An extensive review of various technologies for enhancing the thermal and optical performances of parabolic trough collectors

A wide range of engineering industrial applications require both the thermal and optical efficiencies of the system to be maximized with a reasonable low penalty for the friction factor and subsequently low losses in pressure. Among the family of concentrated solar power systems, parabolic trough collectors (PTCs), which have recently received significant attention, face similar challenges. The current work presents an extensive review of the PTC systems comparing recent and past technologies, which are widely being used to improve and enhance the thermal and optical efficiencies. Furthermore, the techniques used for single and two‐phase flow modeling in numerical simulations, design variables, and experimental processes have been discussed in detail. The article also presents different numerical methods and analytical approaches of implementing the nonuniform solar distribution with different design parameters. Four main technologies are comprehensively addressed to effectively enhance the thermal performance of the PTCs; changing working heat transfer fluids, replacing the working fluids by nanofluids (single and hybrid) that have higher thermal–physical properties than those of base working fluids, inserting different tabulators with various design configurations, and finally combining the advantages of nanofluids and swirl generators in the same application. The article also critically summarizes the studies investigating the enhancement of thermal performance: use of novel design of PTCs and passive heat transfer enhancement techniques. Finally, a wide range of numerical and experimental studies are proposed for the future work related to the aforementioned main technologies.


| Concentrated solar power technology
It is widely known that global warming has become a defining issue of our time, with consequences that include shifting weather patterns, rising sea levels, and compromised food production. To address global warming, clean, renewable, and sustainable sources of energy should be identified to reduce the amount of CO 2 emissions. Solar thermal energy is one of the viable solutions to reduce reliance on fossil fuels, decrease the level of greenhouse-gas emissions, and meet the requirements of human societies with electrical power, water heating systems, and other industrial processes. Concentrated solar power (CSP) plants, in particular, rely on the direct normal irradiance, which can be described as the amount of solar energy received per unit area on the surface held normal to the rays of the sun. CSP plant technology can be categorized into four main families depending on the method used to collect and concentrate the solar radiant energy: (a) parabolic trough collectors (PTCs), (b) linear Fresnel reflectors, (c) parabolic dishes, and (d) solar towers. The operating principle of each technology is shown in Figure 1 (Blanco and Miller 1 ), while their main properties are listed in Table 1 (Philibert and Frankl 2 ). Presently, the most cost-effective and commercially developed technology among CSPs is the PTC system, particularly for medium-temperature applications, thus these systems are the subject of the present review.

| Fundamentals of PTC
As shown in Figures 2 and 3, PTC systems can be basically regarded as large heat exchangers, with the major components being the solar absorber, the glass envelope, the positioning system, the support structure, and the reflector surface; some of the main components of PTC systems are described below.

| Reflectors
This element consists of high specular reflectance (more than 88%) mirrors and structural components used to reflect the solar energy onto the receiver. Mirrors are normally made from low-iron float glass (approximately 4 mm thickness) of large solar transmittance, silvered from the back, and coated with selective coatings to maximize their solar reflectance (SR = 0.93) and durability. The installation, as well as the mounting of the structures, has a large effect on the overall performance of the plant (Kreith and Goswami 3 ).

| Absorber tube
The solar receiver converts the absorbed incident solar radiation into the thermal energy which is carried through the absorber via the heat transfer fluid (HTF; described below). This component (also called a heat collection element [HCE] or receiver) is the most important element in the PTC system, and is made typically from a steel tube that is coated with a multilayer cermet coating to provide very good optical properties, low thermal emissivity, and large solar absorptivity. Its length is generally 4 m between the two support braces and might be extended to 150 m. The inner and outer diameters of the absorber tube are typically of about 66 mm and 70 mm, respectively, whereas the inner and outer diameters of the glass envelope are of about 115 mm and 120 mm (Price et al 4 ). The annular space between the absorber tube and the glass envelope is generally kept at vacuum conditions (air pressure in the gap typically maintained at 0.013 Pa) to further reduce the heat losses (Hachicha et al 5 ).

| Heat transfer fluid
The function of the HTF is to collect the thermal energy absorbed by the receiver and to transport it to the storage system or directly to the power block in the case of solar thermal power plant (STPP) application. Selecting the appropriate HTF is application-specific and depends on the operating conditions and design peculiarities of each installation. Ideally, HTFs should have good thermal stability, should be able to operate safely throughout the range of temperatures of interest, should have good chemical compatibility with the tubing wall materials, and finally should be low cost and environmentally friendly. Additionally, a high thermal conductivity, high heat capacity, and large heat transfer coefficient are normally desired to maximize the heat transfer effectiveness, together with a low viscosity and a small thermal expansion coefficient to reduce pumping power and thermal expansion concern (Nahhas et al 6 ).
The main objective of this article is to critically review experimental and numerical investigations carried out on the thermal and optical performances of PTC systems, focusing specifically on reducing the thermal losses, reducing pumping power requirements, and enhancing the thermal efficiency by changing the working fluid, using nanofluids (single and hybrid) or by inserting swirl generators inside the absorber tubes. Another important objective is to discuss in details the effect of collector design on the thermal and optical performances taking into account shape parameters, mirror structure, absorber design, tracking system, absorber ends, absorber materials, and envelope characteristics. In comparison with recently published review papers on solar thermal energy, such as Jebasingh and Herbert, 7 Abdulhamed et al, 8 and Bellos and Tzivanidis, 9 this article differs in terms of scope, focus, and coverage. In particular: • The scope is here restricted to PTC systems and their applications, as documented in available experimental F I G U R E 2 The structure and elements of parabolic trough collector, from www.dlr.de.com 12  and numerical scientific studies dating as far back as 1986. • The present work provides a comprehensive account of promising technologies that can be used to improve the thermal performance of PTC systems (notably, nanofluids and swirl generators), and includes a critical assessment of the techniques that have been devised to take into account the nonuniform heat flux distribution of solar receivers. • The present work includes a comprehensive account of available models for estimating the thermo-physical properties of nanofluids for use in practical applications. • Providing important data for thermo-physical properties of single and hybrid nanofluids over a range of fluid inlet temperature and different particle sizes.
The practical significance of PTC systems is rather broad: to date, PTC systems have been successfully used in a range of applications, including power generation, water treatment (desalination and/or pasteurization), air conditioning and refrigeration, and hot water production, as summarized in Table 2 where selected key reference studies are also included. Figure 3 schematically illustrates a typical PTC system, which consists of a tubular receiver located along the focal line of the parabolic trough (mirrors). The receiver includes a metallic tube (externally covered by a selective coating) where the HTF flows, which is contained within an annular envelope usually made from glass. The heat transfer models for PTC systems are based on the thermal energy balance between the working fluid and the surrounding. Radiant energy from the sun is concentrated onto the receiver: part of this energy is absorbed by the HTF. Some of this energy is sent back to the glass envelope by radiation and natural convection, and some of it is lost via the support brackets by conduction mode. The last part (lost energy) can cross to the glass envelope by conduction as well and then from the glass envelope would pass it to the ambient by convection and to the sky by radiation.

| Mathematical analysis of the geometrical design
The geometrical profile of the typical PTC can be described by the following expression (Duffie and Beckman 21 ): The parameter f L is the focal line, which represents the position of the solar receiver. This parameter is determined by the following formula: In the equation above, w a is the width of the collector's aperture and φ r represents the rim angle. This angle can be calculated by the following expression: The variable r r is the rim radius which can be obtained from the following formula: Other important parameters related to the collector's geometry are the total collector aperture area A a and the outer surface area of the solar absorber A o , which can be calculated as follows: The parameter L is the length of the collector aperture. From the above equations, the geometrical Electrical power generation Larrain et al, 10 Hachicha et al 5 2 Water desalination process Jafari et al, 11 Raja and Vijay 12 3 Water pasteurization process Bigoni et al 13 4 Air-conditioning and solar refrigeration Fadar et al, 14 Al-Alili et al 15 5 Hot water production Hewett et al 16 6 Pumping irrigation water Larson 17 7 Solar cooker Noman et al 18 8 Industrial processes Larcher et al, 19 Kizilkan et al 20 concentration ratio (GCR) represents the collector's aperture area to the outer surface area of the absorber as following:

| Optical analysis of PTC's design
In this section, the optical efficiency and other related parameters are discussed. Based on the energy balance concept, the solar irradiation absorbed (Q abs ) by the collector is divided into two main parts; useful energy (Q u ) and heat losses (Q loss ) as follows: The typical optical efficiency (η o ) of the PTC is calculated from the absorbed solar energy (Q abs ) divided by the available solar energy (Q s ) as given below: The typical optical efficiency (η o ) varies with changing the incidence angle (θ) of the solar irradiation which can also be modeled and obtained depending on the incidence angle modifier (K) from the following expression: The modifier K(θ) is a function of geometrical parameters of the PTC additional to the incidence angle, which can be given by the following formula derived by Gaul and Rabl 22 : The previous expression considered the end loss of the PTC and cosine loss leads to calculating an accurate expression of the optical efficiency. The parameter (η o, max ) represents the maximum optical efficiency of the typical PTC, which is given by: The parameters (ρ opt , γ, τ, and α) are the optical reflectance, the intercept factor, the envelope transmittance and the receiver absorbance, respectively. For the optimum design of the commercial PTC, the intercept factor value is close to 1. However, the envelope transmittance and the receiver absorbance are design-specific variables that usually vary between 0.9 and 0.95. The optical reflectance takes usually values between 0.9 and 0.93 depending on all possible optical errors such as tracking error, shading coefficient, and so forth. Therefore, the maximum optical efficiency of a conventional PTC with a zero incidence angle is approximately 75% (Behar et al 23 ).

| Thermal analysis of PTC's system
In this section, the main parameters related to the thermal performance of the PTC are presented. These include the thermal efficiency, the thermal exergy, the solar available radiation, the useful exergy and useful energy, the heat transfer behavior, the friction factor, and the related pressure drop. The useful thermal energy (Q u [W]) carried by the HTF is determined by using the thermal energy balance on its control volume, which is given in the following equation (Duffie and Beckman 21 ): The solar energy (Q s [W]) that is absorbed by the solar collector can be determined as the solar beam radiation (G b [W/m 2 ]) multiplied by the reflector aperture area (A a ) as reported in the equation below: Then, the collector thermal efficiency is the ratio of the useful thermal energy to the absorbed solar energy, which can be given in the following expression: However, the overall collector efficiency is the ratio of the useful thermal energy to the absorbed solar energy taking the effect of pumping power into consideration, as suggested by Wirz et al 24 as follows: where η el is the electrical efficiency of the power block which was taken as 32.7%. However, W p is pumping power (W) and can be calculated by the following equations: where V . is volumetric flow rate (m 3 /s) and ΔP is the pressure drop (Pa) which can be calculated by using the Darcy-Weisbach equation as follows: where f is friction factor, U is the fluid velocity (m/s), L is the absorber length (m), D i is the inner absorber diameter (m), ρ is the fluid density (kg/m 3 ), and τ is the wall shear stress (Pa). The useful thermal exergy (E u [W]) output from the solar collector can be calculated from the following equation (Yazdanpanahi  et al 25 ): where T f represent the average fluid temperature (K) and T am is the ambient temperature (K). The last term of pressure drop is typically very small in practical applications, especially with liquids working fluids, and can therefore be neglected. The available solar exergy (E s [W]) can be calculated from the following equation suggested by Petela 26 : The sun temperature in the above equation is (5800 K) which is the real temperature in its outer layer. The exergetic efficiency then can be calculated as the ratio of the useful exergy to the input exergy, as follows: It is very important to take the exergetic efficiency into account because it is related to the maximum possible produced work. However, the thermal losses (Q loss [W]) from the outer surface of the absorber tube to the inner surface of the glass envelope are represented by the thermal radiation and thermal natural convection which can be written as follows (Bhowmik and Mullick 27 ): The variable k eff is the effective thermal conductivity, which can be calculated from the following expression: where b in the above equation is (0.5(D ie − D o )), and Ra b represents the Rayleigh number based on the gap between the absorber tube and glass envelope, and can be expressed by: The parameter β represents the thermal expansion coefficient 1/K and g is the gravitational acceleration (m/s 2 ). Nevertheless, the thermal losses in the annular space when operated under vacuum conditions are represented by only radiation mode since the pressure is too low and the free molecular convective heat transfer can be neglected. Thus, the radiation heat loss from the outer surface of the solar absorber to the inner surface of the glass envelope can be given in the following equation (Duffie and Beckman 21 ): The subscripts i and o refer to the inner and outer surfaces of the absorber tube, respectively, while ie and oe refer to the inner and outer surfaces of the glass envelope, respectively, and ε is the surface emissivity. Depending on the concept of energy balance on the solar collector, it is obvious that the heat losses from the solar receiver to the glass envelope is the same as the thermal energy transferred by conduction through the glass envelope and from the glass envelope to the surroundings by radiation and to the ambient by convection. As such, the thermal losses from the glass envelope can also be calculated as follows (Bhowmik and Mullick 27 ): where σ is Stefan-Boltzmann constant which is approximately 5.67 × 10 −8 W/m 2 K 4 and ε oe represents the emissivity of the glass envelope which depends strongly on the temperature of the outer surface of the glass envelope and its material made from. The convection heat transfer coefficient of the ambient can be calculated from the equation below, as suggested by Bhowmik and Mullick 27 : The parameter V w is the wind speed, which is normal to the axis of the solar receiver. However, the sky temperature is a function of ambient temperature and can be given by the following equation (Swinbank 28 ): It should be noted that in the case of removing the glass envelope entirely from the PTC system, the thermal losses would transfer directly from the absorber tube to the ambient and surrounding, that is, the parameters of absorber tube should be used instead of those of the glass envelope in the thermal losses expression (Equation (27)) resulted in the following formulation: The emissivity of the solar receiver ε o depends strongly on the temperature of the outer surface of the solar receiver, receiver materials, and selective coatings. However, the convection heat transfer coefficient of the ambient in the case of removing the glass envelope can be calculated from the following formulation: In addition to the previous equations of the useful thermal energy, the thermal energy transferred from the wall absorber to HTF is the main parameter of heat transfer analysis, which strongly depends on the convection heat transfer coefficient. Therefore, the useful thermal energy can also be given in the form below (Duffie and Beckman 21 ): The parameter A i is the inner surface area of the absorber tube. However, the convection heat transfer coefficient is determined from the Nusselt number Nu, which depends on the absorber geometry and flow conditions. Besides, two important nondimensional numbers are involved in the calculation of Nu number: the Reynolds number Re and Prandtl number Pr. For the case of solar absorber, these numbers (Nu, Re, and Pr) are given in the equations below (Incropera et al 29 ): The variables k, ρ, U, μ, and C p are fluid thermal conductivity (W/m K), fluid density (kg/m 3 ), fluid velocity (m/s), fluid dynamic viscosity (Pa s), and fluid specific heat capacity (J/kg K), respectively. In the solar absorber, the turbulent flow occurs with Re number greater than or equal to 4000 and Nu number can be predicted with empirical correlations for turbulent pipe flow, such as those of Petukhov 30 Either of these two equations can be used for the validation (the latter is in fact a modification of the former to extend its range of validity to lower Reynolds number values; where the ranges of applicability overlap the two correlations provide comparable predictions). The variable f is the friction factor, which strongly depends on the Re number and can be given by the turbulent flow correlation of Petukhov 30 However, for tubular flow in laminar conditions when Re ≤ 2300, the Nu number (at constant heat flux) and friction factor can be predicted as follows ( Table 3, where ΔT is the average fluid temperature above the ambient temperature ( C) and I is the solar irradiation (W/m 2 ). To estimate the maximum efficiency under dynamic conditions, Xu et al 34 tested an outdoor rig and compared the results with a simple multiple linear regression solver. The reported maximum efficiency for the outdoor rig was around 42%. To further understand the receiver heat losses in the PTC system, Lei et al 35 performed measurements for a new design solar receiver using energy balance for steady and quasi-steady-state equilibrium conditions. Results revealed that the thermal emittance and the receiver temperature, which are very important parameters in the calculation of thermal losses, were both affected by nonuniform heat flux. Moreover, experimental correlations have been proposed of total thermal losses per meter of absorber length for any collector with a glass envelope and restricted to some limitations as clarified in Table 4.
Coccia et al 36 manufactured a low-cost PTC system called UNIVPM.01 to evaluate the thermal efficiency of the collector. Under different operating conditions, they were able to conclude that the thermal efficiency of the collector deteriorated with an increase in the thermal input (the slope efficiency was found to be around −0.683). To study the end losses, Li et al 37 undertook an experimental study with different geometries using the method of reduction; lengthening the receiver, adding end plane mirrors, inclining the PTC, and so forth. Moreover, Wu et al 38 also performed an experimental research to measure thermal losses from the PTC system using a new molten salt characterized with a low melting point of 86 C and operation temperature of 550 C. The working fluid was circulated over 1000 hours in the thermal system; Figure 4 shows the experimental rig equipment. This new molten salt resulted in lower risk at start-up, operation, and shut down of the system, as compared with working fluids with higher melting point. On the other hand, higher thermal loss was obtained compared with the PTC using thermal oil due to higher working temperature of molten salt.
Researchers mentioned in the preceding studies considered the typical type of solar absorber material (ie, steel) whereas Geete et al 39 examined the thermal performance of the fabricated PTC using four arrangements: copper-engine oil (a pipe is made from copper and engine oil is the working fluid), copper-water, mild steel-engine oil, and mild steel-water combinations. According to their results, the highest temperature difference was 59 C using mild steel-engine oil arrangement operated at 12:30 PM with a mass flow rate of 0.0024 kg/s. To study the performance of the solar field as a whole, Kumaresan et al 40 and Sivaram et al 41 investigated experimentally the performance of a PTC with a storage system during the charge process. They measured the solar irradiation intensity using a pyrheliometer at every 15 minutes and temperatures of HTF (water) at inlet and outlet using thermocouples connected with a data acquisition system. Moreover, they measured errors related to the fundamental data, that is, mass flow rate, temperature, and solar insolation using the root sum square approach in order to determine the collector efficiency. It was pointed out that the instantaneous collector efficiency is highly dependent on two important factors: useful heat gain and incident beam irradiation; the experimental set up Kumaresan et al 40 is presented in Figure 5.
To gain more understanding about the PTC mechanisms, Kumar and Kumar in [42] used two different modes: tracking and south facing under the Indian climate with and without a glass envelope. As a consequence, the maximum outlet temperature was observed at the minimum mass flow rate (T = 54.7 C at m = 0.001 kg/s of the south facing orientation and T = 45.6 C in the mode of tracking). Furthermore, by increasing the mass flow rate for all the south facing cases (0.024 kg/s), the thermal efficiency was increased to 53.33% with glazing and to 46.17% without glazing. The interesting observation noticed from this research is that there is no significant change in the thermal efficiency by further increasing the mass flow rate beyond 0.024 kg/s. Tajik et al 43 investigated experimentally the thermal efficiency of the solar PTC using porous medium instead of classical working fluids. Three different fill cases have been examined; free absorber, partly filled with copper foam and fully filled copper foam, see Figure 6 for more details. Results revealed that the overall thermal loss coefficient with fully filled copper foam case has reduced to 45% and thus the thermal efficiency increased accordingly.
Recently, Agagna et al 44 experimentally investigated the optical and thermal performances of a small-scale parabolic trough power plant called (MicroSol-R) with a single storage tank system, the system diagram is presented in Figure 7. Three PTCs are installed in this platform in different directions: one of them is oriented in North-South direction whereas others are oriented in East-West directions. The optical efficiency range obtained was between 40% on December (13:00) and 77% on June (8:00-16:00). Mouaky et al 45 studied the thermal performance of the 186 kWth PTC under a semi-arid climate in Morocco concerning the effect of soiling on the energy production of the system. Results revealed that the proposed design can produce 388 Tons of steam at 500 kPa.
Regarding the exergy performance in PTCs, the huge amount of exergy destruction results from the concentration of sunrays on the absorber coatings. One possible solution has been provided recently by Wang et al 46 by comparing experimentally the exergy destruction considering the rotatable axis performance and a fixed axis oriented in North-South direction under the Chinese climate. The proposed idea of rotatable axis has reduced the exergy destruction and thus the exergy efficiency of the PTC could be enhanced by 3% annually. This is because the angle of the PTC can be easily perpendicular to the sun location with rotatable axis compared with the fixed one; the diagrams of both configurations are illustrated in Figure 8. However, Bakos 47 studied experimentally the effect of performing tow-axes tracking system compared with a fixed-axis system oriented in the South direction under the Greece climate. The solar energy collected has enhanced up to 46.46% with the proposed system.

| Analytical and numerical investigations
The mathematical models in the early time of PTC technologies were simplified and therefore not adequate for predicting the effective thermal performance, for informing design procedure analysis, or for controlling the accuracy of numerical predictions. Therefore, the numerical computation of the collector thermal performance and the assessment of the optical efficiency were really difficult to accurately obtained (Jeter 48 ). Researchers paid attention after that and significantly improved the mathematical models and combined both optical and thermal features besides all components of the PTC system in order to effectively assess their behavior (Price et al 4  considerably more expensive and time consuming than numerical simulations, and not all parameters of interest can be easily measured. In this section, different works are presented showing the main modeling approach and their achievements. Within a PTC system, there still remain a number of issues that needs addressing, one of them being the performance of the solar collector tube receiver. Due to the inherent design of the solar collector tube (one side always exposed to the direct sunlight and the other to reflect light through mirrors), the heat flux around the periphery is never uniform. This nonuniform heating within the pipe leads to local stratification and other heat flux mixing problems, eventually reducing the operational efficiency of the whole plant. Various methodologies currently exist to mathematically address this problem of nonuniform heat flux distribution around a solar receiver. Jeter 49 studied this problem with an analytical model where he derived a semi-finite formulation from the first integral of the concentrated flux density differential equations for the types of trough collectors. Thomas and Guven 50 also studied the effect of the heat flux distribution around the receiver of a PTC system for several optical configurations. It was deduced that the heat flux around the collector receiver is nonuniform in the circumferential direction for the horizontal tubes but symmetrical for the vertical receivers.

| Ray-tracing method
To really understand the nonuniform heat flux distribution around the absorber tube numerically and how to apply the nonuniform heat flux distribution in Computational fluid dynamics (CFD) solvers, the Ray-tracing technique is very common tool used to analyze and design the optical optimization and performance of the PTC. This technology provides detailed information about the optical features of the PTC with many surface options of imaging equations (Gaussian, Newtonian, etc.). In the literature, several tools use the ray-tracing technology, including SimulTrough, Opticad, SolTrace, TracePro, and ASAP (Advanced Systems Analysis Program); some visualization examples found in literature are presented in Figure 9. However, for the analysis of the optical characteristics of the PTC system, researchers in the numerical field have used extensively the Monte Carlo Ray Tracing (MCRT) model by either writing their own codes or utilizing the previous tools.
Grena 51 reported optical simulation of the PTC with and without glass envelope under realistic solar irradiation using a ray-tracing approach in three dimensions. The optical properties were considered as wavelengthdependent and the light-ray was taken as the basic element of simulations. More aspects have been also modeled realistically such as investigating the effect of tracking error and studying the intensity absorbed by the solar receiver. Yang et al 52  and tracking errors, whereas the solar rays were assumed to be nonparallel. The obtained result is the local concentration ratio (LCR) profile of an ideal PTC which was compared with the analytical results of Jeter. 49 The resulting curve showed the same trend as Jeter's.
He et al 53 produced an optical model based on combining the MCRT model with finite volume method (FVM) to solve the conjugated heat transfer models in the PTC considering the effect of various geometric concentration ratios and different ring angles on the optical performance. Their results have been compared with the analytical results of Jeter, 49 finding less than 2% average errors. They found also that the heat flux distribution curve was divided into four regions: direct radiation region, heat flux decreasing region, heat flux rinsing region and the region of shadow influence. Cheng et al 54 performed a CFD simulation on the receiver tube in three dimensions using the k-ε turbulence model. The MCRT model was combined with CFD solver in order to apply the nonuniform heat flux distribution. The authors compared results with the measurements of Dudley et al 33 and reported a difference of roughly 2%.
Cheng et al 55 developed their own MCRT code for a general-purpose numerical model of concentrating solar collectors (CSC). The model investigated and analyzed the photo-thermal conversion procedures in three different applications of the CSC (ie, PTC systems, parabolic dish collectors, and pressurized volumetric receiver systems). The reliability of the output curves was also compared with Jeter 49 results and good agreement was shown. Another numerical attempt to apply the nonuniform heat flux distribution was proposed by Hachicha et al, 5 where the authors performed a finite volume based numerical investigation with the Ray Trace model to develop an optical model for determining the nonuniform heat flux distribution around the solar receiver. The results were compared with analytical results of Jeter 49 with a maximum deviation of less than 8%.
Later, Zhao et al 56 developed their own MCRT simulation code to optimize and calculate the heat/density flux distributions on the solar receiver, considering in their simulations rim angles, GCRs, glass envelope transmittance, receiver absorption, envelope reflectivity, mirror reflectivity and nonparallelism of the sun rays (using cone optics). Their results yielded good agreement with Jeter. 49 Moreover, Kaloudis et al 57 represented the approximated LCR by using 7-curve fitting equations compared with the MCRT model suggested by Cheng et al. 54 The curves generated are third degree polynomial functions in a form of: where ; is an absorber angle and b 3 , b 2 , b 1 , b 0 are constants have different values depending on the range of the absorber angle, given in Table 5.
Liang et al 58 proposed their own code for three different optical models based on the ray-tracing method. Each model has its own optical approach: the first model is based on the MCRT method, the second model is based on the initialization of the photon distribution with Finite Volume approach, while the third model is based initially on the FVM to determine the ray locations and then by multiplying reflectivity, transmissivity and absorptivity changed to the photon energy method. The third model was superior where the computational effort was less than this of the first model by 60% and the running time was shorter than that of the first model by 40%. Liang et al 59 extended their own previous code to present four different optical models using the Monte Carlo Method and finite volume approach, combined with a novel approach to initialize the profile of photons and to describe the reflecting, absorbing, and transmitting processes; the photon distribution in both cases is presented in Figure 10. The finding results yielded good accordance compared with Jeter 49 findings.
Houcine et al 60 established their new code using a numerical approach based on ray-tracing 3-Dimensions 4-rays (RT3D-4R) under realistic optical properties and F I G U R E 9 Visualization of the parabolic trough collector under nonuniform solar energy using raytracing model [Colour figure can be viewed at wileyonlinelibrary.com] solar coordinates (one axis and dual tracking system) of the PTC system. Moreover, they also studied the effects of the rim angle and geometric concentration ratio on the overall gain solar energy reflected on the solar receiver. Results showed good agreement compared with findings of Jeter, 49 He et al, 53 and Hachicha et al. 5 Agagna et al 44 introduced three different models of variable degree of sophistication for PTCs using the MCRT: model 1 is a simple one-dimensional model and simpler, model 2 is a two-dimensional model that can be used to predict the thermal characteristics of the PTC system, while model 3 is the most accurate and can provide detailed information about the realistic nonuniform heat flux distribution on the solar receiver. Hoseinzadeh et al 61 also introduced their own code based on MCRT method to produce optical and thermal models in MATLAB with optimizing three different design parameters: the collector aperture, the solar absorber diameter, and the rim angle. The maximal optical efficiency obtained was 65% for the PTC with 0.6 m aperture width, 100 rim angle and 0.025 m absorber diameter. Cheng et al 62 proposed a novel computational approach of producing a fitting formula of an optical efficiency of the PTC based on combining the MCRT model with the population-based particle swarm optimization algorithm. Results are in good agreement with Jeter. 49 From the scenario explained previously, the main objective of all researchers is to produce the distribution of the LCR, which represents the heat flux distribution around the solar receiver after multiplying it by the direct normal irradiation. Once that is applied properly, there is no need to take the parabolic structure into account. Moreover, all preceding findings have been compared with those of Jeter 49 and presented in Figure 11 over a period of time between 1986 and 2018.

| Design parametric investigations of PTCs
As explained previously, the heat flux distribution is nonuniform over the glass envelope in the circumferential direction of the conventional PTC design. This property, in addition to the thermal performance and optical properties, can be affected by different design parameters such as optical errors, rim angle, material deflection, reflector mirrors, aperture width, receiver geometry, GCR, tracking system, tracking orientation, incidence angle, Re number, inlet temperature of working fluid, and so forth. Therefore, in this section, the numerical and analytical studies concerned these issues are presented.

Part
; The effect of the rim angle on the PTC performance plays a key role in the thermal heat flux behavior, bending deflection in the absorber tube and entropy generation. Khanna et al 63 investigated the effect of deflection, optical errors, and rim angle on the circumferential heat flux distribution. Results showed that the heat flux distribution increased and became more distributed on the circumference with decreasing the wall deflection while the heat flux became more distributed on the circumference with zero optical errors. The optimum rim angle was suggested to be 110 so as to maximize the total heat flux. Wirz et al 24 studied the effect of changing the rim angle on the thermal efficiency using several secondary mirrors and receiver diameters. Results showed that the optimum rim angle which led to the maximum thermal efficiency was also 110 . Moreover, the thermal efficiency was found to increase of 0.8% to 1.6% by applying the secondary mirrors compared with the benchmark design.
Mwesigye et al 64 investigated the effect of rim angle and concentration ratio on the heat transfer and entropy generation. They pointed out that the entropy generation heat transfer, increased with reducing the rim angle and slightly increased with increasing the concentration ratio. Khanna et al 65 found that by increasing the rim angle from 60 to 140 , the maximum temperature difference of the receiver in the circumferential direction was reduced from 16 C to 7 C, and the maximum receiver deflection was also reduced from −9 mm to −1.7 mm. Khanna and Sharma 66 examined also the effect of rim angle, aperture width and optical errors on the total flux availability and solar flux distribution. By increasing the rim angle from 60 to 135 , the maximum difference in solar flux reduced from 46 to 22 kW/m 2 . However, increasing the aperture width led to further increase in the heat flux nonuniformity in the circumferential direction. The same trend has been noticed with increasing the optical error in which the flux availability has also reduced from 45 to 30 kW/m 2 . The authors finally concluded that the rim angle could not be the independent variable to evaluate the thermal performance.
Forristall 67 developed a comprehensive study of heat transfer model using engineering equation solver (EES) by utilizing both one-and two-dimensional heat transfer models. It was concluded that the predicted performance of heat collector was in good agreement with the experimental data of AZTRAK (Dudley et al 33 ). It was also determined that the best material for the absorber tube was type 321 hours stainless steel due to its strength and reduction in the bending problem. Furthermore, the coating type (its emittance is 0.07@ 400 C proposed coating) increased the efficiency by 8.5% whereas the vacuum annulus type led to the best performance. However, the heat flux distribution cannot be implemented as nonuniform distribution in EES. Tao and He 68 studied the heat transfer and fluid flow behavior inside the solar collector and inside the annular gap as well for different Rayleigh numbers and tube diameter ratios (inner absorber diameter/inner envelope diameter). They found that with increasing the tube diameter ratio, the Nusselt number in the annular gap dropped gradually while increasing in the inner tube diameter. They also highlighted that the natural convection process in the annular gap must be considered when the Rayleigh number is higher than 10 5 .
To calculate the optical efficiency of PTCs, Huang et al 69 proposed a new analytical model which was modified and integrated to study the collector performance of a PTC with a vacuumed tube envelope using a numerical integration algorithm program considering the effect of different tracking error and different displacement error. Lu et al 70 investigated analytically the effect of both uniform and nonuniform heat transfer distributions on the thermal performance under on-sun and off-sun conditions. They reported that the receiver heat transfer was nonuniform with a larger heat loss and surface temperature under on-sun conditions, while the receiver heat transfer was more or less uniform with only slight differences in surface temperature and heat loss coefficient under off-sun conditions (zero beam irradiation); therefore, the better performance for the solar PTC was evaluated to be under the nonuniform heat flux distribution. Another numerical approach proposed by Cheng et al 71 was aimed at combining the MCRT model with the FVM in a parametric study on the heat flux density and temperature distribution. It was suggested by the authors that the solar heat flux distribution curves should not be divided into four areas as indicated by other researchers; He et al. 53 Wu et al 72 examined the heat loss from a PTC with annular gap in conjugated heat transfer configuration using the FVM coupled with the (MCRT) model and the standard k-ε turbulence model. It was concluded that the thermal loss resulted from bellows is about 7% of the total thermal loss. Moreover, it was found that an inverse relation exists between the HTF velocity and the temperature gradient of the absorber metal. However, an alternative numerical approach to represent the nonuniform heat flux was presented by Okafor et al 73 using the sine equation expression in terms of concentrated base-level heat flux under laminar flow regime. Different Re numbers, different receiver diameters, and different fluid inlet temperatures have been considered to study their effect on the secondary flow. Ray et al 74 preformed numerical 3D simulations considering the glass envelope as semitransparent and modeling the selective coating on the outer surface of the solar absorber with a range of DNI (750-1000 W/m 2 ) and different mass flow rate of the working fluid (1.7-17.6 kg/s). Results showed that the temperature difference in the circumferential direction decreased by 71.95% with increasing the mass flow rate from 1.7 to 17.6 kg/s and the thermal efficiency has been affected slightly with increasing the DNI as well as mass flow rate.
Tripathy et al 75 examined the effect of different absorber materials on the thermal and mechanical performances using steel, copper, Bimetallic and Tetralayered laminate with different flow rates. According to their results, the effect of changing the absorber material on the transferred energy to HTF is quite small and can be neglected. However, it has a considerable influence on the bending owing to the thermal expansion and selfweight. They found that steel causes poor temperature distribution in the circumferential direction due to its lower thermal conductivity, whereas copper behaves better, but has heavier self-weight. Finally, the Tetralayered laminate provided the best temperature distribution and reduced the maximum deflection by 45% to 49% as compared with steel.
Donga and Kumar 76 studied the thermal performance of the PTC with absorber tube misalignment at a range of volumetric flow rate (5.65-33.9 m 3 /h), slope error range of (0-3 mrad) and two different receiver diameters of 70 mm and 80 mm. It was pointed out that the thermal efficiency is only affected slightly (reduction up to 3%) by receiver dislocation in the presence of slope errors. Moreover, there was insignificant effect on the thermal efficiency by the receiver misalignment with zero slope error. The effect of incidence angle on the PTC performance has been addressed recently by Zou et al, 77 where they investigated the thermal performance of the PTC depending on nonideal optical parameters including sunshape, incidence angle, tracking error, slope error, and absorber alignment error. Results illustrated that the thermal efficiency has significantly dropped by 41.11% as the incidence angle increased from 0 to 60 . Moreover, increasing slope errors and tracking errors caused considerable reduction in the thermal efficiency.
Recently, Xu et al 78  Reduction in thermal losses when using water as working fluid.

Forristall 67 Numerical
Testing the effect of different working fluids on the thermal performance.
Selected (Xceltherm 600 and Syltherm 800) as the best candidates which led to noticeable increase in the thermal efficiency and reduction in the heat losses.
Gong et al 84 Experimental The ends of absorber were covered by heat insulator.
46.18% reduction in heat losses.
Roesle et al 85 Numerical Keeping low pressure in the gap between the receiver and the glass jacket using a vacuum pump.
If the operating temperature increases to more than 400 C, the absorber tube would suffer from extreme heat losses.
Lei et al 35 Experimental Using a new solar receiver with a high vacuum system and a vacuum gauge.
The new design provided better thermal performance since the heat losses drastically reduced.

Yaghoubi et al 86 Experimental and numerical
Three types of cover used in parabolic trough collector; vacuum, lost vacuum, and broken glass tube.
Heat losses in cases of lost vacuum and broken glass tube were 46% and 58.5%, respectively, larger than that of vacuum tube leading to a drop of 3%-5% and 19%, respectively, in the overall system performance. noticed when using liquid sodium compared with other fluids and the temperature profile on the circumferential direction became more uniform. Moreover, the PTC with larger aperture performed better than this with smaller in terms of absorbing more energy and reducing the thermal gradient. Norouzi et al 81 studied numerically the effect of different parameters on the collector's performance including absorber materials, Re numbers, nanofluids, and rotational speed of the absorber in 2D and 3D unsteady models. It was concluded the collector's efficiency using Aluminum absorber material is 25% larger than any other materials with rotational speed of 0.25 rad/s and volume fraction of 3%. It was also suggested that, because the thermal efficiency could either increase or decrease as the rotational speed is changed due to the fluctuating performance of the thermal efficiency, the rotational speed should be chosen properly. Figure 12 shows the effect of rotational speeds.

| THERMAL LOSSES
The most important issue in PTC systems is how to minimize the overall heat losses which would act to greatly improve the thermal performance of PTCs which in turn leads to gradually enhance the overall collector efficiency. On the other hand, the absorber heat loss has a negative effect on decreasing some parameters, thermal properties, flow quantity, and the HTF temperature delivered by the solar field. For this reason, the HCE should be effectively designed to minimize heat losses to the free air. The process of covering the receiver tube with a glass envelope acts to reduce the radiative and convective heat losses to the environment. Furthermore, coating the absorber tube with a selective coating (having large absorption rates, more than 0.95) helps also in reduction of radiative heat losses. To seek a further reduction in the thermal losses, the gap between the receiver and glass envelope can be operated under vacuum conditions with very small air pressure (0.013 Pa), which helps to significantly reduce the natural convection heat loss. Another possible approach is designing the absorber tube to be long (L ≥ 4 m) and choosing the absorber diameter to be small relative to the collecting aperture, which leads to minimization of conduction heat losses at the absorber ends (Burkholder and Kutscher 82 ). A summary of various techniques to improve the thermal performance of the PTC system is provided in Table 6.

| EFFECT OF CHANGING HTFS ON THERMAL AND HYDRAULIC PERFORMANCES
The working fluid is one of the most important elements in determining the thermal performance of PTC systems. Recent estimates until reported that there are about 63 fully operational STPPs with PTC systems around the world. Sixty-one of these plants use thermal oils as the working HTF with the maximum working temperature of 398 C. The main reasons for the use of thermal oils are: low vapor pressure, affordable price, long life, and thermal stability. However, this does not in any way mean that thermal oils are the best candidates for the working fluid as they also have some key drawbacks, including the limitation of temperature (around 400 C), and environmental toxicity and flammability (Blanco and Miller 1 ). There are currently three alternative HTFs that have been examined in the literature: liquid-water/steam (referred to direct steam generation), pressurized gases, and molten salts. Each of these working fluids has its own advantages • The plant configuration is simpler.
• The steam temperature is larger.
• No pollution and no fire hazard.
• No thermal storage system.
• The solar field control is more complex.
• Pressure in the solar field is larger.
Compressed gases More than 500 • The steam temperature is larger.
• Thermal storage is cheaper.
• No pollution and no fire hazard.
• Heat transfer coefficient is smaller.
• The solar field control is complex.
• Higher pressure in the solar field.
• Pumping power required is larger.
• The steam temperature is larger.
• Thermal storage is cheaper.
• No pollution and no fire hazard.
• Electricity self-consumption is larger.
• Design of solar field is complicated.
and disadvantages when compared with thermal oils. A brief comparison between different working fluids is presented in Table 7. It can be clearly observed from this table that none of the considered fluids is a perfect solution as they all have some constraints or technical issues that need to be resolved. A further comprehensive review of the different HTFs used in the PTC systems is summarized in Table 8. Larger solar irradiation has been absorbed when using super-critical carbon dioxide.

| THERMAL PERFORMANCE IMPROVEMENT BY ADDING NANOPARTICLES
One of the most useful techniques to improve the thermal performance in PTCs is to add metallic or nonmetallic nanoparticles to the base working fluid which leads to the creation of a so-called nanofluid. The added nanoparticles having different thermal properties than those of the base working fluid make the working fluid mixture more efficient and effective; in particular, the higher thermal conductivity and lower specific heat T A B L E 9 Thermal properties of particles used in previous studies capacity which leads to enhance the overall performance of the absorber tube. Furthermore, the presence of nanoparticles in the base fluid helps also in a notable decrease in effective thermal stresses on the absorber tube. However, a further increase in nanoparticle volume fractions can lead to the agglomeration and clustering of the nanoparticles inside the solar receiver thereby resulting in increasing the requirement of pumping power. For this reason, the nanoparticle volume fraction has to be optimized for an efficient heat transfer augmentation and reasonable friction factor and accordingly pressure drop. The nanoparticles utilized currently in the PTC applications can be metallic (like Al, Ag, Au, Cu, Fe, etc.), nonmetallic (such as Al 2 O 3 , CuO, Fe 2 O 3 , SiO 2 , TiO 2 , NiO, ZnO, etc.), or carbon nanotubes (CNT) includes single-walled nanotubes (SWCNT) and multi-walled carbon nanotubes (MWCNT). The thermal properties of a wide range of nanoparticles are described in Table 9 over a range of inlet temperatures and different particle sizes.

| Proposed correlations of thermophysical properties
From a numerical modeling perspective, a nanofluid can be simulated using either as a single-phase or a twophase model. Both of these approaches have been used in literature with the two-phase model approach being the more accurate one. However, the selection of the thermophysical properties is critical, when it comes to ensuring acceptable predictions via modeling nanofluids. For this reason, various models and correlations from the literature are presented below.

| Density of nanofluid, ρ nf (kg/m 3 )
The mixture of base fluid and nanoparticles is considered to be a heterogeneous mixture which can be composed of different parts and can easily be distinguished either by the naked eyes or by a microscope, see Figure 13. The total mass of both solid and fluid materials can be introduced in the heterogeneous mixture in terms of densities as expressed below (Pak and Cho 109 ): 6.1.2 | Specific heat capacity of nanofluid, C p, nf (J/kg K) This property can be derived based on the energy balance for incompressible substances which is expressed in the following way (Xuan and Wilfried 118 ), which is used very commonly in the literature: Another correlation was proposed by Pak and Cho 109 based on the volume fraction of two substances is given by the following formulation: It should be noted that the correlation proposed by Xuan and Wilfried 118 (Equation [43]) is widely applicable and more accurate than the one given by Pak and Cho 109 (Equation [44]) as the latter correlation is based on a universally representing property, that is, the nanofluid density. Further evidence is provided by O'Hanley et al, 119 which compare the results from both the correlations with the experimental data of different nanofluids. O'Hanley et al, 119 reported that the results predicted by the Xuan and Wilfried 118 correlation were much closer to the experimental data than those predicted through the Pak and Cho 109 correlation for all nanofluids.

| Dynamic viscosity of nanofluid, μ nf (kg/m s)
The dynamic viscosity of solid-fluid suspension was first proposed analytically by Einstein 120 and Einstein 121 based on the molecular model, which considered the solid particles as noninteracting spheres as follows: This model is only applicable to nanofluids with low volume fraction ≤2%. After that, Brinkman 122 developed the previous analytical model by adding the effect of the velocity modification resulted from the presence of sphere particles and giving the following formulation for uniform mixture: This model is assumed to be applicable for high concentration ratio, φ ≤ 4%. However, this model has been extended further by Batchelor 123 to take the Brownian motion effect into account in addition to the hydrodynamic interactions of the sphere particles with a volume fraction less than 10%: μ nf = μ f 1 + 2:5φ + 6:2φ 2 À Á : ð47Þ For a typical volume fraction, the last three models would produce almost identical results. For example, at 1% (0.01) volume fraction, the effective viscosity (μ nf /μ f ) of the last three models are 1.025, 1.0254, and 1.0256, respectively. Another analytical attempt was performed by Happel 124 considering the tangential stress resulted from the presence of solid particles under creeping flow conditions: However, this expression produces very high nanofluid viscosity compared with the preceding models. On the other hand, experimental studies have also contributed different expressions of dynamic viscosity of nanofluid, one being performed by Buongiorno 125 where the author used the experimental data of Pak and Cho 109 and correlated the dynamic viscosity for both γ-Al 2 O 3water and TiO 2 -water and presented in the following expressions, respectively: μ nf = μ f 1 + 5:45φ + 108φ 2 À Á : Khanafer and Vafai 126 considered the same experimental data of Pak and Cho 109 and derived the following formulations of the dynamic viscosity for both nanofluids (γ-Al 2 O 3 -water and TiO 2 -water), respectively: μ nf = μ f 1 + 23:1φ + 1525φ 2 À Á ð51Þ Although all four previous viscosity models are based on the same experimental data, the factors in the corresponding expressions are apparently different. However, the resulted viscosity values for the same nanofluid are comparable. Another experimental study was performed by Wang et al 127 where they measured the viscosity of Al 2 O 3 -water, which was higher than that measured by the Pak and Cho 109 by 2.5 times. That could be due to the effect of particle size and shape or might be due to the effect of non-Newtonian flow behavior, which has a vital role in nanofluid measurements. However, Maiga et al 128 used the same data of Wang et al 127 and derived the following expression: It is noticeable that factors of this model are considerably smaller than those of Pak and Cho 109 but clearly larger than those of analytical correlation proposed by Batchelor. 123 This model is very common and widely used in the available literature and it can be recommended for more accurate results. Chen et al 129 measured experimentally the effective viscosity of another nanofluid (TiO 2 -ethyl glycol) and derived the following correlation: This correlation is valid for a volume fraction up to about 10%. It is noticeable from the correlations presented previously that the viscosity equation is currently modeled with a polynomial expression of degree two. However, some authors, including Mooney 130 followed by Tseng and Chen 131 and Tseng and Lin, 132 proposed a viscosity equation in the exponential form as below: To conclude, the exponential expression for the nanofluid viscosity is not recommended due to higher values predicted as compared with the polynomial expressions. Moreover, a small error in volume fraction calculation would lead to significant error in the viscosity value when using the exponential function. Therefore, it is currently recommended to utilize the polynomial function with degree two based on the temperaturedependent base fluid viscosity (Michaelides 134 ).
6.1.4 | Thermal conductivity of nanofluid, k nf (W/m K) The first model for calculating the electrical conductivity of a heterogeneous solid-fluid mixture of spherical particles was proposed by Maxwell 135 in the following expression: This model is only applicable for a volume fraction less than 1%. The same analytical investigation had been proposed by Bruggeman 136 to derive an expression of thermal conductivity of nanofluid with different regular shapes. The resulted correlation is given by: The coefficient n represents the particle shape. It is 3 when the particle is sphere and 6 for cylinders. For irregular shape, Hamilton and Crosser 137 proposed a generic model to include different shapes of irregular particles and derived the following correlation: The parameter Ψ represents the shape factor. For a sphere particle shape, Ψ = 1 and the above expression will be reduced to the Maxwell's expression whereas Ψ = 5 for cylindrical particle shapes. However, Bruggeman 136 proposed another model based on homogenous spherical solid-fluid mixture with no limitations to the volume fraction. This model supplies prediction slightly better than those discussed previously and can be presented in the following correlation: where Δ = ½ 3φ −1 ð Þk s + 2−3φ ð Þk f 2 + 8k s k f : Another model was derived by Nan et al 138 based on very long aspect ratios of particle sizes and assumption of (k s k f ) which is appropriate for very high thermal conductivity particles such as CNT, SWCNT, and so forth. This model is represented by the following expression: This expression cannot be applied for general nanofluids since it is only derived for high-thermal conductivity nanoparticles.
Khanafer and Vafai 126 developed a model from experimental data of Al 2 O 3 and CuO particles mixed with water base fluid. The derived expression is a statistical expression of thermal conductivity of nanofluid at ambient conditions which is given by: The parameter α in the above equation represents the particle radius (in nm). This formula introduces adversely relation between the thermal conductivity of nanoparticles and base fluids and also there is no explanation about how to define the particle size for nonspherical particles.
Yu and Choi 139 introduced an expression for the thermal conductivity of nonspherical particles suspended in a base fluid based on the Interfacial Layer concept. Their mode is written for the heterogeneous mixture in the following formulation: The values δα and α are empirical parameters which are assumed to be 2 and less than 5 nm, respectively, in their study. However, the nonlinear behavior of the thermal conductivity observed with nanofluids is not accurately predicted by this model. Others models are presented in more details in Michaelides. 134 The previous discussion clarifies that the thermal conductivity of nanofluids depends strongly on different parameters: both conductivities of fluid and solid particles, mixture temperature, a volume fraction value, and size dimensions of particles.

| History of investigations using nanofluids in PTCs
To the best of the author's knowledge, there are a few experimental studies, which used nanoparticles in PTCs analysis, and the majority of them used water as the base working fluid. Chaudhari et al, 140 Subramani et al, 141 and Bretado et al 142  It was noticed that a significant improvement in thermal efficiency was obtained with increasing the volume fraction where it was 31% with volume fraction of 0.00045% whereas it reached up to 76% with the largest volume fraction compared with the base fluid.
On the other hand, the experimental investigation using ethylene glycol (EG) as a base fluid was conducted by Kasaeian et al 146 using MWCNT and nanosilica nanoparticles with volume fractions of 0.1%, 0.2%, and 0.3%. The preparation of nanofluids was done by dispersing the nanoparticles inside the based fluid using a magnetic stirrer for 5 hours at 900 rpm in order to avoid the effect of particle agglomeration and using ultrasonic bath after that with power of 60 W from 0.25 hour in order to avoid the particles destruction. The authors found that the thermal efficiency at 0.3% concentration was 17% higher than that obtained by the base working fluid. The summarized review of previous investigations illustrating the use of nanofluids in PTCs of numerical studies and main findings is listed in Table 10.

| Hybrid nanofluids in the PTC applications
All investigations presented previously for PTC systems have concentrated on single nanofluids, that is, mixtures that include one type of nanoparticles suspended in a single base fluid. The hybrid nanofluids concept is basically achieved by adding at least two types of nanoparticles in a single or a combination of base fluids. In fact, mixing two or more metallic or nonmetallic particles until reaching the homogeneous phase is definitely promising technical approach to enhance thermo-physical properties, hydrodynamic behavior and accordingly the thermal characteristics compared with the single nanofluid. Researchers started paying attention to this technology since 2013. The major application of hybrid nanofluids is renewable energy applications, and in particular solar collectors. However, using this technology in solar applications whether numerically or experimentally is extremely rare. This is due to the difficulty of describing numerically the thermal properties of hybrid nanofluids and implementing this technology in the realistic systems (Minea et al 113 ). The thermo-physical properties of hybrid nanofluids are discussed deeply in Babar and Ali. 156 However, the thermal properties of some hybrid nanoparticles that are found in previous studies are presented in Table 11. Regarding the experimental and numerical investigations in PTC systems using hybrid nanofluids, Bellos and Tzivanidis 158 compared numerically the performance of single nanofluids (Al 2 O 3 and TiO 2 ) with volume fraction of 3% and hybrid nanofluid (1.5% Al 2 O 3 + 1.5% TiO 2 ). Results showed that up to 1.8% improvements in the thermal efficiency when using hybrid nanofluids while only 0.7% with single nanofluid. Menbari et al, 159 Menbari and Alemrajabi, 160 and Menbari et al 161 studied experimentally the effect of (γ-Al 2 O 3 + CuO) suspended in hybrid base fluids of water and EG with different volume fractions, different solar irradiance and different flow rates. They pointed out that the thermal efficiency was higher in the case of dispersing hybrid nanoparticles than using single nanoparticle. It was also noticed that the larger enhancement in the thermal efficiency was marked when using water as a base fluid since the mixture of water-EG has a disadvantage of boiling and freezing temperature which is higher than those of pure water. As per their findings, the maximum thermal efficiency obtained was 48.03% using the largest volume fraction for hybrid nanoparticles with water whereas the minimum thermal efficiency recorded was 29.97% using the smallest volume fraction of hybrid nanoparticles with water-EG base fluid. Okonkwo et al 157 investigated numerically the behavior of new hybrid particles (greensynthesized) OLE-TiO 2 and BH-SiO 2 with water as base fluid using 3% volume fraction under different fluid inlet temperatures and different flow rates. Results showed that the thermal efficiency was enhanced by 0.073% and 0.077% when using OLE-TiO 2 and BH-SiO 2 , respectively, with increasing in heat transfer coefficient by 128% and 138%. Other types of hybrid nanofluids (Ag + MgO), (Al 2 O 3 + Cu), and (GO + Co 3 O 4 ) have been numerically investigated by Minea et al 113 with both single base fluid (water, EG) and hybrid base fluid (water + EG) in the laminar flow regime. The authors reported an increase in the convection heat transfer coefficient between 115% and 125% when using (GO + Co 3 O 4 ) and base fluid of (water + EG).

| THE EFFECT OF INSERTING SWIRL GENERATORS ON THE THERMAL PERFORMANCE
The use of swirl generators inside the receiver tube is a passive technique can be used to enhance the convection heat transfer rate. These devices could be shaped as twisted tapes, fins, coils, wires, and spiral grooved tubes etc. The flow across such devices has important features, such as an intense mixing between flow in the near-wall region and main-stream, a reduction in the thickness of the thermal boundary layer, and an increment in the tangential velocity component. Such techniques improve the thermal efficiency of PTC, minimize the cost, reduce the thermal gradient of the absorber tube and improve the overall system reliability subsequently. A wide range of insert types have been studied in the past. Kasperski and Nem s 162 investigated the effect of multiple-fin arrays inside the solar receiver on the thermo-hydraulic efficiency of the PTC compared with the smooth receiver. Up to 14% efficiency enhancement resulted in the case of half-pipe finned arrangement when there is no limitation of the ambient velocity. Song et al 163 studied numerically the effect of helical screwtape with a core rod inside the receiver of the PTC on the thermal performance. Results proved that the usage of the helical screw-tape decreased the maximum temperature and heat losses by a small amount (less than those predicted by the tubular tube by six times at 0.11 kg/s and inlet temperature of 373 K). On the other hand, the pressure drop increased with increasing the mass flow rate by four times in the typical receiver while the pressure drops increase by 23 times in the case of using the helical screw tape insert.
Mwesigye et al 164 studied numerically a new type of insert called a twisted type with wall-detached inside the solar receiver. Results revealed that the temperature gradient of the absorber tube in the circumferential direction was reduced by 68% and the thermal efficiency was increased by 5% to 10% at a twist ratio of greater than 1 due to the presence of twisted tapes. Furthermore, the largest reduction in the entropy generation was about 58.8%. Chang et al 165 investigated numerically a new type of inserts in which they used concentric and eccentric rod tabulators in different positions with molten salt as a base fluid. The normalized Nusselt number resulted from the simulations increased from 1.1 to 7.42 times with respect to the typical solar receiver. Bellos and Tzivanidis (2018b) 166 used a star-design as a tabulator inside the solar receiver with different dimensions of star configurations. According to results obtained based on the optimum star configuration, up to 60% enhancement in the heat transfer coefficient and 14% reduction in thermal losses whereas up to 900% increase in the pressure drop. Recently, Liu et al 167 studied numerically conical strip inserts in the PTC system considering the effect of the geometrical parameters including a central angle, pitch ratio, and hollow diameter of inserts additional to different flow conditions. Results clarified that using this type of inserts led to an increase in the Nusselt number by 45% to 203% with a large reduction in both thermal losses and entropy generation reached to 82.1% and 74.2%, respectively. Moreover, the overall enhancement in thermal efficiency and exergetic efficiency increased by 0.02% to 5.04% and 5.7%, respectively.
A large number of papers in the literature presented different types of inserts, some of them are shown in Figure 14. Besides, many types of swirl generators are individually investigated in previous studies taking into account the effect of geometrical arrangements of inserts, various rotating positions of inserts, different flow conditions, various ambient conditions, and a wide range of solar irradiations. Table 12 presents all abbreviations that are used in Table 13 which summarize the previous works and their main achievements.

| EFFECTS OF THE COLLECTOR DESIGN ON THE THERMAL PERFORMANCE
The structure of the solar receiver is very important factor that should be taken into account to improve the thermal performance. A new structure of a PTC was presented by Bader et al 201 in which the mirrored solar collector was made from pneumatic polymer which was mounted on a frames made from precast concrete. Results showed that the maximum solar concentrating ratio was 151. Wang et al 202 studied numerically the reliability of the collector by employing a secondary homogenizing reflector (HR). They reported that the absorber cylinder with the new configuration could be uniformly heated. This was accompanied with a slight decrease of about 4% efficiency due to the optical losses where a significant drop was noticed at the highest operating temperature. Behar et al 23 proposed new structure components such as reflectors and receivers rather than using the typical ones. The new collector was examined under different conditions and it was found that, at the large operating temperatures, there was a small divergence in the estimation of the heat losses. Increasing the concentration ratio of PTC is one of the most important solutions that make this technique more economic and competitive compared with other solar systems. Considering this advantage, Sanchez and Rosengarten 88 proposed a new type of PTC using a second-stage flat mirror. The concentration ratio increased up to 80%. Additionally, the heat flux distribution became more uniformly around the receiver. Fuqiang et al 203 numerically tested a new design of a PTC in which the tube was designed as an asymmetric outward corrugated convex. Two very important features were observed: the heat transfer enhancement improved while the thermal strain in the absorber receiver decreased. To study the effect of nocircular solar receivers, Bellos et al 154 numerically tested the effects of absorber geometry (sign wave) on the thermal efficiency of the IST-PTC with three different HTFs. According to their findings, the thermal efficiency improved by 4.55% compared with the typical configuration. Another new design was numerically investigated by Wang et al,204 in which the length, aperture width and the diameter of a collector were designed to change gradually along the mean flow direction. The new design proposed enhancement in the methanol conversion rate by 8.35% to 15.85% larger than this proposed by the typical design.
Recently, Bitam et al 205 studied numerically a new design of S-curved/sinusoidal absorber receiver. They found that the Nusselt number and thermal efficiency increased by 63% and 3%, respectively, as compared with the traditional design, whereas the friction factor increased by 40.8%. In the same year, Liang et al 206 proposed experimentally a new PTC with a cavity receiver. The receiver is connected to two inclined fins which act to absorb the energy concentrated. The idea is to avoid the possible nonuniform distribution of the flow in such applications. The maximum thermal efficiency was 48%. Peralta and Gleckman 207 designed experimentally a new support structure of the PTC system using lumber material. They examined the new design numerically and they expected that the mean intercept factor is greater than 95%. Li et al 208 proposed a novel design of the absorber receiver in the shape of a linear cavity with a lunate channel depending on the effect of the black cavity. The new design provided better behavior in terms of thermal performance, in particular the temperature distribution, compared with the typical receiver.
Another novel design of the solar receiver, proposed by Wang et al, 209 is covered with infrared reflectors (IR) on the upper part of the solar receiver from both sides. Authors concluded that the maximum reduction in thermal loss at the absorber temperature of 600 C was 43.8% whereas the thermal efficiency enhancement was 16.7%. Investigating the effect of the focal line is also taken into consideration by Kulahli et al 210 in which they proposed a new design for the parabolic trough with a changing focal length in the axial direction. The maximum enhancement in the thermal efficiency was 0.21% and 0.63% improvement in the thermal gain compared with the conventional design. Some of the aforementioned new designs are listed below in Figure 15.

| FURTHER DISCUSSIONS
Enhancement in PTC systems performance can be achieved using numerous technologies, as illustrated in the preceding discussions. These technologies can F I G U R E 1 4 (Continued) enhance the thermal and hydraulic performances, or they can improve the PTC optical characteristics, which in turn leads to higher thermal energy production, lower thermal losses, lower thermal stresses, optimized tracking systems, reduction in the manufacturing cost, optimized rim angle and collector shape parameters, and so forth. As clearly noticed, the previous studies aimed to improve the optical efficiency are fewer than those aimed to enhance the thermal performance. These technologies are extensively investigated numerically whereas the experimental works are relatively rare.
The usage of nanofluid technology is an effective approach to gradually improve the PTC thermal efficiency. Both metallic and nonmetallic nanoparticles can be suspended into the base fluids with different volume fractions or different weight percentage. Even though some studies (such as Ferraro et al 211 214 There is no doubt that increasing the nanoparticle volume fraction would increase the heat transfer performance and reduce the thermal losses on the absorber tube, but at the same time the nanofluid stability will also be affected, leading to agglomeration and clustering of nanoparticles resulting in greatly enhancement in F I G U R E 1 4 (Continued) the pumping power required to force the flow through the absorber tube and accordingly reducing the collector efficiency. Therefore, the nanoparticle volume fraction or weight concentration should be optimized for effective thermal and hydraulic performances of PTCs.
Another main approach that can be employed to effectively enhance the thermal performance of the absorber receiver is inserting swirl generators or other flow-modifying inserts (tabulators) inside the HCE with different shapes and different positions. In comparison with the nanofluid approach, using tabulators is more cost-effective, and their actual implementation rather simple. The usage of inserting tabulators acts at enhancing the thermal properties of HTF and improving the turbulence performance inside the absorber tube which in turn leading to significantly improve the    Kurşun 196 Re: 2 × 11%-101% Rings attached T.T.
--(Continues) thermal performance. However, the maximum enhancement reported to date in the heat transfer coefficient was approximately 375%, when using three segmental rings as proposed by Ghasemi and Ranjbar. 186 Moreover, using circular fins inside the HCE enhanced the heat transfer coefficient by 360% compared with the typical performance (Reddy and Satyanarayana 168 ), while using half-pipe finned also contributed to enhancing the thermal efficiency of the PTC by 13% as reported by Kasperski and Nem s. 162 On the other hand, the main challenge associated with this method is the potential pressure shocks due to the presence of swirl generators or tabulators, which could lead to glass envelope breakage. The third possible technology which may be employed to improve the thermal performance of PTC is to combine the previous two technologies, nanofluids and flow-modifying inserts, in the same system. For example, Amina et al 184 reported a 150% enhancement in heat transfer coefficient when using fins with nanofluids. In another study, the exergy enhancement achieved was approximately 16.51% when using twisted tape with Al 2 O 3 -thermal oil nanofluid (Okonkwo et al 195 ). For this method to be effective, clearly the nanofluid and the flow-modifying insert have to be optimized simultaneously and synergistically.
As regards PTC systems performance enhancement, in conclusion, areas that require further investigation include: • The optimization of the volume fraction or weight concentration of nanoparticles to fine-tune the performance of nanofluids, as well as investigations on the long-term stability of nanofluids. • Notwithstanding their potential superior performance, hybrid nanofluids have received little attention, both experimentally and numerically, so that more studies are clearly needed to duly assess their potential. Using hybrid nanofluid instead of mono fluid (single fluid) is expected to double the thermal efficiency of the PTC, Bellos and Tzivanidis. 158 Therefore, this is a large room of research for the scientific society that has to pay attention and examine different cases of nanofluids; metallic-metallic nanofluids, metallic-nonmetallic nanofluids, and nonmetallic-nonmetallic nanofluids.
Examining multiple base fluids with hybrid nanofluids is also needed. Besides, experimental studies are extremely needed in order to be used for validation in the numerical investigations. • Very few studies have investigated the synergy between nanofluids and flow-modifying insert, so that more studies are clearly needed to duly assess the potential of combining these two performanceenhancement technologies.

| CONCLUSIONS
PTC systems play a key role in solar thermal energy. Numerous technologies and different techniques have been investigated to improve the overall performance of the PTC optically, thermally and hydraulically, using experiments, simulations, or analytical approaches. As previously discussed, PTC systems performance-enhancement approaches can be basically categorized into two main families: technologies used to improve the thermal performance, and technologies used to enhance the optical characteristics. The investigations focused on enhancing the thermal performance are currently more numerous than those addressing the optical performance; probably due to the fact that the tools needed to investigate the thermal characteristics are more extensively available.
In this article, research investigations performed experimentally and numerically to improve the thermal and the optical performance of PTC systems have been reviewed. It is clear that experimental studies are less numerous in comparison with numerical investigations, because of the cost associated with experiments, particularly when carried out at representative scale. Advantages of numerical simulations, in comparison with experiments, include the possibility to run cost-effective parametric studies, and the possibility to focus on aspects that are difficult to duly investigate experimentally, such as the nonuniform heat flux distribution on solar absorber or conjugate heat transfer. Based on the available literature, it can be concluded that the utilization of nanofluids for improving thermal properties is promising but still an emerging field. The knowledge gap in the literature is still considerable in terms of testing different types of nanoparticles with different volume fractions and different base fluids for conjugated heat transfer problems. Moreover, there are still some open questions about the thermal-physical properties of nanofluids which thus require further research. Furthermore, investigating hybrid nanofluids is still restricted to investigations. More contributions are needed, notably testing the effect of metallic with metallic nanoparticles, metallic with nonmetallic nanoparticles and nonmetallic with nonmetallic nanoparticles with/ without hybrid base fluids. Even though a lot of data is available in literature related to the improvement of thermal performance using swirl generators (or other flowmodifying devices) and nanoparticles, there is yet a rather large void when it comes to the use of both nanoparticles and swirl generators together. Studies related to the testing of the combined effect of these are much needed and should be the focus of further research. The use of hybrid nanofluids with swirl generators offers good potential since different inserts could be investigated with numerous types of hybrid nanofluids.