Optimizing Solar Parabolic Trough Receivers with External Fins: An Experimental Study on Enhancing Heat Transfer and Thermal Efficiency ^†

Abstract

Several researchers have shown that the heat transfer performance of solar parabolic trough (SPT) receivers may be improved by increasing their surface area or by adding internal fins to the tubes. Unfortunately, the manufacture of internally finned tubes involves complex processes, resulting in significant cost increases. On the other hand, the addition of external fins to tubes is more technically and economically feasible in a low-resource setting. This study investigates the potential benefits of integrating external fins on the receiver tubes of a low-cost SPT collector system. Experiments were conducted using an SPT system with a focal length of 300 mm and a collector length of 5.1 m, and they were positioned by an automated Sun tracking system. Tests were undertaken using both smooth and externally finned receiver tubes operating at five different water flow rates. The solar receiver with a finned tube was able to provide a maximum water temperature of 59.34 °C compared with that of 56.52 °C for a smooth tube at a flow rate of 0.5 L per minute. The externally finned absorber tube was also found to have a maximum efficiency of 18.20% at an average daily solar intensity of 834.61 W/m², which is approximately 48% more efficient than the smooth tube. The calculations indicate that the experimental SPT system using finned tubes potentially avoids 0.2726 metric tons of CO₂e per year, with finned tubes outperforming smooth tubes by up to 44%. The results show that using externally finned receiver tubes can significantly enhance the thermal performance of SPT collector systems.

1. Introduction

The energy sector in Thailand depends heavily on imported oil and gas products. The current situation of dramatic increases in global crude oil prices and the increased demand for energy have put the country in a tough economic situation and reduced economic growth. Therefore, it is important to find alternative energy sources that guarantee the security of the supply. Solar energy has the greatest potential of all the sources of renewable energy [1,2,3,4,5,6]; therefore, with the limited supply of fossil fuels, the increased use of solar energy has become inevitable. Thailand is located near the equator and has a high potential for harnessing solar energy compared with other countries [7]. In fact, Thailand lies in a region of high solar insolation, where the average insolation intensity on a horizontal surface is approximately 1367 W/m² [3,8], giving an enormous daily energy of 5–7 kWh/m²/d, which is one of the highest in the world [3,9,10]. This presents an opportunity for energy independence and a better future for Thailand.

Solar thermal power plants using concentration technologies are important candidates for providing the bulk solar electricity needed within the next few decades [11,12]. Solar collectors for high temperatures require concentration systems, such as parabolic reflectors. Solar parabolic trough (SPT) systems have been proven to work, and they consist of large fields of parabolic trough collectors with a heat transfer fluid/steam generation system. A parabolic trough solar collector uses a mirror in the shape of a parabolic cylinder to reflect and concentrate the radiation from the Sun toward a solar receiver tube located at the focus line of the parabolic cylinder [10,13,14,15]. The solar receiver tube absorbs the incoming radiation and transforms it into thermal energy, which is collected and transported by a fluid medium circulating within the receiver tube. This method of concentrated solar collection has the advantage of high efficiency and can be used either for thermal energy collection, for generating electricity [16], or for both; therefore, it is an important way to exploit solar energy directly [17]. Furthermore, several studies have shown that solar concentrating plants have great prospects in terms of a low environmental impact and favorable techno-economic factors [18,19,20,21]. For example, thanks to the use of solar concentrator power plants, India has avoided around 170,000 metric tons of CO₂e per year [19], and Pakistan has avoided over 225,000 metric tons of CO₂e per year [21]. Unfortunately capital costs for parabolic collectors are quite high; for example, a 250 MW parabolic solar power plant in the United States costs USD 1.6 billion to build [22]. In Thailand [23], a budget of THB 900 million (approximately USD 30 million) is required for the construction of a 5 MW parabolic solar power plant. Therefore, it is important to explore opportunities to reduce costs, such as the development of the local capacity and the capability to innovate using local materials.

Several studies have been undertaken in an effort to improve PTCs’ performance, such as through modifications to the geometry [24,25,26,27,28,29], enhancing the working fluids [30,31,32], introducing absorber tube coatings [33,34,35], and adding tracker systems [36,37,38]. The study reported in this paper focuses on improving the thermal performance by modifying the geometry, specifically, by using the principle that the heat absorption of the solar receivers increases with an increase in the heat transfer area [28,31]. A common method of modifying the geometry is increasing the heat transfer area between the solar receiver tube and heat transfer fluid [39,40], which results in better overall heat absorption. As a result, thermal performance enhancement is accomplished by manipulating properties such as the system’s geometry; by adding artificial roughness [24,25,26], fins [27,28,29], baffles [41,42,43], wires [44,45,46], swirling devices [47,48,49], and vortex generators; or by manipulating the material of the absorber tube [50,51,52] and the fluid properties [32,53,54].

Several studies have shown that internal fins can enhance heat transfer. Huang, Yu [26] used a computational simulation to study the effect of increasing the surface area inside the absorber tube by using tubes with dimples or protrusions. Bellos, Tzivanidis [30] developed a finned absorber inside the tube to enhance the thermal efficiency. Peng, Li [27] and Zhao, Bai [29] studied the impact of various fin shapes on the heat transfer and performance of solar absorber tubes. Improving a solar receiver tube by changing the geometry and adding fins enhances the thermal efficiency. However, the processes required to manufacture internally finned tubes are difficult and complicated, leading to high production costs, which are incompatible with a low-income setting. Therefore, building on the principle that external fins will increase the surface area for absorbing solar radiation, this study experimentally examines the potential of using external fins to improve the thermal performance of an SPT. While the literature has many examples of internal fins, examples of external fins are limited. A few studies have used external fins, such as Gong, Wang [14], who used computational simulations to study the fins’ shape in an absorber tube (AT) and found that the thermal efficiency of the tube appeared to improve from 75.7% to 76.9% with short, thick AT fins, which increased heat transmission in the AT compared to the finless AT. However, thin and long fins create more frictional loss than wide and short fins due to the length of the tube. A computational study by Gong, Wang [13] led to an improved AT design using hemispherical external fins with flat radiation shielding inside the evacuation ring of the PTC system. It was found that the optical and thermal efficiency was 8% higher than that with the traditional AT design. Even though these computational studies show satisfactory performance results for externally finned absorber tubes, experimental studies are scarce in the literature. Furthermore, none of the previous studies included an economic and environmental assessment of a simple low-cost manufacturing process. This study aims to fill this gap in the design and development of a solar parabolic trough collector system suitable for manufacture in Thailand. It achieves this by experimentally investigating the effects of external fins on the performance of absorber tubes. It provides insight into the temperature of the outflow water, heat transfer, and efficiency as well as an evaluation of the economic and environmental aspects of the system.

2. Materials and Methods

2.1. Basic Concepts of the Parabola and Earth–Sun Angles

The parabolic trough solar collector was constructed by using mirrors in the shape of a parabolic cylinder to reflect and concentrate solar radiation onto an absorber tube located at the focal line of the parabolic cylinder. The absorber tube absorbed the incoming solar radiation and transformed it into thermal energy. A conceptual schematic of the design of the component of the parabolic shape [55] is shown in Figure 1.

The equation for the parabolic trough in cylindrical coordinates is [56]

$$y=\frac{x^2}{4f}$$

(1)

The reflector of a suitable parabolic design typically has focal length (f) to aperture width (W) ratio of about 0.25 as calculated from the equation [56]

$$\frac{f}{W}=0.25$$

(2)

The geometric concentration ratio (CR) of the parabolic trough collector is calculated from the equation [57]

$$CR=\frac{Aperture area}{Receiver area}=\frac{W - D_r}{\pi D_r}$$

(3)

The surface area of the solar receiver (A_r) tube is calculated from the equation

$$A_r=\pi D_r{L}_r$$

(4)

where D_r is receiver diameter and where L_r is receiver length.

On the basis of determining the position of point P on the Earth’s surface in relation to the solar radiation, the parameters required for the design of a solar tracking system can be calculated at any instant if the latitude (l), the hour angle (w), and the Sun’s declination angle (d) are known for that point [8,10,55] as shown in Figure 1. Declination angle (d) is the angular position of the Sun at solar noon compared with the equator, which is 23.45° ≤ δ ≤ 23.45° as computed using

$$\delta =23.45sin\left(360\times \frac{284+n}{365}\right)$$

(5)

The angle of each hour (w) is obtained from

$$\omega =15\left(12-st\right)$$

(6)

The local standard time (st) compared with solar noon, an area test, is obtained from

$$st=Standard time+E-4\left({Long}_{st}-{Long}_{Loc}\right)$$

(7)

2.2. Experimental Setup

The experimental system described in Limboonruang et al. [55] was used to conduct the experiments. The solar parabolic trough collector (SPTC) system was set up with the long axis of the parabola oriented along the north–south direction. The parabolic trough would therefore collect solar radiation in the east–west direction. The experimental system comprised three SPTs as shown in Figure 2, each measuring 1200 × 1520 mm² with a 300 mm focal length, which concentrated sunlight at the focal point. The components of the collector and solar parabolic trough assembly were as follows: (i) solar receiver vacuum tube, (ii) solar parabolic trough collector, (iii) solar hot water tank, and (iv) Sun tracking system. The components and schematic diagram of the system are shown in Figure 2. The solar tracking system for the SPT is shown in Figure 3, and the characteristics of the SPT are shown in

Table 1. Characteristics of each solar parabolic trough collector (SPTC) set.

No.	Parameter	Characteristics
1	Parabola length (L)	1520 mm
2	Parabola aperture (W)	1200 mm
3	Focal distance (f)	300 mm
4	Thickness (mean value)	3 mm
5	Aperture area (Aa)	2.09 m2
6	Collector length (L)	1.52 m
7	Concentration ratio (CR)	8.13

.

The components and geometric parameters of the solar absorber vacuum tube assembly used for the experiment are shown in Figure 4. Two types of absorber tubes were evaluated, specifically, (a) smooth copper tubes and (b) finned copper tubes. The absorber tubes were mounted coaxially within an evacuated glass tube. The vacuum enclosure reduced thermal losses from the absorber tube. The design parameters of the tubes are shown in

Table 2. Parameters of the solar receiver tubes.

No.	Parameter	Volume/Type
1	Receiver material	copper
2	Receiver surface treatment	Heat-resistant black coating
3	Inner copper tube diameter (Dci)	10 mm
4	Outer copper tube diameter (Dco)	12.70 mm
5	Inner glass cover diameter (Dgi)	33.50 mm
6	Outer glass cover diameter (Dgo)	47 mm
7	Glass envelope transmissivity	0.95
8	Receiver length (Lr)	1.52 m
9	Receiver surface area (Ar)	0.23 m2

.

The temperature of the circulating heat transfer fluid (in this case, water) was measured at the test points, T₁ to T₄, on the absorber tubes, and the local ambient air temperature (T_a) was also measured. The distance between the measurement points, T₁, T₂, T₃, and T₄, was 1.7 m as shown in Figure 5. The absorber tube’s glass envelope had an external diameter of 47 mm and an internal diameter of 33 mm. The copper absorber tube was mounted coaxially within the glass envelope, and the envelope was evacuated to help retain heat as shown in Figure 6.

The heat transfer fluid (HTF) used in this experiment was water supplied from a 60-L storage tank. Water’s physical properties are listed in

Table 3. Thermal properties of water at 25 °C.

No.	Parameter	Volume
1	Density (r)	997 kg/m3
2	Boiling point	100 °C
3	Specific heat capacity (Cp)	4180 J/(kg °C)
4	Dynamic viscosity (m)	0.95 × 10−3 kg/m s
5	Thermal conductivity (k)	0.60 W/(m °C)

. The controlled variable in the experiment was the flow rate of the water, specifically, flow rates of 0.5, 1, 2, 3, and 4 L per minute. Data collection was undertaken between the hours of 10:00 and 16:00 local time. The temperature at each test point (T₁ to T₄) and the air temperature (T_a) were measured using type K thermocouples connected to a National Instruments NI-9213 (Manufactured by Apex Waves, NC, USA) data acquisition system and were recorded every minute. A TES-1333R solar power meter (Manufactured by TES Electrical Electronic Corp, Taipei, Taiwan), which has an accuracy of ± 5% according to the manufacturer, was set up beside the SPT and was used to measure the local direct solar light intensity (I_b) in units of W/m² once every minute. The flow rate was measured using a Well PRZ-15 (Manufactured by Pako Engineering Company Limited, Bangkok, Thailand) flow meter, which was connected to the piping system after the circulating pump and controlled the mass flow rate of the working fluid by adjusting the ball valve. The experiment was conducted over ten days in Nakhon Nayok Province, Thailand.

2.3. The Solar Tracking System

The SPT system is located in Nakhon Nayok Province, Thailand, at a longitude of 101.00° E and a latitude of 14.12° N. The time zone is UTC + 07, and its proximity to the equator makes it strategically placed. During experiments, the SPT system was positioned with its parabolic trough’s long axis aligned along the north–south direction. This positioning allowed the trough to collect solar radiation in the east–west direction throughout the experiment. The solar tracking system, shown in Figure 3, controlled the movement of the SPT unit. The solar tracking control system was created using LabVIEW version 2010 and was based on Equations (5)–(7), enabling the programming of position and time settings. The SPT was initially oriented east as the starting position. To start the program, the user had to input the location, time zone, and local time into the software. Once these settings were in place, the program was ready to operate. The system then tracked the daily trajectory of the Sun by rotating the SPT axis from east to west at a constant speed of 0.00415 degrees per second using a stepping motor (ORIENTAL model PH599-A, Manufactured by ORIENTAL MOTOR CO., LTD., Tokyo, Japan) connected to a gearbox designed for a total rotation of 15 degrees per hour [56]. At the end of the day, the SPT returned to its starting position.

The experiment was conducted from 11 to 30 March during Thailand’s summer season. This corresponded to day numbers (n) 70 to 89 for the year. Using Equation (5), the declination angle (δ) of the Sun was calculated to be between −4.41° and 3.22°. Equation (8) [56] illustrates the angle of incidence for the SPT on a north–south axis with a continuous east-to-west trajectory. The resulting calculation showed an angle of 0.997 ≤ cosθ ≤ 0.998.

$$cos\theta =cos\delta$$

(8)

where θ is the Sun’s incident angle and where δ is the Sun’s declination angle.

The concentrating solar system involved a horizontal single-axis solar tracking control system. As a result, the incident angle of the Sun (θ) had an impact on the aperture area’s effective daylight area (A_a). This is demonstrated in Figure 7. To calculate the effective intensity of sunlight falling on the collection area, it was important to take into account the solar intensity on the aperture area and the variable angle of incidence due to seasonal changes. This can be done using Equation (9) [58].

$$I_{eff }=I_{b}cos\theta$$

(9)

where I_eff is the effective intensity of sunlight falling on the collection area, I_b is the local direct solar light intensity, and θ is the Sun’s incident angle. Based on the above equations, the effective intensity of solar radiation was 0.997I_b ≤ I_eff ≤ 0.998I_b, indicating a close approximation to direct solar radiation. Therefore, one may use I_eff ≈ I_b to simplify calculations in this experiment.

2.4. Data Reduction

Average hourly data from all instruments were computed and used for analysis. The equations and the parameters used when processing the data are summarized in

Table 4. Details of parameters and equations used in data reduction.

Parameter	Relation	Units	Equation No.
Mean glass receiver tube temperature	$T_g=\frac{{\sum }_{i=1}^n{T}_{gi}}{n}$	°C	(10)
The mean fluid temperature [28]	$T_{fm}=\frac{T_1 + T_4}{2}$	°C	(11)
Solar energy on the trough aperture [59]	$Q_s=\alpha A_a{I}_b$	W	(12)
Heat absorbed	$Q=\dot{m}{C}_p\left(T_4-T_1\right)$	W	(13)
Daily energy gained by water [60]	$Q_{water}=m{C}_p\left(T_{final }- T_{initial}\right)$	kJ	(14)
Overall efficiency	$\eta =\frac{\dot{m}{C}_p\left(T_{final}-T_{initial}\right)}{{\alpha A}_a{I}_b}$	-	(15)
Water velocity	$v=\frac{\dot{V}}{A_c}$	m/s	(16)
Reynolds number	$Re=\frac{\rho v{D}_{ci}}{\mu }$	-	(17)

.

2.5. Economic Evaluation

A financial cost and revenue analysis of the SPT system was undertaken using the initial project cost and net present cost (C_NPC). This was used to determine the economic viability of the SPT system in order to estimate the project value by analyzing the investment value. This included the project’s payback period (PB), net present value (NPV), and internal rate of return (IRR).

The net present cost (C_NPC) can be calculated using the equation [61]

$$C_{NPC}=\frac{C_{TALC}}{CRF\left(i,N\right)}$$

(18)

where C_TALC is the total annualized cost (USD/year) and where CRF(i, N) is the capital recovery factor for the STP system for this case study, which can be calculated as [61]

$$CRF\left(i, N\right)=\frac{i{\left(1+i\right)}^N}{{\left(1+i\right)}^N-1}$$

(19)

where N is the product’s lifetime (year) and where i is the actual interest rate (%).

The net present value (NPV) can be estimated using the equation [62,63]

$$NPV={\sum }_{i=1}^n\frac{R_i}{{\left(1+r\right)}^i}-Initial investment$$

(20)

where R_i is the cash flow for i period, n is the life of the SPT system project (year), and r is discount rate, and the internal rate of return (IRR) can be shown as follows in Equation (21) [62,63]:

$${\sum }_{i=1}^n\frac{R_i}{{\left(1+IRR\right)}^i}-Initial investment=0$$

(21)

To estimate the payback period (PB), one must know the initial investment and the duration of the asset’s expected cash flow. The following formula (22) [62,63] is used to calculate the PB:

$$PB=\frac{Initial investment}{Expected annual cash inflow.}$$

(22)

2.6. Uncertainty Analysis

This section presents the experiment’s inherent uncertainties. The solar power meter, type K thermocouples, flow meter, and data acquisition were used to collect the various types of data from the experiment. The standard uncertainty (F_z) of the parameters in the data calculation can be computed using Equation (23), where Y_z is the accuracy of the devices [64], and the uncertainty X_(b) can be computed using Equation (24) [64]:

$$F_Z=\frac{Y_Z}{\sqrt{3}}$$

(23)

$$X_{\left(b\right)}=\sqrt{\begin{array}{c}{\left(Uncertainty of Solar power meter\right)}^2+{\left(Uncertainty of Thermocouple\right)}^2+\\ {\left(Uncertainty of Flow meter\right)}^2+{\left(Uncertainty of Data logger\right)}^2\end{array}}$$

(24)

Table 5. Accuracy and uncertainty of measuring instruments.

Instrument	Units	Range	Accuracy (%)	Uncertainty (%)
Solar power meter	W/m2	0–2000	±5	±2.886
Thermocouple type K	°C	−270 to 1260	±0.75	±0.433
Flow meter	Liters per minute	0.0 to 4.0	±1.6	±0.924
Data logger acquisition	°C	-	<0.02	±0.011

provides each device’s accuracy and uncertainty. As a result, the overall uncertainty error for the experiment was 3.06%.

3. Results and Discussion

This experiment aims to compare the thermal performance of solar absorbers fitted with (a) smooth and (b) externally finned tubes. The primary variable studied in this experiment is the flow rate of the heat transfer fluid in the absorber tubes.

3.1. Solar Radiation with Time

Figure 8 shows the variation in solar radiation with time. The experiment was conducted over 20 days. The complete experimental data for solar radiation over 20 days on clear and cloudy days are shown in Figure A1. However, only the data from the 10 days with the least cloud cover were selected for processing as shown in Figure 8. It is pertinent to note that, on all days, the total amount of solar energy received by the collector was almost identical. As expected, solar radiation is time-dependent, with a sharp rise between 10:00 and 11:00. During the morning period, solar radiation ranged from 474.45 to 1127.84 W/m², reaching a maximum between 11:00 and 13:00 and then beginning to fall from 13:00 to 16:00. The average solar radiation observed was 834.61 W/m² over the 10 days selected for the experiment. This solar radiation profile is typical for around 8–10 months per year in Thailand [65,66], illustrating that the PTC will perform well through the majority of the year. However, in practical applications, the measured solar power values can vary over time due to other atmospheric factors, such as wind, pollution, and atmospheric dust. These factors can all result in a decrease in the fraction of solar radiation reaching the collector.

3.2. Outlet Water Temperature

Figure 9 shows the effect of varying the flow rate of the water in the smooth and finned copper absorber tubes. The data were obtained by running the experiments at different flow rates, ranging from 0.5 to 4 L per minute. As expected, the fluid outlet temperature decreased with an increase in the flow rate, and it can be observed that the finned tubes consistently provided a higher outlet temperature than the smooth tubes at the same flow rate. It can be seen that a maximum outlet temperature of 56.52 °C at 0.5 L per minute was achieved for a smooth tube, and a maximum outlet temperature of 59.34 °C at 0.5 L per minute was achieved for a finned tube. The average daily ambient air temperature was 38.20 °C. Therefore, the results show the effect of the mass flow rate and temperature difference. Higher temperature differences result from lower mass flow rates because the working fluid spends a longer time receiving energy at a lower water velocity. Since the primary function of the SPT collector is to provide heat, running the collector at a lower flow rate is more beneficial in terms of higher outlet temperatures. Furthermore, because a lower flow rate implies a reduced pumping power requirement, the overall system efficiency improves as shown in a prior study [67,68]. However, a solar receiver at a higher temperature implies a higher rate of heat loss from the solar absorber. As indicated in previous studies [28,69], heat loss can be reduced by installing insulation on the solar receiver’s surface, which will decrease the temperature of the solar receiver and minimize the overall heat loss.

Figure 10 shows the smooth and finned copper absorber tubes’ maximum output water temperature as a function of the water flow rate.

Table 6. Outlet water temperature of smooth and finned absorber tubes.

Flow Rate (Liters per Minute)	Maximum Water Temperature Smooth Tube (°C)	Maximum Water Temperature Finned Tube (°C)	Difference (°C)	Difference (%)
0.5	56.52	59.34	2.82	4.75
1.0	54.77	56.33	1.56	2.77
2.0	53.87	54.90	1.03	1.88
3.0	52.12	53.80	1.68	3.12
4.0	51.27	51.91	0.64	1.23

compares the outlet water temperatures of the smooth and finned tubes. It can be observed that the externally finned copper tubes delivered higher temperatures than the smooth copper tubes at all the flow rates studied. With a flow rate of 0.5 L per minute, the maximum output temperature of the finned tube was 59.34 °C; this is 2.82 °C more than that of the smooth copper tube, representing a 4.75% increase. When the flow rate was increased, the output temperature decreased for both types of tubes. It should be noted that some of the abnormal data shown in Figure 9 and Figure 10 were due to the occasional passing of clouds and changes in wind, which caused fluctuations in the effective solar intensity and affected the outlet water temperature. However, the graphs’ trends returned to normal after the clouds passed.

Figure 11 shows the series of increasing temperatures (“Temperature Difference”) between the measuring points in the absorption tube: $T_2-T_1$, $T_3-T_2$, $T_4-T_3$, and $T_4-T_1$. It can be seen that the total number of temperature differences, $“T_2-T_1”+ “T_3-T_2” +{“T}_4-T_3”,$ was equal to the temperature difference between the temperature sensors, i.e., $T_4-T_1$. There was a significant temperature difference between T₂ and T₁ compared to points T₂ and T₃ as well as T₃ and T₄. This was due to the fluid passing through the insulation before entering the absorber tube, which caused a significant difference in the early stages. However, when the fluid passed through the absorber tube, the flow conditions became more similar, resulting in a lower temperature change in the subsequent period. The experimental results are plotted at different flow rates for the smooth and finned copper tubes. As expected, the temperature difference decreased with an increase in the flow rate, achieving the maximum temperature difference at a flow rate of 0.5 L per minute. It was also found that the temperature difference of the finned tubes was higher than that of the smooth copper tubes, which was true for all the flow rates. This was due to the greater heat-absorbing area of the finned tube. This is consistent with another published study [29,30,70]. Furthermore, the length of the SPT collector affects the temperature difference and efficiency. A longer system will enhance overall efficiency, albeit at the expense of requiring more pumping power due to increased frictional losses.

3.3. Useful Energy

Figure 12 shows the heat transfer as a function of the water flow rates for the smooth and finned copper tubes. It can be seen that the heat transfer rate in the smooth absorber tubes was almost constant for all the flow rates; however, there was a significant difference in the finned absorber tubes, especially at lower flow rates. The results show that the finned tubes achieved a heat transfer rate of 1375.55 W at the low flow rate of 0.5 L per minute, 43.9% higher than that of the smooth tubes at the same flow rate. This was because the surface area for absorbing the solar radiation was much larger (due to the fins) than the surface area for the heat transfer between the working fluid and the tube. The results therefore suggest that externally finned tube absorbers need to be operated at low flow rates to maximize their useful energy output. Furthermore, this result illustrates the need for the modelling of the heat transfer in this sort of system, given the fact that conventional correlations are unlikely to be applicable.

3.4. Efficiency

Figure 13 shows the thermal efficiency of the SPT collector as a function of the water flow rate for the smooth and finned absorber tubes. The overall efficiency is computed based on the thermal energy generated from a solar receiver compared with solar irradiation. It can be seen that a flow rate of 0.5 L per minute gave a maximum efficiency of 18.2% and 12.3% for the finned and smooth tubes, respectively. This trend was likely due to increased heat losses at higher flow rates. Furthermore, it can be observed that the efficiency was consistently less than 20%, which is well below the expected efficiency of more than 40% [30,71]. However, there were many factors that could contribute to the low efficiency. For example, this low-cost collector was developed using local skills and materials. Other contributory factors to the low efficiency include the refraction of sunlight as well as imperfections in the control mechanisms and movement mechanisms of the system, particularly the accuracy of tracking the solar path of the Sun.

ASHRAE standard 93 (2003) [72] was used to estimate the thermal efficiency of the SPT in terms of the input temperature and ambient temperature during steady-state conditions. Equation (25) [73] shows that overall thermal efficiency

$$\eta =F_R{\eta }_o-\frac{F_R{U}_L}{CR}\left(\frac{T_{in}-T_a}{G}\right)$$

(25)

where F_R is the factor of heat removal, η_o is the optical efficiency, and U_L is the overall loss coefficient.

The results from the experiment were used to plot SPT efficiency curves using standard least squares technical plotting. The slope is the term “F_RU_L/CR”, and the intercept is the term “F_Rη_o”. From Figure 14, it can be seen that the slope was 0.027 and that the intercept was 0.186. Therefore, the equation for the overall thermal efficiency of the solar parabolic trough collector can be written as

$$\eta =0.186 - 0.027\left(\frac{T_{in}-T_a}{G}\right)$$

(26)

Figure 14 presents a thermal performance curve based on the data collected throughout the experiment. The line of the least squares fit equation is shown in the graph and indicates that the collector had an intercept efficiency of about 18%, which is much lower than expected, as established in earlier studies [74,75,76] and that it reduced with the flow rate. It can be observed that, as the mass flow rate increased, the term “(T_in−T_a)/G” increased, resulting in a decrease in efficiency. Therefore, it can be seen that the change in efficiency depends on the parameter of the temperature difference in the term “(T_in−T_a)/G”.

Figure 15 shows that a tube with external fins consistently outperforms a smooth tube in a solar receiver. The trend of the efficiency with the term “(T_in−T_a)/G” observed in this study is similar to that found in earlier research [75,76,77]. It can be observed that the efficiency was much higher at lower values of the term “(T_in−T_a)/G”, which further supports the suggestion that a lower performance at higher flow rates is a result of increased heat losses. This is because the losses will be proportional to the temperature difference between the fluid and the ambient air. Additionally,

Table 7. Comparison of efficiency and heat transfer parameters for both tube types.

Case	Heat Transfer (W)	Maximum Efficiency (%)	Equation
Finned tube	1375.55	18.20	y = −0.065ln(x) − 0.1991
Smooth tube	955.65	12.30	y = −0.112ln(x) − 0.4105

compares the efficiency and heat transfer parameters for both cases, finned and smooth tubes. The finned solar absorber tube was about 48% more efficient than the smooth tube, mainly due to improved energy absorption.

3.5. Environmental Impact Evaluation

In Thailand, fossil fuels account for 91.5% of the nation’s total power generation. Natural gas makes up more than 70% of these fossil fuels [78,79,80]. These fossil fuels are the main source of CO₂ emissions (CO₂e) [79]. The solar parabolic trough system does not directly release carbon dioxide (CO₂) during its operation because it does not use fossil fuels to generate heat. Using Equation (27) [19,81], it is possible to determine how much CO₂ is released during the process of making energy equivalent to that generated by the SPT system:

$${CO}_{2}emissions=Activity Data (from SPT) \times Emission Factor$$

(27)

where CO₂ emissions (CO₂e) are expressed in kg and where the emission factor is equal to 0.5986 kgCO₂e/kWh [80] for Thailand in this case study.

Figure 16 shows the reduction in the CO₂ emission rate when using the SPT system as a function of the water flow rate for the smooth and finned copper tubes. It can be seen that the reduction in the rate of CO₂ emissions was significantly different in the finned tube, especially at lower flow rates. The results show that the finned tubes offer the possibility to reduce CO₂ emissions by 0.2726 metric tons of CO₂e per year at a low flow rate of 0.5 L per minute; this is about 44% more than that of the smooth tubes (

Table 8. The avoided CO₂ emission rate was achieved by using an SPT system for both cases at a flow rate of 0.5 L per minute.

Case	Energy (kWh/day)	Carbon Footprint (Metric Tons of CO2e/day)	Carbon Footprint (Metric Tons of CO2e/Year)	Rate Increase (%)
Finned tube	1.376	0.0007	0.2726	43.92
Smooth tube	0.956	0.0005	0.1894	-

) at the same flow rate. This is because finned tubes generate more heat energy. Similarly, the results suggest that externally finned tube absorbers need to operate at low flow rates to maximize the useful energy. These results show that the substitution of fossil fuel use with STP systems can help avoid CO₂ emissions (CO₂e) and hence deliver environmental benefits.

3.6. Cost Analysis of the Solar Parabolic Trough System Projects

The SPT system used in this work was designed and constructed in Thailand. The duration of the project was 20 years. The total initial investment cost was equivalent to USD 10,526.32 at an interest rate of 6.75%. In

Table 9. Economic results for the solar parabolic trough system (for this case study).

Energy (kWh/day)	Annual Energy (kWh/year)	Initial Investment (USD)	Year Investor IRR Achieved (Year)	Interest Rate (%) [63]	Weighted Average Cost of Capital, WACC (%) [82]	Net Present Value, NPV (USD)	Internal Rate of Return, IRR (%)	Payback Period, PB (Year)
1.376	502.24	10,526.32	20	6.75	8.31	988.87	9.57	8.77

, the project’s financial analysis results show that the net present value (NPV) was USD 988.87, which is greater than zero. The internal rate of return (IRR) was 9.57%, which is higher than the loan rate. The specified discount rate was 6.75%, and the payback period was approximately 8.77 years, which is within the project’s implementation period. Consequently, when comparing the study results with the investment decision criteria, the project was worth the investment.

4. Conclusions

This paper compares the thermal performance of smooth and externally finned absorber tubes used in solar parabolic trough (SPT) receivers. An SPT with a focal length of 300 mm and a length of 5.1 m was designed and built in order to investigate its ability to generate heat using water as a heat transfer fluid at flow rates ranging from 0.5 to 4 L per minute. The water was circulated through solar absorber tubes of two types, specifically, a smooth tube and a tube with external fins. The tubes were placed at the focal point of the parabolic trough. The conclusions of this study include the following:

• The results show that the externally finned absorber tube demonstrated an improved thermal efficiency of up to 48% over and above that of the smooth absorber tube. This was attributed to the fact that the finned outer surface had more area for energy absorption.
• The externally finned absorber tube provided a higher fluid exit temperature than the smooth absorber tube at the same flow rate. With a flow rate of 0.5 L per minute, the maximum output temperature from the finned tube was 59.34 °C, which is 2.82 °C more than that of the smooth tube, representing a 4.75% increase.
• The results also show that, at the low fluid flow rate of 0.5 L per minute, the finned tubes achieved a heat transfer rate of 1375.55 W, which is about 44% more than that of the smooth tubes, with an efficiency of 18.2%, which is around 48% more than that of the smooth tubes.
• The research found that the experimental SPT system using finned tubes potentially avoided CO₂ emissions to the amount of 0.2726 metric tons of CO₂e per year, with the finned tubes outperforming the smooth tubes by about 44% at a flow rate of 0.5 L per minute.
• The main conclusion of this paper is that externally finned absorber tubes are an inexpensive and easy-to-manufacture method to significantly improve the thermal performance of SPT systems.

For future works, it is recommended to study parameters for optimizing the geometry of the fins, such as the shapes, widths, thicknesses, and spaces between each fin, including the reflector sheets at both ends of the solar collector. Numerical analyses could be carried out to optimize the geometrical characteristics, which would reduce the time and experimental validation costs.