conversion, with the absorber tube being central to heat collection efficiency. This study investigates the potential for improving heat transfer within the PTC absorber tube using Fiberfrax 140 coated with Al 2 O 3 as a novel reflector material. The research is driven by the ongoing pursuit of enhanced PTC performance. A standard modeling approach was employed, utilizing Computational Fluid Dynamics (CFD) analysis with SolidWorks Flow Simulation software, coupled with solar simulations to assess collector performance under varying conditions. Environmental parameters of Bauchi such as temperature, humidity, and wind speed were sourced from the Nigerian Meteorological Agency (NiMet). Optimization techniques were implemented to establish the optimal design configuration. The optimal design parameters were determined as a focal length of 700mm and a rim angle of 90°. Simulations were conducted daily from 8:00 AM to 5:00 PM, encompassing the period of January to June. A mass flow rate of 0.2 kg/s, informed by existing literature, was employed in the simulations. The results indicate improved collector performance throughout the simulated period, with peak thermal efficiency ranging from 70% to 82%.


Nomenclature
represent a mature technology within the realm of solar thermal systems.These collectors excel at capturing solar energy and converting it into usable thermal energy.Their design incorporates a curved mirror reflector that concentrates sunlight onto a receiver tube.Within this tube circulates a heat transfer fluid (HTF) responsible for absorbing the concentrated solar energy and conveying it toward the designated application (Fuqiang et al., 2017).Maximizing the overall performance of PTCs hinges on achieving efficient heat transfer within the receiver tube.Gong et al. (2021) conducted a comparative study on heat transfer enhancement using different fins in a semi-circular absorber tube for large-aperture trough solar concentrators, the finding shows that the introduction of fins to an absorber tube can enhance its thermal efficiency, leading to improvements from 75.7% to 76.9% with short and thick fins and further to 77.3% with long and thin fins within a flow velocity range of 0.4-1.5 m/s.While the long and thin fins exhibit superior heat transfer enhancement, the overall heat transfer performance factor, which considers frictional losses, is higher for short and thick fins.Additionally, increasing the number of long and thin fins does not significantly improve heat transfer performance.Wang et al. (2013) conducted a numerical study of heat transfer enhancement in the receiver tube of direct steam generation with parabolic troughs by inserting metal foam, this study examines the impact of metal foam layout (top/bottom), geometrical parameter (H), and porosity (φ) on flow resistance, heat transfer, and thermo-hydraulic performance.The analysis reveals that the optimal thermo-hydraulic performance, considering increased flow resistance, occurs when H = 0.25 (bottom).In this configuration, Nusselt number (Nu) increases approximately 5-10 times, with a corresponding increase in friction factor(f) of 10-20 times, and the PEC ranges from 1.4 to 3.2.On the other hand, optimal thermal performance is achieved when H = 0.75 (top), resulting in Nu increasing around 10-12 times, factor(f) increasing 400-700 times, and the PEC ranging from 1.1 to 1.5.Furthermore, adopting the bottom layout significantly decreases the maximum circumferential temperature difference on the outer surface of the receiver tube by approximately 45%, leading to a substantial reduction in thermal stress.The findings indicate that, for a constant layout and porosity, the geometric parameter H has a significant impact on thermal performance.Conversely, for a constant layout and H, the porosity effects on thermal performance are relatively minor.features longitudinal vortex generators (LVGs) situated exclusively on the side of the absorber tube exposed to concentrated solar radiation (CSR).Through numerical analysis employing the finite volume method (FVM) and the Monte Carlo ray-trace (MCRT) method, the innovative absorber tube and its associated parabolic trough receiver with a smooth absorber tube (SAT-PTR) were studied, comparing and validating them based on the field synergy principle (FSP).Subsequently, an exploration of the impacts of Reynolds number, heat transfer fluid (HTF) inlet temperature, incident solar radiation, and LVG geometric parameters was conducted.The study revealed that the heat transfer enhancement mechanism of the novel absorber tube aligns well with the field synergy principle.Moreover, the proposed UMLVE-PTR demonstrated superior comprehensive heat transfer performance compared to the SAT-PTR across a broad spectrum of influential factors, encompassing diverse working conditions and geometric parameters.Liu et al. (2021) proposed a novel parabolic trough receiver by inserting an inner tube with a wing-like fringe for solar cascade heat collection, In this study, a new design for a parabolic trough receiver, referred to as the Novel Parabolic Trough Receiver (NPTR), was introduced.The NPTR incorporates an inner tube and wing-like fringe to enhance heat collection efficiency and provide varying levels of thermal energy.High and low-temperature heat transfer fluids, namely thermal oil and water, flow through the absorber and inner tube, respectively.A three-dimensional computational fluid dynamics model was developed to analyze the NPTR's performance, focusing on the impact of geometric parameters and the thermal conductivity of the inner tube.The study recommends the NPTR design with a β (angle) value of 180° based on the detailed investigation of various geometrical parameters.Furthermore, the performance of this suggested design was assessed under different direct normal irradiances (300-1000 W/m2) and oil inlet temperatures (400-650 K).In comparison to traditional parabolic trough receivers, the NPTR demonstrated a significant reduction in heat loss by 33.1-50.1%,leading to an overall efficiency improvement ranging from 0.61% to 7.67%.Additionally, the proportions of heat gains for oil and water in the total solar input energy varied between −18.8% and 63.5% and 8.39% and 77.6%, respectively.The temperature gains for oil and water ranged from −1.4 K to 19.5 K and 5.4 K to 18.8 K, respectively.Panchbhaya, (2020) researched numerical investigation of heat transfer enhancement in solar receivers.The research focused primarily on finding a passive means of enhancing heat transfer inside solar receiver tubes while minimizing pressure drop.The performance of the heat transfer enhancement was evaluated by performing numerical simulations to determine thermohydraulic behavior.An appropriate turbulence model was selected and compared to existing literature.The use of multiple twisted tapes was initially investigated with helically twisted tapes.A novel enhancer design, the half-pitch helically twisted tape, is proposed to be used in solar receiver tubes.Optimization was performed on the half-pitch helically twisted tape and a full simulation was then conducted at elevated temperatures and pressures with an applied nonuniform onesided heat flux.The results showed that the half-pitch helically twisted tape performs satisfactorily with an acceptable pressure loss, achieving a thermal enhancement factor of approximately 0.95.Benabderrahmane et al. ( 2020) investigated the heat transfer enhancement of a tube receiver for a parabolic trough solar collector with a central corrugated insert.In their study, a tube receiver with a central corrugated insert was introduced as the absorber tube to increase the overall heat transfer performance of the tube receiver in a parabolic trough solar collector (PTC) system.The Monte Carlo ray tracing method (MCRT) coupled with the finite volume method (FVM) was used to investigate the flow characteristics and heat transfer performance of the tube receiver for the parabolic trough solar collector system.The numerical results were successfully validated against existing empirical correlations in the literature.These results indicated that introducing the corrugated insert inside the absorber tube of the parabolic trough receiver can effectively enhance heat transfer performance.The average Nusselt number can be increased up to 3.7 times compared to a smooth absorber.While the overall heat transfer performance factor was found to be in the range of 1.3-2.6.The results also indicate that heat transfer increases with increasing corrugated insert twist ratio and decreasing pitch between two corrugations.Previous studies have explored various methods to improve heat transfer in parabolic trough solar receivers.These include adding fins or inserts to the absorber tube, using different-shaped tubes, and even employing nanofluids.Studies show that these techniques can enhance heat transfer efficiency by up to 77.3%, but some methods come with trade-offs like increased pressure drop.The ideal solution depends on factors like desired temperature, flow rate, and cost.This research aims to numerically investigate heat transfer enhancement of the solar receiver tube of the parabolic trough collector by using Fiberfrax 140 coated with Al2O3 as the reflector of the parabolic trough collector system.

MATERIALS AND METHOD 2.1 Material Selection
The cover was made of Pyrex glass, the receiver tube was made of copper painted with black matte, and the reflector had a mirror surface made of Fiberfax 140 coated with Al2O3.

Pyrex Glass
Pyrex glass is used as a glass envelope in this research owing to its thermal and optical properties.Pyrex glass has a high transmittance of solar radiation, which allows efficient energy collection.It also has a low thermal expansion coefficient, which makes it resistant to thermal shock and allows it to maintain its shape and integrity at high temperatures.In addition, Pyrex glass has a high melting point and is chemically stable, making it suitable for use in harsh environments.

Copper painted with black matte.
Copper painted with black matte as a receiver in a parabolic trough collector offers several advantages.These properties include high solar absorbance, low thermal emittance, and good thermal conductivity.Black matte paint enhances the absorbance of the copper surface, allowing it to efficiently capture solar radiation.In addition, the high thermal conductivity of copper facilitates the transfer of heat from the absorbed solar energy to the working fluid inside the receiver.The low thermal emittance of the black matte surface reduces heat loss by radiation, further enhancing the overall thermal efficiency of the parabolic trough collector.

Fiberfrax 140 coated with Al2O3 reflector.
Fiberfrax 140 coated with Al2O3 reflector is a high-temperature ceramic fiber material that exhibits excellent thermal insulation properties, high reflectivity, and durability.It is capable of withstanding high temperatures and can be used as a lining material for the interior surface of the parabolic trough reflector.(Wang et al., 2021).Table 1 represents the design parameters of the parabolic trough collector.A 2800 mm aperture width and length of 4000mm of the trough were selected for this study.The reflectivity of the Fibrefrax 140 coated with Al2O3 (reflector) is 96, as reported by Wang et al. (2021).The transmittance of the glass cover obtained from the Solidworks flow simulation was 0.96.(2017).The other design parameters were determined using Equations 1-7.

Mathematical modeling 2.2.1 Rim Angle
The design of the reflector includes optimum rim angle.The angle between the optical axis and the line between the focal point and the collector rim (focal distance also known as focal length) is called rim angle (ϕr) shown in Figure 1.

Aperture Width
The parabolic-trough collector is designed in the shape of a parabolic trough, and its aperture is the width of the parabolicshaped reflector.This reflector concentrates sunlight onto the focal line or point where the receiver tube is located.The receiver tube typically contains a heat-absorbing fluid, such as a heat transfer fluid or molten salt, which absorbs concentrated solar energy and converts it into heat.The aperture width was taken as 2.8m

Focal Length
The focal length is a critical parameter in the design of a parabolic trough collector because it determines the concentration of sunlight at the focal line.A shorter focal length results in a more tightly focused beam of sunlight, increasing the concentration; however, it may require more precise tracking and alignment.the longer focal length provides a broader focus, which can be more forgiving in terms of tracking accuracy but may result in lower concentrations.The choice of focal length is often a trade-off between the concentration levels, collector size, tracking accuracy requirements, and specific application or system design considerations.It plays a crucial role in optimizing the overall performance and efficiency of the parabolic trough collector in converting sunlight into thermal energy.
Focal length is given by.

The Aperture Area
The aperture area of a parabolic trough collector defines the opening through which sunlight is captured and concentrated on a receiver.It is a crucial component in solar energy harvesting systems, in which a parabolic reflector focuses sunlight onto a receiver tube along a focal line.This tube contained a heat-absorbing fluid, and the size of the aperture area influenced the amount of sunlight captured.A larger aperture area enhances solar energy absorption, but practical considerations, such as cost and efficiency, impact its design.The interplay between the aperture area and system components allows parabolic trough collectors to convert sunlight into concentrated thermal energy for various applications.
The aperture area is given by.
Inner surface area of the receiver is given by: surface area of the receiver is given by: To capture all of the reflected direct solar radiation, the receiver tube's minimum outer diameter must meet the following criteria: Where   is the parabola's radius and   is the sun beam angle (or acceptance angle).According to several theoretical investigations, the least feasible acceptance angle that results in the highest concentration is 0.53° (Bharti & Paul,2017).

Concentration Ratio
The concentration ratio in a parabolic trough collector is defined as the ratio of the area of sunlight captured by the reflector to the area of the receiver tube.Higher concentration ratios result in more intense sunlight reaching the receiver, increasing the temperature of the heat transfer fluid, and consequently improving the overall efficiency of the system.concentration ratio is calculated by using following equation:

Modeling and Simulation
The present study employed the SolidWorks software as the principal modeling tool to develop a thorough and precise model.Furthermore, the advanced features of SolidWorks flow simulation were harnessed, with additional utilization of the SolidWorks solar radiation studio.This methodological approach guarantees a resilient and accurate portrayal of the model, facilitating precise analysis and evaluation within the confines of an academic framework.

Simulation set up.
In the SolidWorks Flow Simulation, the Finite Volume Method (FVM) is employed to solve fluid flow and heat transfer problems.This method discretizes the computational domain into a set of control volumes, where the conservation equations for the mass, momentum, and energy are integrated over each control volume.The FVM is well suited for handling complex geometry and is commonly used in commercial CFD software such as SolidWorks Flow Simulation.
The following Navier-Stokes equations of mass, momentum and energy is applied in CFD analysis in SolidWorks.

Discrete Ordinate (DO)
SolidWorks solve radiation transport equation using Ray tracing method (Discrete transfer) and Discrete ordinate method.In this study Discrete ordinate method was chosen as a method of solving the radiation transport equation (RTE).
The discrete ordinate (DO) method is a numerical approach used to solve the radiation transport equation that describes how radiation moves through a medium.This method discretizes the equation in the space and direction, divides the domain into cells, and discretizes the angular space into discrete directions.Each direction represents a ray of radiation, and these rays are traced through the medium to determine their interaction and intensity.This method solves the intensity of radiation along each ray, considering absorption, emission, and scattering.The intensity values were then integrated in all directions to obtain the total intensity at each location in the domain.The process is iterative, with the intensity values updated until convergence is achieved.The discrete ordinate method provides an efficient way to simulate radiation behavior in complex systems, such as parabolic trough collectors, aiding their design and optimization for various applications.The radiation transport equation is given by: .( ⃗ ′ ,  ⃗).Ω ′ …( 12)

Solar Radiation
The solar radiation analysis in the SolidWorks Flow Simulation started with the activation of the flow simulation add-in.Subsequently, project naming was facilitated through the application of the SolidWorks wizard, ensuring adherence to S.I units for methodological consistency across the simulation phases.The internal analysis, fluid flow, conduction, radiation, and solar radiation were chosen.The procedural sequence involved the judicious selection of Bauchi as the solar radiation setting, wherein additional parameters such as environmental temperature were configured.Furthermore, the time and date parameters were meticulously adjusted for the Discrete ordinate category.The introduction of gravity in the Y-direction, set at -9.87 m/s², facilitated convection heat transfer considerations.
The selection of an appropriate fluid medium and the designation of copper as the default solid material have been executed.Subsequently, the configuration of the thermal boundary conditions resulted in the establishment of a default outer wall.The heat transfer coefficients for outer surfaces was set as 10 W/(m² K).All radiative walls were explicitly categorized as nonradiative because the appropriate properties are set during radiative surface setting.

Computational Domain
Figure 2 shows the computation fluid domain for the simulation of fluid (Air and Water).A three-dimensional (3D) approach was adopted in the computational domain setting for this simulation to comprehensively model and analyze the system.To define spatial boundaries, specific parameters were carefully chosen to ensure an accurate representation of the physical environment.

Model Assumption
The following assumptions were made when modelling the Parabolic trough collector. i.
The parabolic Trough Collector was considered within the framework of steady-state and then transient conditions. ii.
There is no great difference between cover and ambient temperature level. iii.
The flow is fully developed, and it can be characterized by a constant heat transfer coefficient along the tube.

Energy and Efficiency 2.4.1 Useful Energy
Every estimate of a solar system requires consideration of thermal efficiency, available solar radiation, and useable energy.The energy balance in a working fluid's control volume can be used to calculate the amount of usable energy it contains.

Solar Energy
Calculating the solar energy accessible in the collection area requires multiplying the solar beam radiation by the reflector aperture area.

Thermal efficiency
Thermal efficiency of the collector is given by:

Thermal Losses
The difference between the usable heat (Qu) and the solar energy absorbed (  ) is used to compute the thermal losses of the receiver (  ) Where The incident angel modifier (K) is depended on the incident angle on the collector aperture () and can be calculated as below for the LS-2 module (Dudley et al., 1994).
The angle () in the above equation is expressed in degrees.The collector is tested for a zero-incident angle in the current study; therefore, the incident angle modifier is equal to 1.This strategy is used by Bellos et al. ( 2018) The optical efficiency is the product of the reflectance (ρ), of the intercept factor (γ), of the transmittance (τ) and of the absorbance (α).
Thermal efficiency can also be given as If the heat losses (Qloss) are known, equation ( 17) may be used to compute the heat loss coefficient of the collector, which expresses the specific heat losses of the absorber.

… (28)
Mean heat convection coefficient is given by (Bellos et al, 2016): The collector efficiency factor is given as The collector flow factor F" is given as Heat removal factor can be calculated using.
The collector useful energy gain per unit of collector length ′  is given as The actual useful energy gain of the collector is given as 3.0 RESULT AND DISCUSSION Table 2 presents the monthly average simulation results for the temperatures of the glass cover, receiver tube, working fluid, solar irradiation, useful energy, solar energy, and thermal efficiencies of the solar parabolic trough collector obtained hourly during the simulation.The maximum monthly average glass cover temperature recorded was 58.7°C, and the minimum was 30°C.The monthly average temperature of the absorber tube increased with time, with the maximum recorded as 80.6°C in April.The maximum monthly average temperature of the working fluid obtained during the simulation was 79.45°C, which was also recorded in April.The maximum and minimum solar irradiation values were 1188 W/m² and 408 W/m², respectively.The maximum and minimum useful energy values obtained were 10774 J and 3439 J, respectively, in April and January.Similarly, the maximum and minimum solar energy values obtained were 13216 and 4569 J, respectively.The maximum thermal efficiency observed is 82% indicating that the use of Fibrefrax 140 coated with Al2O3 as a reflector enhanced the performance of the collector when compared to the results of 68.

3.1
Solar irradiation: The solar irradiation (Is) shows in Figure 5, illustrates a consistent seasonal increase from January to June, with peak values around noon ranging from 944 to 1188 W/m2.This upward trend aligns with the progression from winter to summer, indicating heightened availability of solar energy during the day.The collector's ability to capture and utilize this increasing amount of solar irradiation reflects its efficiency in harnessing sunlight for thermal applications.

3.2
Temperature fluid Fluid temperatures (Tf) experienced a steady rise from January to June, reaching peak values between 70.07 and 79.45 degrees Celsius at noon.These temperatures indicate the collector's proficiency in absorbing and retaining heat, with the peak temperatures corresponding to the period of maximum solar exposure.The direct correlation between solar irradiation and elevated fluid temperature underscores the effectiveness of the collector in converting sunlight into thermal energy as illustrated in Figure 6.

Receiver temperatures:
Figure 7 shows the recorded receiver temperatures (Tr) followed the expected trends for a well-designed parabolic trough collector.These temperatures exhibited a consistent ascending pattern from January to June, reaching a peak around noon.The observed stability during operational hours underscores the reliability of the collector in effectively absorbing solar energy.This crucial attribute ensures optimal operating conditions, enabling the collector to consistently harness and convert solar irradiation into thermal energy.

Glass cover temperatures
Figure 8 shows the recorded glass cover temperatures (Tc) followed an ascending pattern from January to June, with peak values occurring around noon.The stability observed during the operational hours highlights the efficiency of the collector in concentrating and retaining solar energy.This consistency is paramount for maintaining optimal conditions within the collector, facilitating continuous and reliable energy capture throughout the designated operational timeframe.The synchronized positive trends in both receiver and glass cover temperatures underscore the integrated performance of the collector in effectively absorbing and concentrating solar energy.

Useful energy.
The data of useful energy (Qu) from Figure 9 shows the collector's remarkable ability to convert solar irradiation into thermal power.Both parameters exhibited a seasonal increase, reaching their zenith around noon.Notably, the overall values in March, April, and May were consistent, indicating enhanced solar energy conversion during the transition from late winter to early summer.This period shows the collector's heightened effectiveness in capturing and utilizing solar energy in thermal applications.

Thermal Efficiency
From Figure 10 Thermal efficiency (Eth) data revealed seasonal variations, demonstrating a general increase from January to June.Peak efficiency, ranging from 70% to 82%, occurs around noon, showing the collector's adaptability to changing solar conditions.March, April, and June exhibited higher overall efficiency, emphasizing the collector's capacity to optimize energy conversion during these months.This adaptability is a key attribute that allows the collector to efficiently harness solar energy across diverse environmental conditions.It's noteworthy that a previous study by Bellos et al. (2018) conducted a performance evaluation of a cylindrical insert for a parabolic trough solar collector, resulting in a maximum thermal efficiency of 68.2%.Garcia et al. (2019) performed Modeling and simulation to determine the thermal efficiency of a parabolic solar trough collector system and the maximum thermal efficiency obtained was 80% and the use of Fibrefrax 140 coated with Al2O3 as a reflector in the current study evidently enhanced the collector's performance.

Figure 2 :
Figure 2: Computational Fluid Domain of the Simulation of Air 2% obtained by Bellos et al. (2018) and 80% obtained by Garcia et al. (2019).The surface plot in Figure 3 displays the distribution of the air temperature within the trough collector model.The simulation was conducted specifically for January at 8 am.The fluid entering the collector had an inlet temperature of 25°C.The plot reveals that the maximum temperature reached by the air within the collector was 44.07 0 C.

Figure 3 :
Figure 3: Minimum Temperature of the fluid (Air)

Figure 6 :
Figure 6: Temperature of the fluid plotted against time.

Figure 7 :
Figure 7: Temperature of the Receiver plotted against time.

Figure 8 :
Figure 8: Temperature of the Glass plotted against time.

Table 1 :
Design Parameter of the Parabolic Trough Collector