Heat Transfer and Thermal Efficiency Enhancement of Parabolic Trough Collectors Using Al₂O₃–Therminol VP-1 Nanofluids

Abstract

A parabolic trough collector (PTC) is a linear concentrating system consisting of a parabolic-shaped reflector with a receiver tube positioned along the focal axis. In this study, the performance of a parabolic trough solar collector is evaluated, with aperture area, collector length, breadth, Rim angle, and inner and outer absorber diameters of 5.54 m², 3.65 m, 1.52 m, 70°, 0.048 m, and 0.05 m, respectively. The experiment was conducted at Ranchi, India (23.35° N and 85.30° E). During this day, marked by a cloudless sky, the ambient temperature ranged from 27 °C to 39 °C. The global solar radiation ranged from (630 W/m² to 975 W/m²), and the wind speed varied between (0.8 m/s and 1 m/s). Aluminium oxide (Al₂O₃) and Therminol VP-1-based nanofluid were employed as the working fluid. The different volume fractions of nanoparticles were taken, and the evacuated tube PTC performance was analysed. When Al₂O₃–Therminol VP-1 of varying concentration (0–4%) and mass flow rate of 0.041 kg/sec is used, it has been observed that the receiver’s heat transfer performance improved with an increment in nanoparticle volume fraction. Temperature-dependent properties were applied to the thermal efficiency, exhibiting a notable increase of approximately 7.2% when the volume fraction ascends from 0 to 4%. At elevated Reynolds numbers, the efficiency decreases compared to lower volume fractions. These results contribute to understanding the effect of nanoparticle concentration on PTC performance.

1. Introduction

The continuous reliance on fossil fuels and non-renewable energy sources has significantly harmed the environment. Global emissions from coal-fired electricity and heat generation have increased by 2.1% [1]. Governments worldwide are rapidly recognising the critical need for environmentally sustainable alternatives, particularly in response to growing concerns about climate change. In response to increased demand for fossil fuels, the transition to solar energy stands out as an efficient approach to a zero-carbon future. Many environmental assessment studies show that renewable energy supplies only 26.5% of the world’s energy demand. Projections by the International Energy Agency, the European Solar Thermal Energy Association & Greenpeace suggest that by 2030, CSP could contribute 3 to 3.6% of the worldwide energy supply, rising to 8 to 11.8% by the year 2050. There is a need for a significant capacity increase, which remains unproven. Also, some forecasts show a potential reduction in CSP costs to USD 0.05/kWh by the year 2025 [2].

The MENA region is characterised by its optimal conditions for Concentrated Solar Power (CSP) due to its abundant amount of sunshine, minimal precipitation, and expansive flat terrain near transportation networks, which holds global importance. Its proximity to Europe, where environmentally friendly electricity is highly valued, adds to its appeal. Addressing an electricity crisis in oil-producing nations such as Saudi Arabia, Algeria, Niger, Venezuela, etc., relies on generators, causing fuel consumption and pollution. The potential integration and exploration of solar energy in the future could significantly contribute to global renewable energy solutions [3]. Solar energy can be harnessed through photovoltaic (PV) technology, converting it into electrical power, or via solar concentrators, transforming it into thermal energy. Both solar photovoltaic and concentrators are viable for solar energy. Lazarrin [4] conducted a thermodynamic assessment with economic evaluation, revealing detailed costs of PV exceed the cost of equivalent thermal collectors. Solar thermal collectors capture and concentrate solar radiation to produce heat energy. Based on the technique used to gather solar energy, CSP technology is classified into linear concentration and point focusing. Significant CSP projects often utilise a linear concentrating system, particularly PTCs, widely employed in power generation and industrial process heating. Researchers are interested in its broad temperature range (150–800 °C), making it highly valuable for power-related applications, contributing significantly to research and advancements in solar technology [5]. PTCs have essential elements: a highly reflective parabolic surface, a support structure, and a heat receiver tube. The curved parabolic surface of the PTCs is employed to redirect sunlight onto the receiver tube, which contains the working fluid for heat absorption. Traditional Newtonian working fluids, such as molten salt, water, and air, exhibit poor thermophysical properties, decreasing collector efficiency [6]. Optimising the efficiency of PTCs necessitates rigorous geometry modelling, selection of careful receiver tube material, and HTF. Nanofluids are becoming popular in various sectors, including healthcare equipment, solar energy, fuel cells, and heat exchangers, showing their importance, versatility, adaptability and expanding utility [7]. Nanofluids help to improve heat transfer from the receiver tube, making PTCs more efficient. The most common nanoparticles known for their characterization are copper oxide (CuO), copper (Cu), titanium dioxide (TiO2), silicon dioxide (SiO₂), aluminium (Al), aluminium oxide (Al₂O₃), iron (Fe), iron oxide (Fe₂O₃), and zinc oxide (ZnO). Nanoparticle concentration as well as diameter within the fluid are important points for system efficiency and optimal performance. Incorporating nanoparticles into traditional heat transfer fluids helps to improve their thermal properties. Chandrasekhar et al. [8] conducted an experiment measuring the thermal conductivity of Al₂O₃ -H₂O nanofluid at varying nanoparticle concentrations from 0.33 vol% to 5 vol%, demonstrating higher values compared to normal water. Gupta et al. [9] observed a 39.6% enhancement in instantaneous efficiency for a flat plate solar collector (FPSC). This improvement occurred by the direct use of Al₂O₃–water nano fluid with 20 nm Al₂O₃ nanoparticles used at a volume fraction of 0.005%. The study found that a volume fraction of 0.005% gives increased solar absorption and reduces the risk of heat loss. Khullar et al. [10] predicted a 5 to 10% efficiency enhancement for a parabolic concentrator with a nanofluid with spherical aluminium nanoparticles in Therminol VP-1 compared to a standard parabolic solar collector. Sokhansefat et al. [11] investigated Al₂O₃ nanoparticles in thermal oil, confirming a 14% improvement in the heat transfer coefficient within the PTC. Zadeh et al. [12] show the enhanced heat transfer rates in PTCs using Al₂O₃/oil nanofluid. Bellos et al. [13] have used SolidWorks Flow Simulation to perform an energy and exergy analysis on Al₂O₃ in heat transfer oil. The finding shows an important performance improvement in the PTCs, especially at high operating temperatures. Bianco et al. [14] examined turbulent forced convection in a circular pipe with an Al₂O₃-H₂O nanofluid, finding Reynolds numbers ranging from 104 to 105 and particle volume fractions of 1.0% to 6.0%. This shows a positive correlation between heat transfer enhancements, elevated Reynolds numbers, and increased volume fractions of nanoparticles. Bayat and Nikseresht [15] have done a numerical investigation to find heat transfer and convective turbulent flow characteristics within a circular pipe. The study involved using Al₂O₃ nanoparticles dispersed in both ethylene glycol as well as water. Mwesigye et al. [16] have investigated the thermodynamic performance of PTC by incorporating Syltherm 800 with Al₂O₃ nanoparticles to reduce entropy generation through numerical analysis conducted with the help of ANSYS^® 16.2. The outcomes of their study show a notable 7.6% improvement in absorber energy efficiency by using nanofluid [17,18].

An extensive literature review has shown many studies utilising Al₂O₃ nanoparticles with water as the base fluid. However, an important gap still exists in the existing literature regarding using Al₂O₃ nanoparticles with Therminol VP-1 as the base fluid for high-temperature applications in a parabolic trough collector.

Hence, the present research objective is to find the performance of PTC using Al₂O₃ nanoparticles with Therminol VP-1 oil as the base fluid. Therminol VP-1 was selected for its consistent physical and thermal properties across a wide temperature range (up to 250 °C), while Al₂O₃ was selected for its enhanced thermal and optical properties. In the present experimental phase, an assessment was conducted on the efficiency of a PTC that employed Therminol VP-1 oil in combination with Al₂O₃ nanofluid. The study also involved performing calculations to analyse heat transfer within the solar collector. Additionally, a mathematical model was used to assess the performance of the solar collector system. The outcomes from the mathematical model were subsequently verified against the findings obtained by the experimentation.

2. Experimental Setup

The proposed experimental setup consists of the following components with their respective specifications.

2.1. Parabolic Trough Solar Collector

Parabolic collectors (PTC) are fabricated by using and shaping a sheet of reflective material. The central receiver is positioned exactly at the focal point. PTC has dimensions of 3.65 m in length and 1.52 m in width, as shown in Figure 1 and Figure 2 and

Table 1. Geometric and optical parameters of the parabolic trough collector (PTC) used in this study.

Parameter	Value
Receiver (absorber tube) length, L	3.65 m
Collector aperture width, W	1.52 m
Aperture area, Aa	5.54 m2
Absorber tube outer diameter	0.05 m
Absorber wall thickness	0.0016 m
Concentration ratio, C	9.36
Rim angle, ψ	70°
Measured solar irradiance range in Ranchi (summer)	300–1100 W/m2
Glass envelope material	Borosilicate
Glass envelope outer diameter	0.11 m
Glass envelope thickness	0.005 m
Mirror reflectance, ρ	0.95
Glass solar transmittance, τ	0.92
Receiver solar absorptance, α	0.91
Glass long-wave emissivity, ε	0.9
Nanofluid mass flow rate	0.041 kg/s

. The depth and rim angle of the parabola are considered as 0.54 m and 700. A reflective sheet with specular reflectivity of 0.95 was used (MIR Labs, Moradabad, Uttar Pradesh, India) [19,20], selected for its high ability to reflect solar radiation effectively toward the absorber tube. The collector length measures 3.65 m, and the total aperture area of the parabolic trough solar collector is 5.54 m². These collector dimensions have been determined by using the Parabola 2.0 software (version 2.0). The collector’s performance and efficiency are significantly influenced by its orientation. The optimal approach applied to positioning the collector is to align it to maximise sun exposure and open sunshine conditions, with the long axis either in a north–south direction or an east–west direction as per local latitude angle. The current study selected the east–west orientation for convenience and enhancement. PTC features a broad acceptance angle that helps to mitigate the need for frequent seasonal adjustments. A tilt angle of 45° and manual tracking are used to enhance the absorption of diffused radiation during the experiment.

2.2. Evacuated Tube as an Absorber Tube

Evacuated tubes act as high-performance receiver elements in the solar collector assembly. They are made of sealed glass tubes from which air has been removed, creating a vacuum environment around the heat transfer region (often configured as a heat-pipe structure). This vacuum layer suppresses air movement, which minimises heat losses due to convection and helps maintain strong thermal performance, particularly under elevated operating temperatures. Notably, the vacuum minimises convection loss and diminishes conduction loss. The evacuated tube measures 3.65 m in length. Its glass cover has internal and external diameters denoted as Dgci = 0.11 m and D_gco = 0.12 m, respectively. The absorber tube within the evacuated tube features inner and outer diameters, precisely, D_abri = 0.046 m and D_abro = 0.050 m, respectively. In this experimental work [21,22], the evacuated tube features an absorptivity (α) of 0.91 and a surface emissivity (ε_abr) of 0.08. For the glass cover, the transmissivity (τ) is 0.92, and the emissivity (ε_gc) stands at 0.9. The absorber tube’s intercept factor (γ) is 0.9 [23]. Copper was selected as the material for the absorber tube, featuring a thermal conductivity that varies with temperature. The absorber tube is covered by borosilicate glass with a thickness of 0.005 m. The absorber tube is coated with a high-temperature black coating.

2.3. HTF Preparation with Nanoparticle

2.3.1. Heat Transfer Fluid

The heat transfer fluid employed within the absorber tube was Therminol VP-1, a readily available and widely used HTF in Parabolic Trough Solar Collector (PTSC) systems. Therminol VP-1 is a synthetic heat transfer fluid comprising 25% (C₁₂H₁₀) diphenyl and 73.5% diphenyl oxide. This versatile fluid finds application in various industries, including hydraulic processing, plastics, and chemical reactions. Therminol VP-1 possesses a standard boiling point of 257 °C [24] and exhibits its optimal performance when operating in the liquid phase within the temperature range of 12 °C to 40 °C. Detailed thermo-physical properties of this HTF can be found in the manufacturer’s data sheets. These properties are primarily influenced by operating temperature rather than pressure. As a result, temperature-dependent characteristics for each property were established using polynomial functions derived through regression analysis [25,26,27,28].

For $\mathbf{285.15} \mathbf{K}\le \mathbf{T}\le \mathbf{698.15} \mathbf{K}$,

The specific heat capacity (J kg⁻¹.K⁻¹):

$$c_p(T)=2.125\times {10}^3+T[-11.017+T(0.49862+T(-7.7663\times {10}^{-5}+4.394\times {10}^{-8}T))]$$

(1)

The density (kg.m⁻³):

$$\rho (T)=1.4386\times {10}^3+T[-1.8711+T(2.737\times {10}^{-3}-2.3793\times {10}^{-6}T)]$$

(2)

The thermal conductivity (W/m ⁻¹.K ⁻¹):

$$k(T)=0.14644+T[2.0353\times {10}^{-5}+T(-1.9367\times {10}^{-7}+1.0614\times {10}^{-11}T)]$$

(3)

The dynamic viscosity (m.Pa.s):

For the temperature range of $285.15 \mathrm{K}\le \mathrm{T}\le 373.15 \mathrm{K}$

$$\mu (T)=3.661\times {10}^2+T[-3.0154+T(8.3409\times {10}^{-3-}7.723\times {10}^{-6}T)]$$

(4)

For $373.15 \mathrm{K}\le \mathrm{T}\le 698.15 \mathrm{K}$,

$$\mu (T)=23.165+T[-0.1476+T(3.67\times {10}^{-4}+T(-3.9844\times {10}^{-7}+1.6743\times {10}^{-10}T))]$$

(5)

2.3.2. Nanoparticles

Al₂O₃ nanoparticles find extensive utility in various applications and research endeavors due to their exceptional stability and performance, particularly when compared to other, more expensive nanoparticles. The corundum morphology is the most prevalent among the various forms of crystalline alumina. This structure combines octahedral and oxygen ions to shape a closely knit hexagonal crystallographic aspect. These nanoparticles are renowned for their remarkable corrosion resistance and high hardness [29].

In this research, the thermophysical characteristics of Al₂O₃ were taken as follows:

The density of Al₂O₃ nanoparticles was adopted as a constant value based on the findings by Eastman et al. [30].

$${\mathit{\rho }}_{\mathit{n}\mathit{p}}=\mathbf{3960} \mathbf{k}\mathbf{g}/{\mathbf{m}}^{\mathbf{3}}$$

(6)

The thermal conductivity of Al₂O₃ nanoparticles was determined as a function of temperature [31].

$${\mathit{k}}_{\mathit{n}\mathit{p}}=\mathbf{5.5}+\mathbf{34.5}\mathit{exp}(-\mathbf{0.0033}(\mathit{T}-\mathbf{273})\left)\right(\mathbf{W}/\mathbf{M}.\mathbf{K})$$

(7)

The heat capacity of nanoparticles concerning temperature was similarly derived using the following expression [31].

$${\mathit{C}}_{\mathit{p},\mathit{n}\mathit{p}}=\mathbf{1.0446}+\mathbf{1.742}\times {\mathbf{10}}^{(-\mathbf{4})}\times \mathit{T}-\mathbf{2.796}\times {\mathbf{10}}^{\mathbf{4}}\times {\mathit{T}}^{(-2)}(\mathbf{K}\mathbf{J}/\mathbf{K}\mathbf{g}.\mathbf{K})$$

(8)

Table 2. Al₂O₃ nanoparticle material properties used in this work at different temperatures [32].

Properties	Temperature (K)
Thermal properties	400 K	600 K	800 K
Specific heat capacity (Cp) Jkg−1K−1	940	1110	1180
Thermal conductivity (λ) Wm−1K−1	32.4	18.9	13

exhibits the characteristics of the alumina nanoparticles at distinct temperatures [32].

2.3.3. Nanofluid Preparation and Stability

The Al₂O₃–Therminol VP-1 nanofluid was prepared using a two-step method. Initially, the required amount of Al₂O₃ nanoparticles was dispersed in Therminol VP-1 using mechanical stirring, followed by ultrasonication to improve dispersion uniformity. No surfactant was used to avoid potential alteration of thermo-physical properties at elevated operating temperatures. During experimentation, the nanofluid was continuously circulated using a pump, which helped maintain particle suspension under practical operating conditions. Visual inspection and repeated thermal cycling indicated no noticeable sedimentation or agglomeration over the experimental duration.

A single-phase modelling approach was adopted for the Therminol VP-1 nanofluid, as this methodology has been shown to be effective for nanoparticles with diameters below 100 nm and low to moderate volume fractions [33]. Thermo-physical properties were evaluated using established correlations from the literature, with density calculated using classical solid–liquid mixture relations [34,35,36]. The absence of observable sedimentation under forced convection conditions supports the applicability of the single-phase assumption in the present study.

$${\rho }_{nf}=(1-\varphi ){\rho }_{bf}+\varphi {\rho }_{np}$$

(9)

As detailed in the references, the specific heat capacity was determined through a widely accepted formula, which assumes thermal equilibrium between the particles and the surrounding liquid.

$${\mathrm{C}}_{p,nf}={\displaystyle \frac{(1-\varphi )c_{p,bf}{\rho }_{bf}+\varphi c_{p,np}{\rho }_{np}}{{\rho }_{nf}}}$$

(10)

Numerous nanofluid viscosity estimation models can be found in the existing literature. The dynamic viscosity utilised in this investigation was derived from a model established through meticulous least-square curve-fitting of experimental data, as documented in references. This model expresses dynamic viscosity as presented in [37].

$${\mu }_{nf}={\mu }_{bf}(123{\varphi }^2+7.3\varphi +1)$$

(11)

Equation (11) was selected to yield higher viscosity values, as it was observed that the widely employed Einstein model tends to underestimate viscosity. In the case of thermal conductivity, the Bruggeman model, accounting for interactions among spherical particles at varying inclusion concentrations, was employed. This model provides thermal conductivity as described in [38,39].

$$k_{nf}=0.25[(3\varphi -1){\lambda }_{np}+(2-3\varphi ){\lambda }_{bf}+\sqrt{\Delta }$$

(12)

where

$$\Delta ={\left[(3\varphi -1){\lambda }_{np}+(2-3\varphi ){\lambda }_{bf}\right]}^2+8{\lambda }_{np}\lambda$$

(13)

The Bruggeman model exhibits validity across a broader spectrum of volume fractions and converges towards Maxwell’s effective medium theory at lower volume fractions.

3. Experimentation

The experiment was conducted during the pre-monsoon summer period of Ranchi, Jharkhand, India. The location of the experiment site is situated at a northern latitude of 23.35° and an eastern longitude of 85.33°. On this particular day, characterised by a clear sky, the temperature ranged from 27 °C to 39 °C, while the wind speed fluctuated between 0.8 and 1.0 km/h, and DNI ranged from 638.3 W/m² to 965 W/m². The total duration of the experiment spanned 6 h, during which various parameters were recorded, including the temperatures at the absorber’s inlet and outlet. The investigation commenced at 9:00 AM and extended until 3:00 PM, a timeframe chosen to leverage the peak solar radiation hours, specifically from 11:00 AM to 2:00 PM. The observations were recorded with Therminol VP-1 oil and Al₂O₃ nanofluid. A solar power meter was used to measure the DNI, also known as beam radiation, which is the component of sunlight that comes straight from the sun to the receiving surface without being scattered or reflected by the atmosphere.

Uncertainty Analysis

Standard uncertainty is evaluated using calibration records together with the instrument manufacturer’s stated accuracy, and it is essential for producing reliable measurements because it accounts for both calibration-related deviations and inherent instrument constraints. It is commonly reported as a standard deviation (standard uncertainty) or as an expanded uncertainty that includes a stated coverage factor. Its significance lies in the assessment of both accuracy and precision in measurements, thereby ensuring the reliability of results for subsequent analyses. The determination of the measuring device’s standard uncertainty follows a specific methodology.

Standard uncertainty is calculated by dividing the instrument precision value by $\sqrt{3}$ [40,41,42,43,44,45]

$$\Delta {\eta }_i=\sqrt{\left\{{\left[{\displaystyle \frac{\partial \eta }{\partial F_R}}\Delta F_R\right]}^2+{\left[{\displaystyle \frac{\partial \eta }{\partial s}}\Delta s\right]}^2+\left[{\displaystyle \frac{\partial \eta }{\partial U_l}}\Delta U_l\right]+\left[{\displaystyle \frac{\partial \eta }{\partial T_a}}\Delta T_a\right]+\left[{\displaystyle \frac{\partial \eta }{\partial T_i}}\Delta T_i\right]\right\}}$$

(14)

The instantaneous solar efficiency was evaluated with an overall uncertainty of 4.5%, obtained by combining the measurement uncertainties of the pyranometer (±5.5%), flow meter (±4.1%), anemometer (±3%), and thermocouples (±0.5 °C).

4. Thermal Modeling of the PTC System

The collector’s thermal efficiency is defined as the ratio of the useful heat gain to the solar energy incident on the collector’s aperture area.

$${\eta }_{th}={\displaystyle \frac{Q_u}{Q_s}}$$

(15)

The solar energy delivered to the absorber is given by (the diffuse component of solar radiation is assumed negligible):

$$Q_s=A_{a}S$$

(16)

where ${\mathrm{A}}_{\mathrm{a}}$ is the effective aperture area of the concentrator, given by:

$$A_a ={\displaystyle \frac{w-D_o}{\pi D_o}}$$

(17)

Under steady-state conditions, the energy balance for the absorber can be written as:

$$Q_u=A_{a}S-Q_l$$

(18)

The absorbed energy term Q1 can be expressed in terms of the overall heat-loss coefficient as:

$$Q_l =U_l{A}_{abo} (T_{ab}-T_a)$$

(19)

By combining Equations (5) and (6), we obtain:

$$Q_u=A_a\left[S- {\displaystyle \frac{U_l}{C}}\right]$$

(20)

where C is the concentration ratio and ${\mathrm{A}}_{\mathrm{a}}$ is the effective aperture area given by

$$C={\displaystyle \frac{w-D_{o}L}{\pi D_o}} \mathrm{and} A_a=(w-D_o)L$$

(21)

Equation (20) can also be written as [46]

$$Q_u=h_f\pi D_i(T_{ab}-T_{fi})=m.C_p(T_{ab}-T_{fi})$$

(22)

where the heat transfer coefficient inside the surface of the absorber is $h_f={\displaystyle \frac{Nu.k}{D_i}}$.

By combining Equations (8) and (10) and eliminating the absorber-tube temperature, we obtain:

$$Q_u=F^{’}[S-{\displaystyle \frac{U_l}{C}}(T_{fi}-T_a)](W-D_0)L$$

(23)

where ${\mathrm{F}}^{\mathrm{’}}$ is the collector efficiency, a factor defined by [45]

$$F^{’}={\displaystyle \frac{1}{U_l\left[\frac{1}{U_l}+\frac{D_o}{D_i{h}_f}\right]}}$$

(24)

Using the Hottel–Whillier–Bliss formulation, the useful heat gain can be expressed as:

$$Q_u=F_R(w-D_o)L\left[S-{\displaystyle \frac{U_l}{C}}(T_{fi}-T_a)\right]$$

(25)

where ${\mathrm{F}}_{\mathrm{R}}$ is the heat removal factor defined by [47,48]

$$F_R={\displaystyle \frac{m{C}_p}{\pi D_{o}L{U}_l}}\left[1-\exp \left\{{\displaystyle \frac{F^{’}\pi D_o{U}_{l}L}{m{C}_p}}\right\}\right]$$

(26)

Using Equations (12)–(14), the useful heat gain can be evaluated, and the system efficiency can then be obtained from Equations (3) and (4).

4.1. Overall Loss Coefficient and Heat Transfer Correlation

Consider the absorber tube and glass cover as one long, concentric tube in a system. Based on convection and reradiation losses, the rate of heat loss per unit length is given by [45].

$${\displaystyle \frac{Q_l}{L}}=h_{p-c}(T_{ab}-T_c)\pi D_o+{\displaystyle \frac{\sigma \pi D_o(T_{ab}^4-T_c^4)}{\left\{\frac{1}{{\epsilon }_p}+\frac{D_o}{D_{ci}}\left(\frac{1}{{\epsilon }_c}-1\right)\right\}}}$$

(27)

where ${\mathrm{h}}_{\mathrm{p}-\mathrm{c}}$ = convective heat transfer coefficient between absorber tube and glass cover, which can be defined by

$$h_{p-c}={\displaystyle \frac{2k_{eff}}{D_{o}In\left(\frac{D_{ci}}{D_o}\right)}}$$

(28)

where ${\mathrm{k}}_{\mathrm{e}\mathrm{f}\mathrm{f}}$ is the effective thermal conductivity, given by Raithby and Hollands’ relation

$$k_{eff}=0.317{(R_a^{*})}^{1/4}k$$

(29)

where the modified Rayleigh number $R_a^{*}$ is shown in Equation (30):

$${(R_a^{*})}^{1/4}={\displaystyle \frac{In\left(\frac{D_{ci}}{D_{co}}\right)}{L_c^{3/4}\left(\frac{1}{D_o^{3/5}+D_{ci}^{3/5}}\right)}}{R}_a^{1/4}$$

(30)

The Rayleigh number is calculated by

$$R_a=9.81\left({\displaystyle \frac{1}{T_m}}\right)(T_{pm}-T_c){\displaystyle \frac{L_c^3}{v^2}}$$

(31)

where ${\mathrm{L}}_{\mathrm{c}}$ is the radial gap between the absorber and the glass cover, given by

$$L_c={\displaystyle \frac{D_{ci}-D_{co}}{2}}$$

(32)

The rate of heat loss can also be defined by

$${\displaystyle \frac{Q_l}{L}}=h_w(T_c-T_a)\pi D_{co}+\sigma \pi D_{co}{\epsilon }_c(T_c^4-T_{sky}^4)$$

(33)

where ${\mathrm{h}}_{\mathrm{w}}$ is the heat transfer coefficient on the outside surface of the cover

$$h_w={\displaystyle \frac{Nu{k}_{air}}{D_{co}}}$$

(34)

Hilpert’s data can calculate the Nusselt number, Nu

$$Nu=c_1{R}_e^n$$

(35)

After substituting the values of ${\mathrm{h}}_{\mathrm{p}-\mathrm{c}}$ and ${\mathrm{h}}_{\mathrm{w}}$, in Equations (14) and (20) are a pair of nonlinear equations that must be solved for the unknowns (${\mathrm{Q}}_1/\mathrm{l}$) and Tc by the trial-and-error method for an assumed value of Tc. If (Tc) is assumed to be —(Tc) calculated < ±1, it gives the new value of Tc. With the converged value of Tc, the new value ${\mathrm{U}}_{\mathrm{l}}$ is calculated, and all the steps are performed from Equation (7) till $(U_l{)}_{assumed}-(U_l{)}_{calculkated}>\pm 1$.

4.2. Assumptions

• The parabolic trough collector is operating under steady-state conditions.
• The absorber experiences a uniform heat flux.
• Due to its reasonable length (approximately 4 m), the collector ensures minimal variation in receiver temperature along the tube.
• Radiative heat exchange from the collector components to the surrounding environment is included in the analysis.
• Temperature differences between the cover and the ambient air and between the receiver wall and the working fluid are assumed to be sufficiently small to be neglected.
• The internal flow is taken as fully developed, with a uniform heat transfer coefficient along the absorber tube.

5. Results and Discussions

The assessment of the thermal storage system and solar collector’s performance is summarised in

Table 3. Performance of solar collectors.

Time	Ta	Tin	Tout	ΔT	Tabr	Ib	Id	Absorbed Solar Flux (s)	Heat Removal Factor (FR)	Heat Gained by the Solar Collector	Instantaneous Collection Efficiency (ƞic)
	(°C)	(°C)	(°C)	(°C)	(°C)	(W/m2)	(W/m2)	(W/m2)	-	(Watt)	(%)
9:00 AM	27	26	26	0	26	638	106	495.21	-	-	-
10:00 AM	29	42	65	23	72	710	109	629.68	0.93	3189.90	63.60
11:00 AM	31	75	100	25	107	918	111	715.59	0.97	3774.28	66.40
12:00 AM	35	106	133	27	140	965	117	753.04	0.98	4026.53	67.39
1:00 PM	38	144	175	31	185	945	114	736.64	0.98	3953.18	67.56
2:00 PM	41	179	209	30	219	851	109	661.55	0.98	3537.97	67.14
3:00 PM	39	213	241	28	26	700	108	543.33	0.98	2912.24	65.88

. Eight to ten experimental trials were conducted, and Table 3 presents the average results derived from these eight trials. From the above observation, the solar collector demonstrates the highest efficiency and heat collection at noon, specifically around noon. Currently, the system achieves a substantial heat gain of 4026.53 watts, with an impressive efficiency of 67.39%. Additionally, our observations underline the direct relationship between solar radiation intensity and the heat acquired by the absorber tube through the HTF.

The experimentation involved continuous monitoring of both direct and diffuse hourly radiation levels. Figure 3 illustrates that the highest hourly direct radiation occurs around noon when the sun is directly overhead, resulting in the maximum solar energy the collector absorbs. In contrast, diffuse radiation remains relatively constant throughout the day, around 155 W/m². Occasional minor spikes in the graph could be attributed to increased solar radiation intensity over the collector or momentary cloud cover, which temporarily exposes the sun.

5.1. Properties of Nanofluid

Enhanced nanofluid concentration results in a heightened nanofluid density due to the increased presence of solid nanoparticles within the base fluid. This increase in substantial mass contribution within the fluid leads to a noticeable overall density augmentation in the nanofluid. Conversely, elevating the temperature of nanofluids brings about a contrasting effect, causing a decrease in their density as shown in Figure 4. This reduction is mainly due to the temperature-driven expansion of both the base fluid and the dispersed nanoparticles. As the temperature rises, the constituent particles acquire thermal energy, causing them to expand and occupy a larger volume within the nanofluid. This dispersion results in an overall density reduction in the nanofluid, highlighting the intricate relationship between concentration and temperature in influencing nanofluid characteristics.

Nanofluid thermal conductivity varies noticeably with both temperature and nanoparticle loading. As the particle concentration increases, the effective conductivity rises because a larger fraction of the suspension is made up of the high-conductivity solid phase. At higher loadings, more particles are present within the base fluid, which strengthens heat-conduction pathways and improves the bulk heat transfer capability of the mixture. This trend is consistent with the behaviour presented in Figure 5.

The temperature of the nanofluid rises as it has a contrasting effect on thermal conductivity. Increased temperatures cause the constituent particles to expand, leading to a larger volume occupied within the fluid. This developed dispersion of particles impedes the efficient transfer of heat, resulting in a decrease in the nanofluid’s thermal conductivity. Thus, nanoparticle concentration and temperature alterations play pivotal roles in influencing the thermal conductivity of nanofluids, with heightened concentration elevating it and elevated temperatures diminishing it.

The noted observations show some distinct trends in specific heat capacities. It has been observed that specific heat capacities tend to increase as the temperature rises. This suggests that materials have a greater ability to store heat energy at higher temperatures. Conversely, we found that specific heat capacities decrease when there is an increase in particle concentrations within the nanofluid. This decrease is particularly evident when comparing the specific heat capacity of the base fluid to that of the nanofluid containing Al₂O₃ particles. In this case, the base fluid exhibited higher specific heat capacity values. This disparity can be attributed to the inherently lower heat capacity of Al₂O₃ nanoparticles compared to the base fluid, as shown in Figure 6.

The present observations reveal that temperature plays a crucial role in enhancing specific heat capacities. At the same time, increased particle concentrations, especially with Al₂O₃ nanoparticles, can lead to decreased specific heat capacities due to the lower heat capacity of these nanoparticles. The kinematic viscosity of nanofluids is significantly affected by both nanoparticle concentration and temperature. The kinematic viscosity rises when nanoparticle concentration in the nanofluid increases, as shown in Figure 7. This occurs because the solid nanoparticles disrupt the smooth flow of the base fluid, increasing viscosity. In simpler terms, higher nanoparticle concentrations make the nanofluid thicker and more resistant to flow, resulting in an elevated kinematic viscosity.

Conversely, temperature plays a contrasting role in shaping the kinematic viscosity of nanofluids. As the temperature increases, the kinematic viscosity typically decreases. This behaviour is because higher temperatures provide the fluid molecules with additional energy, allowing them to move more freely and reducing the resistance to flow. Consequently, the nanofluid becomes less viscous and flows more quickly at elevated temperatures.

5.2. Thermal Performance of PTC

Dispersing nanoparticles in the base fluid modifies the thermophysical properties of the resulting liquid. As the nanoparticle volume fraction increases, there is a concurrent rise in density, thermal conductivity, and viscosity, while the specific heat capacity undergoes a reduction. This escalation in thermal conductivity translates into improved heat transfer performance. Conversely, the heightened density and viscosity necessitate greater pumping power. Although an increasing Reynolds number enhances convective heat transfer, the associated pressure drop rises sharply due to increased viscous resistance. The required pumping power, estimated as ${\mathbf{W}}_{\mathbf{p}}=\mathsf{\Delta }\mathbf{P}\dot{\mathbf{V}}/{\mathsf{\eta }}_{\mathbf{p}}$, scales approximately with $\mathbf{R}{\mathbf{e}}^{\mathbf{2.5}–\mathbf{3}}$, whereas heat transfer enhancement scales with $\mathbf{R}{\mathbf{e}}^{\mathbf{0.6}–\mathbf{0.8}}$. Consequently, beyond an optimal Reynolds number, the rapid increase in pumping power outweighs the marginal heat transfer gain, leading to a reduction in net thermal efficiency. The reduction in efficiency at higher Reynolds numbers is qualitatively attributed to increased pumping power requirements associated with higher flow resistance. Figure 8 shows the variation of the heat transfer coefficient with Reynolds number for several nanoparticle volume fractions of the Al₂O₃–Therminol VP-1 nanofluid.

The thermal efficiency of a system, as depicted in Figure 9, is strongly influenced by both the Reynolds number and the volume fraction when utilising Al₂O₃–Therminol VP-1 nanofluids. Incorporating these nanofluids into the receiver’s absorber tube significantly increases thermal efficiency, particularly at lower flow rates. Regardless of the specific volume fraction considered, thermal efficiency follows a distinct trend: it rises as the Reynolds number increases until it reaches an optimal point, beyond which it diminishes. This phenomenon arises because, past the peak thermal efficiency point, the energy consumption for pumping surges, offsetting the gains in performance. The boost in thermal efficiency is more pronounced at lower flow rates due to substantial performance enhancements and lower energy expenditure on pumping compared to higher flow rates, where pumping power demands are considerably more significant at much higher Reynolds numbers and volume fractions.

When the added pumping power demand exceeds the thermal benefit, the net efficiency can drop below that of a receiver operating with the base fluid alone. The rise in heat transfer performance with higher nanoparticle loading can be interpreted using nondimensional (dimensionless) arguments rather than only qualitative trends. In the absorber tube, convective heat transfer is commonly characterised by the Nusselt number, which depends primarily on the Reynolds and Prandtl numbers, i.e., Nu = f (Re, Pr). Introducing Al₂O₃ particles alters the effective properties of the working fluid—most notably its thermal conductivity and viscosity—and therefore changes both Re and Pr. At intermediate Reynolds numbers, the higher Pr tends to enhance near-wall temperature gradients and promotes greater convective transport, yielding larger Nu and improved heat transfer. In contrast, at sufficiently high Reynolds numbers, the viscosity-driven increase in frictional losses elevates the required pumping power; this penalty can outweigh the heat transfer gain and ultimately reduce the overall thermal efficiency.

The mass flow rate was kept constant; therefore, the observed reduction in thermal efficiency beyond an optimal Reynolds number is mainly attributed to changes in thermophysical properties rather than flow variation. The addition of nanoparticles increases viscosity, which elevates flow resistance and pumping power requirements without a proportional increase in heat transfer. This behaviour is not specific to nanofluids but is associated with the inherent hydraulic and heat loss characteristics of the parabolic trough collector.

As temperatures rise, the thermal efficiency experiences a decline due to the notable increase in thermal losses from the receiver at elevated temperatures. Within the scope of this investigation, a noteworthy improvement in thermal efficiency is observed, with a 7.2% increase achieved for Al₂O₃–Therminol VP-1 nanofluids when the volume fraction transitions from 0% to 4%.

Table 4. Benchmarking the present results against reported Al₂O₃-based PTC investigations.

Study	Base Fluid	Circulation Mode	Nanoparticle Concentration	Reported Efficiency/Enhancement	Key Distinction
Present study	Therminol VP-1	Forced (fixed flow rate)	0–4 vol.%	≈67.4% (≈7.2% enhancement)	Experimental study with high-temperature oil; optimal Re identified
Kalbande et al. (2021) [41]	Soybean oil	Natural (thermo-syphon)	0.1 vol.%	≈60.8%	Integrated TES with latent heat storage
Subramani et al. (2018) [42]	DI water	Forced	≤0.5 vol.%	≈8.5% enhancement	Low-temperature water-based PTC
Ghasemi & Ranjbar (2017) [43]	Therminol-66	Forced	0–4 vol.%	≈10–12% (numerical)	Numerical-only analysis
Bellos & Tzivanidis (2017) [40]	Thermal oil	Forced	≤5 vol.%	Efficiency improvement	Parametric numerical study

summarises a focused comparison of Al₂O₃-based parabolic trough collector studies, highlighting differences in base fluid, circulation mode, and reported performance.

As shown in Table 4, the present study differs from earlier Al₂O₃-based PTC investigations by employing Therminol VP-1 as the base fluid under experimental conditions with a fixed mass flow rate. Compared to water- and vegetable-oil-based systems or numerical studies, the present work achieves higher thermal efficiency and provides practical insight into the trade-off between heat transfer enhancement and hydraulic losses, thereby strengthening its relevance for high-temperature solar thermal applications.

6. Conclusions

This research delved into the thermal performance of a high-concentration parabolic trough collector, examining four distinct volume fractions of nanofluids. Additionally, the study explored the prospect of enhancing the thermodynamic performance of the receiver, considering both Therminol VP-1 and different nanoparticle volume fractions. The study revealed that with increasing nanoparticle volume fraction in the base fluid, the receiver’s heat transfer behaviour improved across all base fluid–nanoparticle blends. At elevated Reynolds numbers, the efficiency decreases compared to lower volume fractions. In this research, a 7.2% increase in thermal efficiency was obtained for Al₂O₃–Therminol VP-1 nanofluids when the volume fraction was increased from 0% to 4%. It is important to acknowledge that despite the benefits of nanofluids in enhancing performance, challenges like particle aggregation, erosion, and limited experience in large-scale usage in solar thermal power plants persist. Ongoing research addresses these issues, and stable nanofluid dispersion can be achieved with low-volume fractions, small particles, and surfactants.

6.1. Limitations

• Sun tracking is vital for sustainable solar collection using parabolic trough collectors; without it, production decreases, raising maintenance costs.
• A parabolic trough collector relies on a concentrated sunlight beam for effective operation. In diffuse light, the concentration is ineffective, leading to a significant drop in production.
• The present study was limited to a single mass flow rate due to experimental constraints; future investigations will consider a wider range of flow rates to examine their influence on Reynolds number, pumping power, and thermal efficiency.
• The experiments were conducted under clear-sky conditions with repeated measurements on the same day; multi-day testing was not investigated in the present study.
• Although nanofluid viscosity increases pumping power requirements, a quantitative analysis of pressure drop and net efficiency was not included in the present study.
• Although nanofluid viscosity and associated pumping power effects were acknowledged, a quantitative evaluation of pressure drops and net system efficiency was not included in the present study.
• While solar photovoltaics (PV) can be installed on roofs, deploying parabolic trough collectors requires substantial land.

6.2. Future Work

Future work should focus on optimising system configurations, exploring advanced materials, and assessing environmental impacts associated with solar thermal technologies. In addition, a techno-economic evaluation considering nanoparticle cost, pumping power requirements, and maintenance aspects would be valuable for assessing the practical feasibility of nanofluid-based systems. The integration of nanoparticles in thermal storage materials also presents a promising avenue for enhanced solar energy utilisation.