Thermal performance evaluation of parabolic trough collector having different inserts and working with hybrid nanofluid

Abstract

This study emphasizes the comparative investigation of the thermal capacity of parabolic solar trough collectors with spherical-shaped balls and two types of elliptical inserts (longitudinal orientation). Hybrid nanofluid is the heat-carrying liquid obtained by mixing CuO and Al₂O₃ nanoparticles in distilled water. Analytical investigations are conducted for 1% vol. concentration of hybrid nanoparticles in distilled water for varying proportions. Computational analysis is chosen to obtain thermal as well as flow trends in the tube receiver. The outcomes disclosed that 13.3%, 10.02%, and 16% improvements are noted for thermal efficiency, Nusselt number, and thermal performance index with elliptical inserts of minor diameter 12 mm in the receiver, respectively, than spherical ball inserts. The highest pump work of 35 W is associated with spherical inserts at 0.033 kg/s.

Keywords

Receiver tube spherical balls elliptical structure nanofluid thermal efficiency Nusselt number

Introduction

In the modern epoch, the situation demands an effective consideration of renewable energy sources. The highly influencing source of sustainable energy is solar energy. Several technologies for solar energy are analyzed and introduced. The most efficient method for saving energy is utilizing the knowledge of nanomaterials and nanotechnology. Simultaneously, the optimal use of solar parabolic collectors along with various inserts is proposed. One such method is the consideration of wavy promoters along with various hybrid nanofluid mediums. Three varying advanced hybrid nanoparticles (Fe₂O₃-TiO₂, Fe₂O₃-GO, and Fe₂O₃-SiC) in Syltherm oil 800 were taken in the receiver of PTC for different concentrations. Nusselt number was enhanced maximum by 150.4% for Syltherm oil-based Fe₂O₃-GO nanofluids of 2.0% vol. concentration than Syltherm oil with wavy promoters.¹ So the results revealed that the presence of Fe₂O₃-GO nanoparticles in oil for 2% vol. content improved the convective heat transfer between the heat-carrying liquid and tube more than other combinations of nanoparticles in the base fluid. Two patterns of ribs with different values of turn (0.3, 0.5, and 0.7) were tested in the tube along with hybrid nanofluids for 0%, 2%, and 4% concentration in terms of volume for PTC collector by Alqarni et al.² Al₂O₃ and CuO nanoparticles in water were taken as the working medium. The two models that were evaluated with a 4% vol. concentration of nanoparticles in water showed the best results. This work aimed to improve the thermal and hydraulic performance of trough collectors with turbulators when utilized with hybrid nanofluids. The Nusselt number for the second pattern of rib inserts with the same volume content of nanoparticles showed an improvement of 3.3% over the first case. Higher Nusselt number values indicated better convective heat transfer rates. One porous receiver tube with internal linear structured fins was numerically investigated by Samiezadeh et al.³ for synthetic oil-Cu-Al₂O₃ hybrid nanofluid as heat transfer liquid. It was evaluated that the higher volume content of Cu particles in synthetic oil improved the gain of temperature at the outlet of the receiver by around 6.4%. Mashhadian et al.⁴ experimentally analyzed the changes of trough collector for Al₂O₃ in water and also for normal water-based multi-wall carbon nanotubes as heat transfer liquid. Three volume concentrations of 0.01, 0.02, and 0.04 were analyzed. It was noted that consideration of hybrid nanofluids, enhanced the efficiency by 197.1% more than normal water. MWCNT-MgO in oil as a heat-carrying liquid for PTC was investigated by Khan et al.⁵ for 0.25%–2% vol. concentration. One corrugated receiver was studied. The end solution showed that efficiency in the case of PTC enhanced for a larger value of nanoparticles content in terms of concentration. The maximum value for energy efficiency was 41.5% for a double fluid corrugated tube at a 2% volume concentration.

On the other side, Bellos et al.⁶ analyzed the influences of 0%, 2%, and 4% content of Syltherm 800-based Cu nanofluid in the form of volume on three patterns of solar collectors: bare tube, vacuumed-circular tube, as well air-circular tube receiver. According to that investigation, the bare structure tube receiver had the best thermal efficiency increment. Maximum enhancement in thermal efficiency for the bare structured tube was 1.58% for inlet temperature 350°C with 4% vol. Hence, higher volume content of nanoparticles in base fluid with higher inlet flow temperature provided better performances. The implementation of hybrid nano liquid is observed as an appreciable technique to obtain larger gains in the form of thermal characteristics. Bellos et al.⁷ determined the influence of 1.5% Al₂O₃-1.5% TiO₂/Oil, 3% TiO₂/Oil, and 3% Al₂O₃/Oil on thermal efficiency improvement. Two times better thermal performance was obtained for 1.5% Al₂O₃-1.5% TiO₂/Oil than a 3% presence of TiO₂ in Oil or Al₂O₃ in Oil alone in terms of volume. Analytical evaluation was done on the impact of the twisted shape turbulator on the energy efficiency, thermal performance, and hydraulic performance with water-based MWCNT-MgO hybrid nanofluid as heat transporting liquid for PTC.⁸ The experiment focused on nanoparticle concentrations between 1% and 3%. Thermal efficiency and exergy efficiency were increased by 45.98% and 31.67%, respectively, with volume content of 3% and Reynolds number of 10,000 to 25,000. Khetib et al.⁹ conducted an analytical analysis to determine the impact of spherical grooves on hydraulic, thermal, and exergy efficiency for PTC using normal water-based hybrid MWCNT-Al₂O₃ nano liquid as heat-conveying liquid (volume contents =1%, 2%, and 3%, respectively). The results showed better improvements with 3% vol. content of nanoparticles in the base fluid. It was observed that the exergy efficiency enhanced from 7.13% to 16.99% at Reynolds number = 2000, vol. fraction = 3%, and for heights of grooves 2.5 mm as well as 3.5 mm than grooves height of 1.5 mm. So, it can be concluded that higher values of vol. content of nanoparticles in the base fluid, Reynolds number, and height of grooves led to better thermal changes. Spherical structured balls in the tube of PTC were numerically tested by Chakraborty et al.¹⁰ Al₂O₃/H₂O for a concentration in terms of volume of 1.5%–4% was taken as the medium of heat transfer with flow ranging between 0.15 and 0.36 kg/s. Outcomes indicated an increased exergy efficiency and thermal efficiency by 42.23% and 64.25%, respectively, for tubes with a spherical structured ball insert of the diameter of 48 mm and an 18 mm spherical structured ball insert for 4% vol. content of Al₂O₃ in water at 0.36 kg/s rate of flow. By considering the same medium for heat transfer with 1%, 1.5%, and 2% vol. content in water, the next study by Chakraborty et al.¹¹ focused on the consideration of the receiver tube of PTC fitted with a helical structured coil. The highest improvement of useful energy gain was noted in the case of a tube fitted with 145 turns coil, which was 32.37% for 0.033 kg/s of nanofluid than normal water. The research work showed that receivers with a higher number of turns coil inserts and vol. content of nanoparticles in water provided better performance. Subramani et al.¹² evaluated the benefit of Al₂O₃/H₂O in one tube of PTC and got an 8.5% thermal efficiency improvement for 2% vol. content of nanoparticles in water. Mwesigye et al.¹³ conducted an analytical investigation as well as noted better changes with Slytherin 800-based Al₂O₃ nanofluid. The volume content of the nanoparticles in the base liquid ranged from 0% to 8%, respectively. The outcomes pointed out that the utilization of nanofluids enhanced the thermal efficiency of PTC by 7.6% with 8% volume content of nanoparticles. Zafaret al.¹⁴ took MgO and Al₂O₃ nanoparticles in water and glycol as a heat-conveying liquid. The nanoparticle volume concentrations were 0.025%, 0.05%, and 0.075%, respectively. The highest thermal efficiency improvement of 25.03% also 24.02% were found for MgO/glycol nanofluid at 0.075% volumetric content at 0.02 and 0.015 kg/s rates of flow, respectively, which means here also it was seen that higher volume content of nanoparticles was preferable.

Similar work was conducted by Subramani et al.,¹⁵ who considered TiO₂ nanoparticles and investigated them. The test samples composed of nanofluids of 0.5%, 0.2%, 0.1%, and 0.05% concentration in water were compared with water (the base fluid) at varying flow rates. In comparison to distilled water, efficiency was improved by almost 8.66% for 0.5% volume content. The effect of CuO/normal water, along with consideration of foam in the tube, was obtained by Heyhat et al.¹⁶ Using 0.1% content in the form of volume of CuO in normal water and foam, the investigation showed that enhancing the flow from 20 to 100 l/h improved efficiency from 55.65% to 79.29%. In this sector, similar investigations were handled in Refs.^17,18 Malekan et al.¹⁹ considered Therminol 66-Fe₃O₄ and Therminol 66-CuO as heat-carrying liquids for 2% and 4% volume concentrations. It was observed that taking a 4% content of Therminol-66-based Fe₃O₄ along with a magnetic field improved efficiency by 4%. Though CuO nanoparticles have better thermal conductivity than Fe₃O₄ nanoparticles. In this investigation, it was noted that under a magnetic field, Fe₃O₄ provided better performance than CuO in terms of collector efficiency. One porous-shaped media in a circular space, as well as 3% content of Al₂O₃ in synthetic oil in the form of volume, was tested by Bozorg et al.,²⁰ which increased thermal efficiency and heat transfer coefficient by 14% as well as 20%, respectively. This happened because of the reduction in the temperature of the tube wall of the receiver, which reduced the heat loss through radiation more notably.

Again, Parlamis et al.²¹ investigated by taking a helical structured screw tap in one receiver of trough collector for experimental setup with air as heat conveying liquid. The total outcomes of the study showed an increment in the form of rise in temperature, causing improvements within the range of 56%–71% in terms of efficiency, proving that helical-shaped screw in tubes provided better heat interaction between the solid and liquid medium. One helical-shaped receiver in the case of a normal receiver for water heating was done by Chakraborty et al.²² The outcomes showed exergy, as well as thermal efficiency of the helical structured tube, were noted to be 4%–5% also 4%–10% more in comparison to the conventional tube. This type of improvement was caused due to the enhanced contact area between water and tube in the case of helical tube in straight receiver tube. This led to better convective heat transfer among the solid and liquid mediums. Rezaeian et al.²³ conducted one experimental investigation for PTC and one direct flow in an evacuated tube. Heat-carrying medium included both CuO nanofluid as well as normal water. It was noted that performance index, as well as thermal efficiency were improved by 1.74% and 71%, respectively, for nanofluid than water. Norouzi et al.²⁴ did an analytical evaluation by taking one rotating receiver tube in the case of a steady receiver tube. Al₂O₃-Therminol with volume content of 0%, 1.5%, and 3% were the heat-conveying liquid. Different materials were considered for receiver tube. The outcomes revealed that efficiency for the aluminum receiver tube was 25% higher than steel receiver for tube spinning velocity of  25 rad/s and nanoparticle content of 3%, respectively . This investigation pointed out that the consideration of rotating receiver reduced the temperature gradient between the center of the tube and the wall. Bezaatpour et al.²⁵ did an examination for PTC along with a revolving tube as well as a magnetic field inducer in the case of nanofluid as a working liquid. Exergetic and hydrothermal changes of PTC were improved by 24% and 101%, respectively. Mehdi et al.²⁶ conducted an analytical study with a porous medium fitted in the receiver along with Cu nanoparticles in water as heat transfer liquid. Nusselt number and thermal efficiency were enhanced by almost 12% and 1.2%, respectively, by improving copper content in normal water, as seen in this investigation. Alnaqiet al.²⁷ tested the influence of two patterns of twisted tapes inside a PTC tube, also MgO-MWCNT/thermal oil in the form of heat-bearing liquid. Raheem et al.²⁸ investigated the hydraulic as well as thermal effects by installing helical-screw tape inside one normal tube for Reynolds numbers of 4400–7000. Performance Evaluation Criteria (PEC) and Nusselt number were increased by 23% and 53%, respectively. Thermal efficiency also Nusselt number were enhanced by 1.2% as well as 12%, respectively, by improving copper content in the form of volume in normal water.

The influence of the modified structure of grooves on the tube of PTC with nanoparticles in base fluid was examined by Mishra et al.²⁹ Copper particles in syltherm-800 for 4% of concentration were taken as the heat-conveying liquid. Again, Fattahi et al.³⁰ utilized a twisted structured tape insert inside a tube of PTC. The effect of inner helical-shaped axial fins in receiver of trough collector was tested by Zaboli.³¹

Based on the prior literature survey, despite several pieces of research being influenced by the modified design of the receiver tube or inserting turbulator in the tube of PTC, comparative examination of trough collector with different types of elliptical and spherical insert with hybrid nanofluid, did not achieve that much attention. In this research work, one comparative investigation is performed in terms of thermal changes for tube fitters with elliptical and spherical structured ball inserts. Al₂O₃-CuO particles in water for 1% concentration in the form of volume are utilized. The rates of flow ranged from 0.016 to 0.033 kg/s. The exact purpose of the examination is to determine the changes in the PTC tube for all the patterns of inserts with a hybrid nanofluid. These modified versions of PTC can be practically utilized in electrical grid, industries, solar refrigerators, cooling applications, etc. and better outcomes can be expected. As observed in the earlier analysis, the consideration of two varying nanoparticles can upgrade the conductivity of the heat-carrying medium, leading to improve thermal performance. The outcomes of the investigation are judged in the form of temperature at the outlet of flow, Nusselt number, exergy efficiency, and thermal efficiency, respectively.

Physical model

For this analytical investigation, the design also simulation of the structure are conducted in ANSYS 22R1 Fluent, as in Figures 1 and 2. These figures are also showing the types of inserts being considered in the study. A copper tube of length 2 m is constructed. The inner circumferential diameters, as well as outer circumferential diameter, are 70 mm as well as 66 mm, respectively.¹⁰ One tube composed of glass, which is perfectly evacuated, is considered over the copper tube to increase the reduction in thermal losses. Parabolic-shaped trough behaves like one reflector, constructed from an aluminum sheet. The tube is positioned at the focal length of the trough. Spherical-shaped balls of 48 mm diameter and elliptical inserted of 48 mm major diameter are considered, respectively. The reason behind choosing this diameter value is that in the earlier studies with these kinds of inserts, the best outcomes are noted at 48 mm of maximum diameter.^10,32 For the elliptical inserts, two values of minor diameters 12 and 24 mm are being simulated. Hybrid nanofluid is the working liquid in this work. It is obtained by combining nanoparticles CuO and Al₂O₃ in distilled water. This entire investigation is performed for 1% vol. concentration of hybrid nanoparticles in water (CuO 75%-Al₂O₃ 25% = Nanofluid-1, CuO 50%-Al₂O₃ 50% = Nanofluid-2, and CuO 25%-Al₂O₃ 75% = Nanofluid-3). The dimensions of the studied models and other parameters for the comparative study are listed in Tables 1 and 2. At a time, 20 equally placed inserts are considered, they are interlinked by a rod of 8 mm diameter.¹⁰ The thermal, as well as physical properties of the heat-carrying liquid are as in Table 3.

Table 1.

Parameters of the examined models.

Parameters	Dimensions
Aperture width (W_a)	1 m
Aperture length (L)	2 m
Focal length of parabola(F)	0.25 m
Aperture area (A_a)	1 m²
Concentration ratio (C)	11
Thickness of wall	1.65 × 10⁻³ m
Receiver outer diameter (D_ro)	60.33 × 10⁻³ m
Inner diameter of cover (D_ci)	109 × 10⁻³ m
Outer diameter of cover (D_co)	115 × 10⁻³ m
Copper receiver tubeabsorbance (α)	96%
Glass cover tube emissivity (ε_gc)	86%
Reflectivity of collector (ρ_r)	80%
Transmittance of collector (τ)	95%

Table 2.

Thermal and physical characteristics for nanoparticles.

Properties	Water	Al₂O₃	CuO
Density (kg/m²)	998.2	3970	6500
Specific heat (J/kgK)	4182	765	535.6
Thermal conductivity (W/mK)	0.613	40	20

Table 3.

Comparison of performance of the present investigation and other investigations.

Author	Types of heat conveying fluid	Types of study	Volume Concentration (%)	Types of insert	Findings
Alqarni et al.²	Copper oxide and alumina oxide nanoparticles in	Numerical	0, 2, and 4	Ribs and holes	This testing proposed a proper point to get improved thermal also hydraulic efficiency for PTC by fixing turbulators and considering hybrid nanofluids. Nusselt number was enhanced maximum by 150.4%
Khetib et al.⁹	Fe₃O₄ and MWCNT in base fluid (water)	Numerical	1–3	Twisted shaped turbulator	For Re of 5000, 10000, 15000, and 20000, Nusselt number increased by 70.93%, 81.16%, 70.63%, as well 56.10%, respectively. Exergy efficiency enhanced from 7.13% to 16.99%
Chakraborty et al.¹⁰	Al₂O₃-based water	Numerical	1.5–4	Spherical shaped balls inserts	Thermal efficiency also exergy efficiency by 71.84% and 43.23%, respectively.
Chakraborty et al.¹¹	Al₂O₃-based water	Numerical	2	Helical structured coil inserts.	The highest value for thermal efficiency is found to be 72.37%. The highest improvement of useful thermal energy found for tube with 145 turn was 32.37% at 0.033 kg/s in case of nanofluid than normal water.
Chakraborty et al.²²	Water	Numerical	______	Helical structured receiver tube.	Highest thermal efficiency was observed as 78.45%. Overall efficiency, exergy efficiency, and thermal efficiency of helical receiver tube of PTC were 3.5%–10%, 4%–5%, and 4%–10% better than that smooth receiver tube of PTC.
Alnaqi et al.²⁷	MWCNT-MgO in base fluid (thermal oil)	Numerical	0.25 to 2	Two twisted structured tape inserts	It was observed that for all examination conditions, the obtained value of PEC for the models became better with larger value of Re till Re = 1 × 10⁴ again then reduced up to Re = 1 × 10⁵
Fattahi et al.³⁰	CuO and Al₂O₃ in base fluid (water)	Numerical	0.02 and 0.04	A twisted shaped tape insert	It was found that efficiency enhanced up to 23% as well as 90% by improving the volume content of hybrid nanoparticle in base liquid.
Zaboli et al.³¹	Multi-wall carbon nanotubes–iron oxide in base fluid (water) and silver and graphene nanoparticles in base fluid (water)	Numerical	4	Inner helical structured axial fins	With Re number (Re = 5000), multi-wall carbon nanotubes/iron oxide indicated better thermal performance than silver–graphene/normal water by around 9.66% as well as 13.68%, respectively
Chakraborty et al.³²	CuO-Al₂O₃ based water	Numerical	1 (for varying composition of Al₂O₃-CuO	Rotating receiver with elliptical inserts.	The highest thermal efficiency value was 82.03%. Maximum improvement for heat transfer coefficient, also thermal efficiency for receiver with 28 mm major diameter elliptical insert (longitudinal orientation), were 44.21% as well as 29.21%, respectively, at 15 rad/s receiver speed.
Present work	CuO-Al₂O₃ based water	Numerical	1 (for varying composition of Al₂O₃-CuO	Receiver with spherical and elliptical inserts.	Maximum thermal efficiency is found as 73.12%. The results pointed that 13.3% also 10.02% improvements are found for thermal efficiency as well as Nusselt number with elliptical inserts of minor diameter 12 mm in receiver than spherical shaped ball inserts.

Consideration of assumptions

Specific heat for hybrid nanofluid is constant.¹⁰

Losses in terms of heat are minor from the side of tube.¹⁰

Throughout the circumference, the uniform intensity of the sun is considered.¹⁰

Tube constructed from glass is perfectly empty.¹⁰

Hybrid nanofluid is considered a Newtonian fluid also incompressible as well as steady flow.¹⁰

Governing equations

Flow of hybrid nanofluid inside the tube obeys Navier–Stokes equations and also the momentum, energy, and continuity equations, shown in the following equations.¹⁰

Equations for continuity:

\nabla . (ρ \vec{V}) = 0

(1)

Equation for momentum:

\nabla ρ \vec{V} \vec{V_{i}} = \frac{- \partial p}{\partial X_{i}} + \nabla (μ . \nabla \vec{V_{i}}) + S_{i}

(2)

V = (V_R, V_θ, V_Z) field velocity.

\nabla ρ \vec{V} \vec{V_{i}} = \frac{\partial p}{\partial X_{i}} + \nabla (μ . \nabla \vec{V_{i}}) + S_{i}

(3)

X_i= R, θ, Z

S_i= Remaining Viscous Terms

i = 1, radial direction

S_{1} = ρ \vec{V_{θ}} \frac{\vec{V_{θ}}}{r} - μ [\frac{\vec{V_{R}}}{r} + (\frac{2}{r^{2}}) (\frac{\partial \vec{V_{θ}}}{\partial θ})]

(4)

i = 2 tangential direction

S_{2} = μ [(\frac{2}{r^{2}}) \frac{\partial \vec{V_{R}}}{\partial θ} - \frac{\vec{V_{θ}}}{r^{2}}] - ρ V_{R} \frac{\vec{V_{θ}}}{r}

(5)

i = 3 axial direction

S_{3} = 0

(6)

Equation for energy:

\nabla (ρ v c_{p} T) = \nabla \times (k \nabla T)

(7)

Boundary conditions

Hybrid nanofluid temperature at the inlet (T_in) is ranged from 298 to 308 K.

Rate of flow is 0.016, 0.025, and 0.033 kg/s at the location of the inlet of the tube.

Outlet is set as an outflow type.

Temperature of ambient (T_am) is 293 to 300 K.

Reflectance of trough (r_con) is 83%.³³

Parabolic-shaped trough is composed of aluminum and the material for the receiver tube and inserts are copper.

Mesh creation

In the present investigation, turbulence modeling is conducted by taking the k-ε model. The solutions are converged in case of the residuals of continuity are less than 10⁻³. Again, the rate of heat transfer is tracked during iterations as well as the solution is noted to be converged for the constant heat transfer rate with numbers of iterations larger than 100. Moreover, to secure mesh independence for the solution, grid sensitivity investigations are conducted for indicative models of PTC in terms of Nusselt numbers.

Tetrahedral-structured mesh is taken for tube, again for the cover of tube constructed of glass, as in Figure 3. Elements are taken for lowest as well as highest sizes of 0.00004794 and 0.003140 m, respectively, with a 1.20 rate of growth. The radiation model is surface-to-surface in ANSYS 22R1 Fluent. Figure 3 shows the mesh generation for the investigated models.

Testing for grid independency

Figure 4 illustrates outcomes for four varying networks of the grid in the case of the investigated cases. Grid-independent outcomes for every case are elaborated in the form of the Nusselt number. Grid tests are run for four grids with type-1 elliptical inserts (with major diameter 48 mm and minor diameter 24 mm) (780450, 1045120, 1345070, 1697800), type-2 elliptical inserts (with major diameter 48 mm and minor diameter 12 mm) (576210, 970625, 1139079, 1490880), spherical ball inserts (657750, 1000120, 1201210, 1565010) at 0.033 kg/s for Nanofluid-1. A meticulous study indicates that the deviation of outcomes for Nusselt number of grids 1345070 and 1697800 is around 0.02% for type-1 elliptical inserts, 0.05% for grids 1139079 and 1490880 in the case of type-2 elliptical inserts, 0.03% for grids 1201210 and 1565010 with spherical ball inserts in the receiver, respectively. At the end, a grid mesh of 1345070 nodes for type-1 elliptical inserts, 1139079 nodes in case of type-2 elliptical insert, and 1201210 nodes for spherical ball inserts is found the most influencing grid to decrease the time related to computation and increase the amount of accuracy.

Mathematical conceptualization

Useful heat gained by fluid while flowing is Q_u, calculated as:

Q_{u} = h \times (π D_{r i}) \times L \times (T_{r} - (\frac{T_{i n} + T_{o u t}}{2}))

(8)

Thermal efficiency η_th is found out as¹⁰:

η_{t h} = \frac{m \times c_{p} \times {(T_{o u t} - T_{i n})}_{u}}{C \times A_{a} \times G_{a}}

(9)

Pump work demand is evaluated as¹⁰

W = \frac{m \times Δ p}{ρ}

(10)

Reynolds number calculated as:

R e = \frac{4. m}{π \times D_{r i} \times μ}

(11)

Nusselt number is being evaluated as

N u = \frac{h \times d}{k}

(12)

Thermal losses solely occurred due to losses associated with radiation, as represented in Eq.(13).³⁴ Heat loss happens because of convection among collector as well as receiver is calculated as:

Q_{l o s s} = \frac{A_{r o} \times σ \times (T_{r}^{4} - T_{c}^{4})}{\frac{1}{ε_{r}} + \frac{(1 - ε_{c})}{ε_{r}} \times (\frac{A_{r o}}{A_{c i}})}

(13)

ε_{r} = 0.000327 T_{r} - 0.065971

(14)

Heat losses caused by the velocity of wind are again considered; the losses associated with wind are evaluated as³⁵:

Q_{l o s s} = π \times D_{c o} \times L \times h_{w} \times (T_{c o} - T_{a}) + ε_{c} \times π \times D_{c o} \times L \times σ \times (T_{c o}^{4} - T_{s k y}^{4})

(15)

h_w as well T_sky are heat transfer coefficient among the surrounding (climate) and also outer periphery of the enveloping tube constructed from glass, and temperature for the sky, is obtained as^36,37:

h_{w} = V_{w}^{0.58} \times D_{c o}^{- 0.42}

(16)

T_{s k y} = 0.0552 \times T_{a}^{1.5}

(17)

Calculation of thermal physical characteristics for hybrid nanofluid

Procedures to discover hybrid nanoparticle characteristics are discussed. Here, base liquid is denoted as (bf), nanoparticle by (np), also nanofluid with (nf), respectively. The content of nanoparticles in terms of volume is represented by (φ). np1 is forAl₂O₃ nanoparticle and np2 in the case of CuO, respectively.

Total content in the form of volume in the case of hybrid nanoparticles is as below:

\emptyset = \emptyset_{1} + \emptyset_{2}

(18)

Density for nanoparticle is obtained as³⁸:

ρ_{n p} = \frac{\emptyset_{1} \times ρ_{n p 1} + \emptyset_{2} \times ρ_{n p 2}}{\emptyset}

(19)

Capacity of specific heat in case of nanoparticles is evaluated as³⁸:

C_{p, n p} = \frac{\emptyset_{1} \times ρ_{n p 1} \times c_{p, n p 1} + \emptyset_{2} \times ρ_{n p 2} \times C_{p, n p 2}}{ρ_{n p} \times \emptyset}

(20)

Thermal conductivity in case of examined nanoparticle is evaluated as³⁸:

k_{n p} = \frac{\emptyset_{1} \times k_{n p 1} + \emptyset_{2} \times k_{n p 2}}{\emptyset}

(21)

The density is calculated as:

ρ_{n f} = ρ_{b f} \times (1 - \emptyset) + ρ_{n p} \times \emptyset

(22)

Capacity of specific heat for nanofluid is obtained as³⁸:

C_{p, n f} = \frac{ρ_{b f} \times (1 - \emptyset)}{ρ_{n f}} \times C_{p, b f} + \frac{ρ_{n p} \times \emptyset}{ρ_{n f}} \times C_{p, n p}

(23)

The thermal conductivity for nanofluid is determined as³⁸:

k_{n f} = k_{b f} \times \frac{k_{n p} + 2 \times k_{b f} + 2 \times (k_{n p} - k_{b f}) \times \emptyset}{k_{n p} + 2 \times k_{b f} - (k_{n p} - k_{b f}) \times \emptyset}

(24)

With the relationship below, dynamic viscosity is calculated as³⁸:

μ_{n f} = \frac{μ_{b f}}{{(1 - \emptyset)}^{2.5}}

(25)

Validation of the methods

The evaluated outcomes are validated to achieve more accuracy than the numerically examined method. The validations are performed in the form of Nusselt number, as well as friction factor in case of fully mature turbulent disturbed flow of normal water in one straight tube acts as a receiver. Correlation as suggested by Gnielinski,³⁹ Petukhov,⁴⁰ also Mwesigye⁴¹ is taken to validate the outcomes. Figure 5, indicates that this examined case for conventional receiver matches satisfactorily with the correlation suggested by Gnielinski in terms of Nusselt number with the highest also least deviation of 2.03% and 1.32%, respectively. Again, friction factor outcomes observed for this investigation match satisfactorily with correlation proposed by Petukhov for the largest and least amount of deviation 6.67% and 5.88%, respectively. The validations are again performed with experimental testing, conducted by Suresh et al.⁴² The least as well as the largest deviation in the case of Nusselt number and friction factor are 2.76% and 4.73%, and 5.98% and 7.76%, respectively.

Gnielinski:

N u = \frac{\frac{f}{8} \times (R e - 1000) P r}{1 + 12.7 \times {(\frac{f}{8})}^{0.5} (P r^{\frac{2}{3}} - 1)}

(26)

Mwesigye:

N u = 0.0104 P r^{0.374} R e^{0.885}

(27)

Petukhov:

N u = \frac{\frac{f}{8} \times R e \times P r}{1.07 + 12.7 \times {(\frac{f}{8})}^{1 / 2} \times (P r^{\frac{2}{3}} - 1)}

(28)

Correlation for friction factor:

Mwesigye:

f = 0.173 \times R e^{- 0.1974}

(29)

Petukhov:

f = (0.79 L n R e - 1.64)^{- 2}

(30)

Results and discussion

Here, the outcomes of the present comparative investigation in the form of exergy efficiency, Nusselt number, pump work, and thermal efficiency requirements for all three types of inserts in the receiver are discussed as well as compared. Solar intensity is taken as 708 W/m².¹⁰ The analysis is done for 1% vol. concentration of hybrid nanofluids in case of various mixtures of CuO as well as Al₂O₃ nanoparticles in normal water (CuO 25%-Al₂O₃ 75% = Nanofluid 3, CuO 50%-Al₂O₃ 50%= Nanofluid 2, and CuO 75%-Al₂O₃ 25% = Nanofluid 1).³² The temperature at the inlet for flow is ranged from 298 to 308 K.³² For all the inserts in the receiver best results are observed at 308 K. So, the results are discussed in this section based on the inlet temperature of the liquid as 308 K.

Figures 6 and 7 elaborates on the outer surface distribution of heat flux for tubes also Figure 7 depicts the graphical presentation of the distribution of heat flux. Since the majority part of heat flux, reflects to the lower periphery of the receiver tube, there is a high chance of damage as well as deformation of the tube. The modified absorber or receiver tube with elliptical and spherical inserts can eliminate this trouble up to some extent than SRT.

Effect of types inserts on the temperature at outlet

Figure 8 features outlet temperatures for three different categories of nanofluids (CuO 25%-Al₂O₃ 75% = Nanofluid-3, CuO 50%-Al₂O₃ 50%= Nanofluid-2, and CuO 75%-Al₂O₃ 25% = Nanofluid-1) at 0.016 kg/s. Also, Figure 9 reveals the temperature at the outlet of flow for the studied cases with Nanofluid-1 against the varying rate of flow. It is noted that as the rate of flow enhances, the distribution of temperature gets a lesser stratified pattern, representing that the heat transfer in the form of conductive gets weakened. At 0.033 kg/s, the prominent mechanism for heat transfer is forced convection, which causes a smaller range of temperature in the tube.

As in Figures 8 and 9, the largest value of outlet temperature is 368 K in the case of receiver tube for elliptical insert with a minor diameter of 12 mm (type-2) at 0.016 kg/s for Nanofluid-1. For the same flow rate, the highest value of temperature at the outlet is obtained as 363 K for receiver tube with an elliptical insert of minor diameter 24 mm (type-1) and 352 K for spherical balls insert with Nanofluid-1. So, in terms of percentage, the temperature at the outlet improved within the range of 4.34%–2.08% for the receiver tube with elliptical inserts than spherical inserts. Since the minor diameter of type-2 elliptical inserts is lesser than other two types of inserts, it will provide more flat surface. As a result, type-2 elliptical inserts in receiver give better surface contact between the solid and liquid medium. Hence, conductive heat transfer is a more prominent mode of heat interaction here, providing a more stratified pattern for temperature at outlet.

The present study points out that temperature at the outlet of the flow reduced with larger values of flow rate regardless of the nanoparticle's proportion in water and types of the insert. These occur because a higher flow rate in the form of mass increases the flow velocity, causing a reduction in the time of flow inside the tube. For instance, the higher value of temperature at the outlet for the tube with elliptical inserts and the receiver with spherical ball inserts are found at 0.016 kg/s for Nanofluid-1.

Also, the results reveal that improved values of the temperature at the outlet for all three types of analyzed models are obtained with higher content of CuO particles in water.

Thermal performance analysis depending on different types of inserts

Analysis based on thermal and exergy efficiency of the investigated models

Figure 10 depicts the thermal efficiency for all types of inserts based on different rates of flow. Evidence of the study is that thermal efficiency dramatically improved with the introduction of nanoparticles in water. At 0.033 kg/s, addition of Al₂O₃ by 25% and CuO by 75% provides a thermal efficiency of 73.12% for type-2 elliptical inserts, 70.05% for type-1 elliptical inserts, and 67.71% for the receiver tube with spherical inserts, respectively. Percentage-wise 14.9% improvement of thermal efficiency is noted for the receiver with type-2 elliptical insert and 11.47% for type-1 elliptical inserts than spherical balls inserts at 0.033 kg/s for Nanofluid-1 (Figure 11).

In the case of Nanofluid-2 and Nanofluid-3, the highest thermal efficiencies for a receiver with type-2 and type-1 elliptical inserts and spherical ball inserts are 70.03%, 68.38%, and 64.34%, and 67.71%, 64.34, and 54.82%, respectively, 0.033 kg/s. In terms of the percentage, 13.3% and 8.76%, and 9.43% and 5.34% improvements are noted for the receiver with type-2 and type-1 elliptical inserts than spherical balls inserts for Nanofluid-2 and Nanofluid-3, respectively, at 0.033 kg/s, as elaborated in Figure 11.

The present investigation reveals that the largest value in the case of thermal efficiency of the investigated models is observed with Nanofluid-1 at 0.033 kg/s. The elliptical inserts in the receiver for longitudinal orientation enhance contact among the surface area in-between solid construction and also fluid than spherical inserts. In comparison to type-1 elliptical inserts, type-2 elliptical inserts can provide a better contact surface among the solid and liquid surfaces. So, the convective mode of heat interaction from heat conveying liquid to solid construction is better with elliptical inserts and it is much better for type-2 elliptical inserts.

Figure 12 reveals that the amount of useful heat gained while flowing is better for elliptical inserts in the receiver tube than spherical ball inserts as the contact surface area is higher in these cases. The largest value for exergy efficiency is observed as 52.34%, 50.24%, and 47.03% for type-2, type-1 elliptical inserts, and spherical inserts in the receiver at 0.033 kg/s for Nanofluid-1.

Thermal performance analysis based on Nusselt number

Figure 13 elaborates the Nusselt number variation for all the models enhanced with a higher value for flow rate regardless of the type of working liquid. The evidence of the investigation is that with Nanofluid-1, the Nusselt number gets better. Maximum values for Nusselt are observed for type-1 and type-2 elliptical insert as 596, 610, and 586 for spherical insert in the tube at 0.033 kg/s, respectively, for Nanofluid-1. Figure 14 reveals the comparative outcomes of the models in terms of Nusselt number. Maximum improvement for Nusselt number for type-1 and type-2 elliptical inserts in the receiver is 7.43%, 10.02% at 0.033 kg/s than a spherical insert with Nanofluid-1. For Nanofluid-2 and Nanofluid-3, the highest improved values for Nusselt number in terms of percentages are 6.32% and 9.03%, and 3.04% and 5.6% for type-1 and type-2 elliptical inserts, respectively, at 0.033 kg/s than spherical inserts. So, the present examination proved that for all the studied models highest improvement for the Nusselt number is obtained at 0.033 kg/s (Figure 14).

This means the CuO particles have appreciable effects at a higher flow rate. As the CuO particle amount increases in the heat-carrying medium, the rate of convective heat transfer also improved, providing better outcomes in the form of Nusselt number.

Again, the introduction of inserts inside the receiver improves the quality of surface contact among the liquid medium and solid structures, hence better convective heat transfers are observed. Improved values for Nusselt numbers are obtained with the receiver tube of type-2 elliptical inserts because preferably best surface contact is possible among liquid medium and solid surface for these kinds of inserts. So, the most acceptable model is the one with type-2 elliptical inserts for Nanofluid-1 as the heat-carrying liquid.

Performance based on pump work demand

The pressure drop with the flow process is the main cause of the increment in pump work demand. Economically, the most acceptable case is the one, which is associated with the least demand for pump work and the highest values for thermal performance. The maximum value for pump work demands is observed at 0.033 kg/s for all the examined cases, irrespective of the type of heat-carrying liquid. This happens because the higher amount of pressure drop is associated with a higher amount of turbulence in the flow. So, as the flow rate amplifies, the pattern of flow becomes more turbulent and causes higher pump work demand.

The largest amount of pump work is 35 W for a receiver of spherical inserts and 32.36 W, and 31 W for type-1 and type-2 elliptical inserts, respectively, at 0.033 kg/s. for Nanofluids-1 (As in Figure 15). Figure 15 reveals that pump work demand for the investigated models does not get that much affected by the type of working medium but gets more influenced by the rate of flow. It is pointed out that for the working flow rate range in this work; pump work demands are higher for spherical inserts at all the flow rates. These happen because the flow gets more tubulated with spherical ball inserts than elliptical inserts and it is least for type-2 elliptical inserts as its geometric structure creates a lesser amount of turbulence for the flow. Now, if the increments are shown in the form of a percentage, 10.9% of increment for pump work demand is observed for tube with spherical shaped ball inserts at 0.033 kg/s for Nanofluid-1 than the receiver with type-2 elliptical inserts.

Comparison of the analytical models in the form of thermal performance index (TPI)

The amount of heat transfer improvement in terms of pressure drop in case of flow is illustrated in the form of thermal performance index (TPI) in Figure 16. Figure 16 reveals the values for TPI for all the examined modes against different flow rates with three types of hybrid nanofluid. The maximum value of TPI is 6.2, 7.6, and 6 for receivers with type-1 and type-2 elliptical inserts as well spherical inserts, respectively, at 0.033 kg/s for Nanofluid-1. Similarly for Nanofluid-2 and Nanofluid-3 highest values for TPI are 6.53, 5.3 for type-1 and type-2 elliptical inserts, and again 6, 4.9 for spherical inserts, respectively, at 0.033 kg/s. If the TPI improvements are presented in the form of a percentage, 16% enhancement is noted for receivers with type-2 elliptical inserts than spherical inserts at 0.033 kg/s for Nanofluid-1. So, this part of the discussion implies that for all the examined models with all types of nanofluid, the highest values for TPI are found at 0.033 kg/s.

Figure 16 is indicating the thermal benefit obtained by taking three varying types of working liquids. As observed in the earlier discussion, higher amount of pressure drops are obtained in the case of spherical balls insert for all the flow rates and varying types of the working medium, and the best amount of convective heat interaction rates are noted with the receiver of elliptical inserts for each operating case with varying flow rate. Improved values of TPI are found for elliptical inserts under every operating condition.

Comparison of the present investigation with earlier studies

Table 3 elaborates on the core difference and the indexes of variations from the compared system. As observed, various innovations to improve the thermal performance of parabolic solar trough collector by taking varying heat-conveying medium and disturbance-creating inserts in receiver under different operating conditions are encouraged presently. Depending upon the earlier literature study and the table, it can easily be concluded that, though several developments are going on PTC, competitive investigation on PTC for spherical and elliptical inserts with low concentration hybrid nanofluid did not achieve that much attention.

Again, it is observed from the result section of the investigation that an appreciable amount of improvements are found in the form of thermal efficiency with these three types of inserts in receiver of PTC.

Conclusion

To upgrade the parabolic structured trough solar collector performance, a thorough examination is conducted by taking various types of inserts. A total of three types of inserts are being taken (spherical ball inserts, type-1 elliptical inserts, and type-2 elliptical inserts) in the receiver tube. Hybrid nanofluid of three varying combinations of particles, Al₂O₃ and CuO are chosen as the heat-carrying liquid medium. The concentration of hybrid nanoparticles in water is 1% in terms of volume for a different combination of nano-particle composition (CuO 75%-Al₂O₃ 25% = Nanofluid-1, CuO 50%-Al₂O₃ 50% = Nanofluid-2, and CuO 25%-Al₂O₃ 75% = Nanofluid-3). The entire analytical investigation is performed in ANSYS Fluent 22R1 for the rate of flow ranging between 0.016 and 0.033 kg/s, respectively. The outcomes of the investigation are illustrated in the form of flow temperature at the outlet, thermal efficiency, exergy efficiency, pump work demand, and thermal performance index (TPI).·Highest temperature at the outlet of the flow is 368 K for tube with type 2 elliptical insert at 0.016 kg/s for Nanofluid-1. Similarly, maximum of 14.9% and 52.34% improvement for thermal efficiency and exergy efficiency is observed with the tube of PTC for type 2 elliptical insert than spherical balls inserts at 0.033 kg/s for Nanofluid-1. For all the investigated models maximum values for efficiencies are noted at 0.033 kg/s. The highest enhancement for Nusselt number of type-1 and type-2 elliptical inserts in the receiver is 7.43%, 10.02% at 0.033 kg/s than a spherical shaped balls insert in the receiver with Nanofluid-1.

Again, The largest value of pump work is 35 W for a receiver with spherical ball inserts at 0.033 kg/s. It is observed that pump work demands are less get affected by the type of nanofluid but more influenced by the flow rate of the heat-carrying medium. The investigation also showed that the highest value of TPI is 6.2, 7.6, and 6 for receivers with type-1 and type-2 elliptical inserts and spherical structured ball inserts, respectively, at 0.033 kg/s for Nanofluid-1.

EAE1156407 -- "Highlights content" was given in separate document and in meta xml it is mentioned as supplemental, But CE was not captured this content as well as they have not included the supplemental section heading also . Please ensure.

Highlights

Hybrid nanofluid (mixture of CuO as well Al₂O₃) is the working fluid, for 1% vol. content in water.

Spherical-shaped balls and two types of elliptical inserts in PTC are analyzed

Highest outlet temperature of flow is 368K for receiver tube with type 2 elliptical insert at 0.016kg/s.

13.3% and 10.02% improvements are found for thermal efficiency and Nusselt number with type 2 elliptical inserts.

Footnotes

Authors' contribution

Dr. Oveepsa Chakraborty: Conceptualization, methodology, software, data curation, writing- original draft preparation, Dr. Biplab Das: Supervision, writing reviewing, Dr. Rajat Gupta: Supervision, writing reviewing.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Oveepsa Chakraborty

Oveepsa Chakraborty presently working as an assistant professor in the Department of Mechanical Engineering of Girijananda Chowdhury Institute of Management and Technology. The author completed her PhD at the National Institute of Technology Silchar. The main area of research of the author is based on solar energy.

Biplab Das presently working as an associate professor in the Department of Mechanical Engineering of the National Institute of Technology Silchar. The author has published more than a hundred articles in reputed national and international journals. Currently working on Solar air collector and drying of agricultural crops. Also, performing a study on heat transfer enhancement in a channel using CFD.

Rajat Gupta presently appointed in the post of director in the National Institute of Technology Silchar. The author has published more than 200 papers in national /international journals and conferences. He chaired many conferences in India and abroad and delivered keynote addresses. His research areas include among others, thermo fluids, non-conventional energy CFD, etc.

Appendix Nomenclature

A	area, m²
C_p	specific heat under constant pressure, kJ/kg K
C	concentration ratio
D	diameter, m
E	exergy, W
G	solar direct beam irradiation, W/m²
h	heat transfer coefficient, W/m²K
k	thermal conductivity, W/mK
L	tube length, m
m	mass flow rate, kg/s
Nu	Nusselt number
ΔP	pressure drop, Pa
Pr	Prandtl number
Pe_D	Peclet number
Q	heat rate, W
R	radius, m
Re	Reynolds number
T	temperature, K
V	velocity, m/s
W	pumping work demand, W
Greek symbols
α	absorber absorbance
φ	nanofluid volume fraction
ρ	density, kg/m³
μ	dynamic viscosity, Pa s
μ_s	dynamic viscosity at the surface, Pa s
ε	emittance
γ	mirror reflectivity
τ	transmittance
Subscripts
am	ambient
bf	base fluid is being
c	cover
ci	inner cover
co	outer cover
f	fluid
in	inlet
nf	nanofluid
np	nanoparticle
np1	nanoparticle of Al₂O₃
np2	nanoparticle of CuO
loss	losses
out	outlet
over	overall
o	reference
r	receiver
ri	inner receiver
ro	outer receiver
sky	sky
th	thermal
tube	receiver surface
u	useful
w	wind
Abbreviations
CFD	computational fluid dynamics
PTC	parabolic trough solar collector
SRT	straight receiver tube

References

Mohammed

Vuthaluru

Liu

. Thermohydraulic and thermodynamics performance of hybrid nanofluids based parabolic trough solar collector equipped with wavy promoters. Renew Energ 2022; 182: 401–426.

Alqarni

Mahmoud

Algehyne

, et al. Improvement of the thermal and hydraulic performance of parabolic trough collectors using hybrid nanofluids and novel turbulators with holes and ribs. Sustain Energy Technol Assess 2021; 47: 101480.

Samiezadeh

Khodaverdian

Doranehgard

, et al. CFD Simulation of thermal performance of hybrid oil-Cu-Al₂O₃ nanofluid flowing through the porous receiver tube inside a finned parabolic trough solar collector. Sustain Energy Technol Assess 2022; 50: 101888.

Mashhadian

Heyhat

Mahian

. Improving environmental performance of a direct absorption parabolic trough collector by using hybrid nanofluids. Energy Convers Manage 2021; 244: 114450.

Khan

Alsaduni

Alluhaidan

, et al. Evaluating the energy efficiency of a parabolic trough solar collector filled with a hybrid nanofluid by utilizing double fluid system and a novel corrugated absorber tube. J Taiwan Inst Chem Eng 2021; 124: 150–161.

Bellos

Tzivanidis

Said

. A systematic parametric thermal analysis of nanofluid-based parabolic trough solar collectors. Sustain Energy Technol Assess 2020; 39: 100714.

Bellos

Tzivanidis

. Thermal analysis of parabolic trough collector operating with mono and hybrid nanofluids. Sustain Energy Technol Assess 2018; 26: 105–115.

Almitani

Alzaed

Alahmadi

, et al. The influence of the geometric shape of the symmetrical twisted turbulator on the performance of parabolic solar collector having hybrid nanofluid: numerical approach using two-phase model. Sustain Energy Technol Assess 2022; 51: 101882.

Khetib

Sedraoui

Ammar

, et al. The numerical investigation of spherical grooves on thermal–hydraulic behavior and exergy efficiency of two-phase hybrid MWCNT-Al₂O₃/water nanofluid in a parabolic solar collector. Sustain Energy Technol Assess 2021; 47: 101530.

10.

Chakraborty

Das

Gupta

. Effect of spherical balls insert in collector tube of parabolic trough collector by considering Al₂O₃-based water. J Braz Soc Mech Sci Eng 2022; 44: 1–17.

11.

Chakraborty

Roy

Das

, et al. Computational analyses of parabolic trough solar collector in the presence of helical coil-insert. Int J Environ Sci Technol 2022; 46: 1–20.

12.

Subramani

Nagarajan

Wongwises

, et al. Experimental study on the thermal performance and heat transfer characteristics of solar parabolic trough collector using Al₂O₃ nanofluids. Environ Prog Sustain Energy 2018; 37: 1149–1159.

13.

Mwesigye

Huan

Meyer

. Thermodynamic optimisation of the performance of a parabolic trough receiver using synthetic oil–Al₂O₃ nanofluid. Appl Energy 2015; 156: 398–412.

14.

Zafar

Ali

Akhter

, et al. Characterization and performance investigation of metallic oxides based nanofluids in compound parabolic concentrating solar collector. Sustain Energy Technol Assess 2022; 54: 102786.

15.

Subramani

Nagarajan

Mahian

, et al. Efficiency and heat transfer improvements in a parabolic trough solar collector using TiO₂ nanofluids under turbulent flow regime. Renew Energ 2018; 119: 19–31.

16.

Heyhat

Valizade

Abdolahzade

, et al. Thermal efficiency enhancement of direct absorption parabolic trough solar collector (DAPTSC) by using nanofluid and metal foam. Energy 2020; 192: 116662.

17.

Tagle-Salazar

Nigam

KDP

Rivera-Solorio

. Heat transfer model for thermal performance analysis of parabolic trough solar collectors using nanofluids. Renew Energ 2018; 125: 334–343.

18.

Mahian

Kianifar

Sahin

, et al. Entropy generation during Al₂O₃/water nanofluid flow in a solar collector: effects of tube roughness, nanoparticle size, and different thermophysical models. Int J Heat and Mass Transfer 2014; 78: 64–75.

19.

Malekan

Khosravi

Syri

. Heat transfer modeling of a parabolic trough solar collector with working fluid of Fe₃O₄ and CuO/therminol 66 nanofluids under magnetic field. Appl Therm Eng 2019; 163: 114435.

20.

Bozorg

Doranehgard

Hong

, et al. CFD Study of heat transfer and fluid flow in a parabolic trough solar receiver with internal annular porous structure and synthetic oil Al₂O₃ nanofluid. Renew Energ 2020; 145: 2598–2614.

21.

Parlamıs

Ozden

Buker

. Experimental performance analysis of a parabolic trough solar air collector with helical-screw tape insert: a comparative study. Sustain Energy Technol Assess 2021; 47: 101562.

22.

Chakraborty

Roy

Das

, et al. Effects of helical absorber tube on the energy and exergy analysis of parabolic solar trough collector – a computational analysis. Sustain Energy Technol Assess 2021; 44: 101083.

23.

Rezaeian

Dehaj

Mohiabadi

, et al. Experimental investigation into a parabolic solar collector with direct flow evacuated tube. Appl Therm Eng 2021; 189: 116608.

24.

Norouzi

Siavashi

Oskouei

MHK

. Efficiency enhancement of the parabolic trough solar collector using the rotating absorber tube and nanoparticles. Renew Energ 2020; 145: 569–584.

25.

Bezaatpour

Rostamzadeh

Bezaatpour

. Hybridization of rotary absorber tube and magnetic field inducer with nanofluid for performance enhancement of parabolic trough solar collector. Renew Energ 2021; 168: 734–749.

26.

Mehdi

Bozorg

Toosi

. A numerical analysis of the effects of nanofluid and porous media utilization on the performance of parabolic trough solar collectors. Sustain Energy Technol Assess 2021; 45: 101179.

27.

Alnaqi

Alsarraf

Al-Rashed

AAAA

. Hydrothermal effects of using two twisted tape inserts in a parabolic trough solar collector filled with MgO-MWCNT/thermal oil hybrid nanofluid. Sustain Energy Technol Assess 2021; 47: 101331.

28.

Raheem

Siddique

Zaryab

, et al. Performance evaluation of adding helical-screw tape inserts in parabolic solar trough collectors as a source of cleaner energy production. J Cleaner Prod 2021; 297: 126628.

29.

Mishra

Senapati

Pandey

. Numerical simulation of solar parabolic trough collector with helical grooves using Cu nanoparticles. Mater Today: Proc 2022; 74: 867–873. https://doi.org/10.1016/j.matpr.2022.11.272

30.

Fattahi

. Numerical simulation of a solar collector equipped with a twisted tape and containing a hybrid nanofluid. Sustain Energy Technol Assess 2021; 45: 101200.

31.

Zaboli

Ajarostaghi

SSM

Saedodin

, et al. Hybrid nanofluid flow and heat transfer in a parabolic trough solar collector with inner helical axial fins as turbulator. Eur Phys J Plus 2021; 136: 841.

32.

Chakraborty

Das

Gupta

. Performance of parabolic trough collector having rotating receiver: effect of elliptical insert and hybrid nanofluid. Int J Energy Res 2022; 46: 15254–15275.

33.

Behar

Khellaf

Mohammedi

. A novel parabolic trough solar collector model – validation with experimental data and comparison to Engineering Equation Solver (EES). Energy Convers Manage 2015; 106: 268–281.

34.

Mwesigye

Meyer

. Optimal thermal and thermodynamic performance of a solar parabolic trough receiver with different nanofluids and at different concentration ratios. Appl Energy 2017; 193: 393–413.

35.

Bellos

Tzivanidis

. Parametric investigation of nanofluids utilization in parabolic trough collectors. Therm Sci Eng Prog 2017; 2: 71–79.

36.

Zhou

. Measurement of the specific heat capacity of water-based Al₂O₃nanofluid. Appl Phys Lett 2008; 92: 093123.

37.

Zhang

Xie

. Heat transfer and flow analysis of Al₂O₃–water nanofluids in microchannel with dimple and protrusion. Int J Heat Mass Transfer 2014; 73: 456–467.

38.

Minea

El-Maghlany

. Influence of hybrid nanofluids on the performance of parabolic trough collectors in solar thermal systems: recent findings and numerical comparison. Renew Energ 2018; 120: 350–364.

39.

Cengel

Ghajar

. Heat and mass transfer: fundamentals & applications. 4th ed. New York: McGraw-Hill, 2011.

40.

Mwesigye

Bello-Ochende

Meyer

. Heat transfer and thermodynamic performance of a parabolic trough receiver with centrally placed perforated plate inserts. Appl Energy 2014; 136: 989–1003.

41.

Petukhov

. Heat transfer and friction in turbulent pipe flow with variable physical properties. Adv Heat Transf 1970; 6: 504–565.

42.

Suresh

Selvakumar

Chandrasekar

, et al. Experimental studies on heat transfer and friction factor characteristics of Al₂O₃/water nanofluid under turbulent flow with spiraled rod inserts. Chem Eng Process 2012; 53: 24–30.