SIMULATION OF A DOUBLE CAVITY TYPE SOLAR TROUGH COLLECTOR

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1 International Journal of Mechanical Engineering and Technology (IJMET) Volume 9, Issue 8, August 2018, pp , Article ID: IJMET_09_08_099 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed SIMULATION OF A DOUBLE CAVITY TYPE SOLAR TROUGH COLLECTOR Mukundjee Pandey and Biranchi Narayana Padhi Department of Mechanical Engineering, International Institute of Information Technology, Bhubaneswar, India Ipsita Mishra Department of Mechanical Engineering, CIT, Centurion University of Technology & Management, Bhubaneswar, India ABSTRACT This paper presents the effectiveness of a novel double cavity receiver as compared to the conventional solar receiver. In this paper temperature variations of heat transfer fluid (HTF) with mass-flow rates are investigated. Further the effects of mass flow rates and inlet HTF temperatures on heat losses, exergy losses, thermal efficiency and exergy efficiency of both solar parabolic trough collectors are compared. The HTF used here in the computational fluid dynamics (CFD) model is water. The novelty of this paper lies in the fact that it provides a CFD method to validate and compare the performance of parabolic collector for a prescribed value of inlet temperature and solar flux with a particular fluid, with which parabolic collector gives the best performance. Keywords: LS-2 PTC, Double cavity type receiver, Computational fluid dynamics, heat losses, Thermal efficiency, and Exergy efficiency Cite this Article: Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra, Simulation of a Double Cavity Type Solar Trough Collector, International Journal of Mechanical Engineering and Technology, 9(8), 2018, pp INTRODUCTION Solar energy is one of the most capable prospects among all forms of renewable energy. The main problem associated with solar energy is to harness it effectively; out of the many ways to harness solar energy, parabolic trough collector (PTC) is one of the most efficient solar collectors for medium and high temperature applications. The main research allied to solar collector is to make it more efficient by increasing its thermal efficiency, as every solar thermal system is directly reliant on solar thermal collectors. There are different ways to determine the performance of the solar thermal collector; either it should be ascertained with experimental results or with the help of CFD tools available to us. Fluent-Ansys is preferred editor@iaeme.com

2 Simulation of a Double Cavity Type Solar Trough Collector by many researchers for the analysis of thermal systems. Sadaghiyani et al. [1] investigated the effect of plug (flow restriction device) on the efficiency of LS-2 PTC. They concluded that variations in positions of plug with varying diameter had significant effects on the performance of PTC. The only way to increase the performance of a solar thermal collector is to enhance its heat transfer properties to HTF by reducing environmental losses through the absorber via glass tube. One problem that every researcher faces during the geometry modelling is about the size of thermal system; as the size of the thermal system increases then the number of meshing cells also increases. The increase in the number of meshing cells leads to slow the computational time and it also affects the quality of work for a huge thermal system. Hao et al. [2] investigated a new method for analysing the performance of solar parabolic trough collector (PTC) for solar thermal applications using similarity principle. By using similarity principle and dimensional analysis, different types of PTCs can be compared via a single scaled physical model. Bellos et al. [3] investigated the performance of PTC with internal fins using gas as working fluid. Exegetically, length of 10mm was proposed based on the various fin lengths. Mwesigye et al. [4] investigated that the use of twisted tape significantly enhances the performance of PTC. It was seen that the heat transfer performance was increased about 169%, the circumference temperature difference was decreased by 68%, and the thermal efficiency was increased up to 10% by using wall-detached twisted tape inserts. He et al. [5] studied the effect of longitudinal vortex generators on one side of the absorber tube with concentrated solar radiation (CSR). They found that this unilateral miltlongitudinal vortex parabolic trough collector (UMLVE-PTR) has good heat transfer performance as compared to that of smooth absorber tube (SAT-PTR) within all working range of conditions and geometric parameters. Jianyu et al. [6] investigated the effect of symmetric outward convex corrugated tube PTC; they examined that by using internal corrugated tubes the heat transfer performance had significantly increased up to 8.4% while thermal strain was decreased by 13.1%. Bello-Ochende et al. [7] investigated the performance of a receiver with perforated plate inserts. They examined the performance of PTC for different geometric parameters of perforated plate including its dimensionless orientation. Bellos et al. [8] investigated the performance of PTC with star flow inserts in its receiver tube. A total 16 number of different cases were studied with the variation in fin length from 15mm to 30mm and its thickness from 2mm to 5 mm. Thermal efficiency enhancements was seen to be higher with increase in inlet temperature and was reached to 1%. Li et al. [9] studied the effect of convective heat transfer characteristics in a fully developed turbulent mixing for an HTF flowing inside a dimpled receiver of PTC. They investigated that the average value of friction factor and Nusselt number for a non-uniform flux distribution (NUHF) was higher as compared to uniform heat flux (UHF) distribution. The performance of dimpled receiver for NUHF was found to be better than that of UHF. Bellos et al. [10] optimised for the number of internal fins required for the performance enhancement of PTC. They investigated that the fins should be placed in the lower half portion of the receiver where high concentration of solar flux impinges, and three number of internal fins in the lower half of receiver raises the thermal efficiency of about 0.51% editor@iaeme.com

3 Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra Figure 1 Energy losses through parabolic trough collector. 2. CFD NUMERICAL SIMULATION METHOD Ansys (FLUENT) software package is used to calculate the concentrated solar flux distribution; as thermal boundary conditions of PTC are exposed to environment and with each other. Ansys (Design modular) is used to create geometry of PTC with assignment of different names in Ansys (Meshing) under named selections of PTC. Also, different interfaces are created between fluid-absorber, absorber-vacuum, and vacuum-glass by selection of names for each elemental interaction of PTC. Figure 2 (a) Parabolic trough solar collector Figure 2 (b) Conventional collector tube cross-section 2.1. MODEL DEFINITION AND MESHING LS-2 Parabolic Trough Collector (PTC) is chosen for the validation of simulation. Figure 2(a) & 2(b) presents the schematic diagram of LS-2 PTC. It consists of a receiver tube and a parabolic concentrator. The receiver tube consists of an absorber tube and a glass tube; vacuum is maintained between the annular region of absorber tube and glass tube. The receiver is a curved sheet in parabolic geometry, which concentrates solar radiation linearly on the PTC. The performance of tracking mechanism has been ignored and optical errors are assumed to be eliminated. All dimensional parameters of LS-2 PTC are listed in Table1, along with its material properties in Table2. The double cavity type of PTC (DPTC) is shown in Figure 2(c). All its dimensional parameters and material properties are assumed to be same as that of LS-2; except that for cross-sectional dimensions of its absorber. The simulated results editor@iaeme.com

4 Simulation of a Double Cavity Type Solar Trough Collector of conventional parabolic trough collector (CPTC) are compared and validated with the experimental results of Dudley et al. Also, the working fluid used here is syltherm-800; but it is used only for the validation of results. However, for the comparison of CPTC with DPTC, water is used as the HTF. The material used for the absorber tube is stainless steel with a thermal conductivity of 53W/Mk. Table 1 Physical parameters of LS-2 collector by Sandia National Laboratories Material Parameter Value Focal length 1.84m Aperture width 5m Receiver length 7.8m Concentration ratio 71 Outer diameter of absorber 70mm Inlet diameter of glass tube 66mm Outer diameter of glass tube 115mm Inner diameter of glass tube 109mm Reflectivity of reflector 0.93 Transmittance of glass 0.95 Coating absorptivity 0.96 Table 2 The main material parameters Thermal conductivity (W/m ) Specific heat capacity (KJ/Kg-K) Density (Kg/ ) Steel Glass Figure 2 (c) DOTC tube cross-section Figure 2 (d) Mess generation of PTC Numerical analysis is based on the following assumptions. a. Heat transfer process is assumed to be in steady state. b. Optical errors associated with PTC are neglected. c. Convection heat transfer occurs within the receiver tube in the fully developed region. d. Radiation heat transfer takes place between glass-cover and absorber tube. e. Heat conduction between absorber tubes, glass tubes and bellows (support brackets) are negligible editor@iaeme.com

5 Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra f. HTFs (syltherm-800 & water) are considered to be incompressible as well as turbulent. g. Syltherm-800 physical properties are assumed to be temperature dependent whereas for water it is considered as constant. h. Boussinesq Approximation model is used to create density as constant in all solvers. Meshing presented in Figure 2(d) was created using Ansys14 (Meshing), a pre-processor furl with Fluent. Hexahedral meshing is applied for all elements of the PTC except for the interior parts of the volume where tetrahedral meshing has been adapted. About cells are generated in meshing of CPTC and cells for DPTC; which is followed by a grid sensitivity test. Three meshing grids were employed for the sensitivity tests of the solution by enforcing grid refinement were , 42250, for CPTC and , , for DPTC respectively. For 2nd and 3rd meshing, the differences of obtained results were lesser than 1%. In order to minimise computation, meshing grid of and cells were used for CPTC and DPTC respectively; with a relevance of 100 in relevance centre fine meshing was adopted Boundary Conditions (B.C) Under the general conditions Pressure-Based solver condition are implemented with a velocity formulation, when an absolute in a steady state is selected. Surface to surface (S2S) radiation model is applied under the Solar Ray Tracing algorithm. Materials are selected and some of the required materials that are not in the library are imported or modified under the user defined mode; which is required to be applied when asked in cell zone conditions. The thermal boundary conditions are as follows: a. Boundary conditions applied at inlet and outlet are following: Inlet: mass flow rate, and T= inlet temperature. Outlet: p 0(zero) gauge pressure in Pa, T= back flow total temperature = b. Boundary condition applied at walls are as follows: The lower half of the receiver is exposed to the reflector and is subjected to a solar flux calculated by view factor of radiation algorithm; whereas top half of the receiver is exposed to open incident solar radiation and is applied to a solar flux of W/ Wall-absorber: opaque B.C is selected within radiation boundary condition with a confirmation of participating in solar ray tracing; absorptivity of 0.96 is considered. Wall-glass: semi-transparent B.C is selected within radiation boundary condition with a confirmation of participating in solar ray tracing; absorptivity of 0.01 and transmissivity of 0.95 are considered. Wall-reflector: semi-transparent B.C is selected within radiation boundary condition with a confirmation of participating in solar ray tracing; absorptivity of 0 and transmissivity of 0.05 are considered The Governing Differential Equations Every computational fluid dynamics (CFD) simulation necessitates the aspiration of distinct conservation laws. To reconcile these equations some interference was considered; as the flow is stationary, fluid is incompressible and Boussinesq approximations are also assumed to be valid. Continuity equation: editor@iaeme.com

6 Simulation of a Double Cavity Type Solar Trough Collector Momentum equation: (1) [ ( )] (2) Energy conservation equation: [ ] (3) Boussinesq approximations: k equation: (4) *( ) + (5) ε equation: *( ) + (6) The turbulent viscosity and production rates are as follows: (7) ( ) (8) The values of standard constants are =0.09, =1.44, =1.92, =1.0, =1.3, and =0.85 Table 3 Typical experimental condition/data obtained from Ref. [11] and comparison with simulation Case Study DNI (W/ Mass flow rate (kg/sec ) Inlet temperature(k ) Experimental (Dudley et al.) Outlet temperature (K) Experimenta l (Dudley et al.) Outlet temperatur e (K) Simulation (Dudley et al.) Efficiency % Experimenta l Dudley et. al.) Efficiency % Simulatio n Numerical Simulation Set-up 1 st step is to create 3-D geometry in Ansys-Design modular. 2 nd step is to create meshing in the pre-processing module of Ansys-Fluent. 3 rd step is to complete post-processing requirements to get valid results in the solution set-up. Under the post-processing module there is a Set-up section where unit named as General exists; and within it pressure-based solver with steady state thermal condition was confirmed. Absolute velocity was selected under this sub-division of solver. Within the division of Models ; energy equation was confirmed. Under the sub-division of Viscous Models, the k-elipson mode was selected in the model component; after which standard condition of k-elipson model was assigned. Enhanced wall treatment was allocated under the near-wall treatment component. Thermal effects and viscous heating conditions were allocated and confirmed under the enhanced wall editor@iaeme.com

7 Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra treatment option. Surface to surface (S2S) condition was selected under the model component of Radiation Model sub-division; solar ray tracing mechanism was confirmed under the solar load component. Direct solar irradiation of 933.7(W/ ) and diffuse solar irradiation 0 (W/ ) were assigned under illumination parameter component of this sub-division with a spectral fraction (V/ (V+IR)) of 0.5. Under Materials section; the materials of PTC are either imported from the library or it can be defined by modifying the existed material parameters. Different zones, like solid or fluid were assigned based on their physical states for each elements of PTC within the Cell Zone Conditions. Three meshing interfaces were created by bounding two interface zones for each of the connecting elements of PTC, e.g. interface-a for bounding interface-htf & interface-absorber, interface-b for bounding interface-absorber & interface-vacuum, and interface-c for bounding interface-vacuum & interface-glass. Values were computed from inlet-fluid under the section Reference values with a reference zone of liquid. Under the section of Solution Methods, simple scheme was selected within the sub-division of pressure scheme. Least squares cell-based condition was confirmed under gradient, pressure was selected as standard; second order upwind condition was confirmed under momentum, turbulent kinetic energy and turbulent dissipation rate based on gradients were applied. 3. NUMERICAL SIMULATION AND VALIDATION The objective of numerical simulation using Ansys-Fluent is to validate the model with Dudley s LS-2 PTC, as well as to compare its performance with novel DPTC. The variation of thermal efficiency of CPTC with experimental model proposed by Dudley et. al and with DPTC are calculated according to relation (9) Where can be expressed as =2DL For calculation of convection and conduction losses same ambient temperature is considered and it is equal to 300K. But for the evaluation of radiation heat losses, the sky temperature has been used and is given as [12]: It is assumed that PTC utilises only undiluted beam irradiation. Thus, for the evaluation of energy flow from the incident solar radiation Petela model is used. This model assumes that the sun is a temperature reservoir of temperature (, with a value of 5770K in outer layers. The exergy flow of undiluted solar irradiation is ( : * ( ) ( )+ (11) The useful energy output is given by the following equation: (10) ( ) (12) The exergy efficiency of PTC exergy, as indicated below: is defined as the ratio of useful exergy to input (13) The exergetic thermal losses ( ) are calculated as: editor@iaeme.com

8 Simulation of a Double Cavity Type Solar Trough Collector The total exergy losses are given as: ( ) (14) 4. RESULTS AND DISCUSSION ANSYS-FLUENT (CFD-CFX) is used for the analysis and performance evaluation of both CPTC and DPTC. Effort is made to optimize the performance of PTC; also, the performance of DPTC is compared to that of the CPTC. Performances of both PTC are compared with different mass flow rate, inlet HTF, and solar incidence angle Effect of mass flow rate This section shows the effect of mass flow rate on the receiver wall temperatures, heat losses, exergy losses and the efficiencies. Figure 4.1 shows that with the increase in mass flow rate there is a decrease in the wall temperatures of receiver for constant solar flux of W/.Because, increase in mass flow rate leads to increase in velocity of the HTF. Due to increase in velocity of the HTF, the fluid elements of differential length get less time for energy interaction with the absorber tube. But, it is not such that due to this less transfer of heat energy occurs from absorber tube to the HTF. It is evident that for the same value of mass flow rate the DPTC receiver s outlet fluid temperature is greater as compared to CPTC. This happens because; absorber as well as glass temperatures of DPTC are less as compared to CPTC. Higher is the temperature of absorber and glass, more will be the losses to environment. (15) Figure 4.1 (a) Variation of temperature vs. mass flow rate Figure 4.1 (b) Variation of Heat Losses vs. Mass Flow Rate editor@iaeme.com

9 Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra Figure 4.1 (b) shows that there is a decrease in the heat losses with increase in mass flow rate, this happens only due to decrease in wall temperature of receiver. However, the convective heat losses through the glass cover predominates the heat losses; and heat loss through the ends is smallest. Also, the heat losses through double cavity type of receiver are less as compared conventional circular type of receiver; as in case of cavity type of receiver the lower and upper part of the receiver are far enough from the glass cover as compared to the conventional/circular receiver. Heat losses through lower part of the receiver are more as compared to other parts because the concentrator focuses all solar radiation that impinges on it to the lower part of the receiver. Therefore, the temperature of lower part of the receiver is highest as compared to other parts and it is evident from Figure 4.1 (c) & Figure 4.1 (d). Also, it can be seen that the outlet temperature of HTF for cavity type of receiver is higher as compared to conventional receiver; and therefore, the end heat losses of cavity type of receiver is more as compared to circular receiver. Whereas vacuum and glass temperatures of cavity type of receiver are lesser as compared to conventional receiver, this is only due to less heat losses in cavity type of receiver. Figure 4.1 (c) Temperature contours of conventional type receiver editor@iaeme.com

10 Simulation of a Double Cavity Type Solar Trough Collector Figure 4.1 (d) Temperature contours of cavity type receiver. Figure 4.1 (e) Variation of exergy losses with mass flow rate Figure 4.1 (e) shows that with increase in mass flow rate the exergy loss decreases, as with increase in mass flow rate leads to low HTF outlet temperature. Also, exergy loss from the absorber ends dominates on all other exergy losses; because of high energy density (W/ ) of absorber ends as compared to lateral surfaces of PTC. The exergy loss from ends of the absorber in case of cavity type of receiver is greater as compared to the conventional type of parabolic trough collector; as outlet fluid temperature of cavity type of receiver is more for the same value of mass flow rate and constant solar flux of W/ editor@iaeme.com

11 Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra Figure 4.1 (f) Efficiency vs. mass flow rate Figure 4.1(f) shows that with increase in mass flow rate there is an increase in thermal efficiency of both parabolic collectors. This happens because of with increase in mass flow rate there occurs a decrease in heat losses and which leads to increase in thermal efficiency. For a particular value of mass flow rate, cavity type receiver shows higher thermal efficiency as compared to conventional one. This is only due to reason that for a particular value of mass flow rate cavity type of receiver has less heat losses as compared to conventional type of it. The exergy efficiency of both parabolic collectors increases first and then decreases. This is due to reduction in outlet temperature of HTF whereas increment in thermal efficiency with increase in mass flow rate. There is an optimal value of mass flow rate based on the exergy efficiency Effect of Inlet HTF Temperature Figure 4.2 (a) Variation of heat losses vs. inlet temperature Now the mass flow rate in case of conventional system is chosen to be kg/sec, as for this there is maximum exergy efficiency. Similarly, mass flow rate of kg/sec is chosen for cavity type of receiver; for both the systems effect of inlet temperature on heat losses with a constant value of mass flow rate is studied. Figure4.2 (a) shows that with increase in inlet temperature of the HTF the heat losses through the parabolic collector increases, because increase in inlet temperature of fluid leads to increase in outlet temperature of HTF; also, it editor@iaeme.com

12 Simulation of a Double Cavity Type Solar Trough Collector can be seen that for the same inlet temperature there is less heat loss for the cavity type of receiver. Figure 4.2 (b) Variation of exergy losses with inlet temperature Figure 4.2(b) shows that with increase in inlet temperature the exergy losses for both type of PTC is increased, this is because increase in temperature leads to increase in available energy of the system. Further outlet fluid temperature is the greatest of all the measurable temperatures of the PTC, therefore available energy and hence the exergy losses for the receiver ends would be greater than all other exergy losses. Figure 4.2 (c) Efficiency vs. Inlet Temperature It can be seen from the Fig 4.2 (c) that increases in inlet temperature of HTF for both types of PTC, leads to decrease the thermal efficiency of the system. Because increase in inlet fluid temperature leads to increase in heat losses and therefore the thermal efficiency of PTC decreases. Further, it can also be seen that increase in inlet temperature of HTF leads to first increase in exergy and then after a peak it starts decreasing; this happens because increase in inlet temperature of fluid leads to decrease in difference of outlet and inlet fluid temperatures editor@iaeme.com

13 Mukundjee Pandey, Biranchi Narayana Padhi and Ipsita Mishra 4.3. Effect of Angle of Incidence on HTF Temperature Figure 4.3 (a) Temperature vs. AoI Figure 4.3 (b) Variation of Exergy loss with AoI Figure 4.3 (a) shows the variation of outlet temperature of HTF with angle of incidence of solar radiation. For cavity type of receiver inlet HTF temperature is taken to be 320 and a mass flow rate of kg/sec is selected based on the exergy considerations. Similarly, for circular type of receiver inlet temperature of HTF is taken to be 360 and mass flow rate of kg/sec is considered. It can be seen from the Figure 4.3 (b) that with increase in angle of incidence (AoI) there is not so much variations in radiation and convective exergy losses of both types of PTC; but there are variations in the exergy losses of ends for both types of receiver. The radiation and convective exergy losses for cavity type of receiver are less as compared to circular receiver. This is because; the glass temperatures and heat losses for circular receiver are greater as compared to cavity type of receiver. The exergy losses of ends for cavity type of receiver is greater than that of circular receiver from 0 to 52.5 but after 52.5 the exergy losses of ends of circular type of receiver outrages the exergy losses of ends for cavity type of receiver. Because, the geometry of DPTC is not circular and hence with increase in AoI most of the concentrated rays not impinges on its lateral surfaces. It is understood that tracking is necessary for DPTC as compared to CPTC with increase in AoI. 5. CONCLUSION DPTC and CPTC are compared with respect to three parameters; effect of mass flow rate, effect of inlet HTF temperature and incident angle temperature. Performance of DPTC and CPTC are compared on the basis of outlet temperature, heat losses, thermal efficiency and exergy efficiency. For cavity type of receiver inlet HTF temperature is taken to be 320 and a mass flow rate of kg/sec is selected based on the exergy considerations. Similarly, for circular type of receiver inlet temperature of HTF is taken to be 350 and mass flow rate of kg/sec is selected. Even though the optimised value of mass flow rate of DPTC is greater as compared to CPTC; as well as the optimised value of inlet HTF temperature of DPTC is lesser as compared to CPTC, the performance of DPTC is higher with respect to the performance of CPTC. The exergy losses of ends for cavity type of receiver is greater than that of circular receiver from 0 to 52.5 incident angle but after 52.5 the exergy losses of ends of circular type of receiver outrages the exergy losses of ends for cavity type of receiver. That means even for a low efficient tracker, the performance of a double cavity type of receive (DPTC) outrages the performance of conventional type of receiver (CPTC) for a tolerance of 0 to 52.5 of incident angle editor@iaeme.com

14 6. NOMENCLATURE Simulation of a Double Cavity Type Solar Trough Collector Nomenclature Greek Symbols Aperture area of collector ρ Density (Kg/ ) D Differential µ Dynamic viscosity (Pasec) D Diameter ε Turbulent dissipation rate or emissivity I Direct normal irradiance thermal expansion β (W/ ) coefficient ( ) K Thermal conductivity(w/ K) Subscripts Specific heat capacity (KJ/Kg-K) in inlet parameters Mass flow rate (Kg/sec) o outlet parameters x, y, z Cartesian coordinates am ambient E Exergy r radiation HTF Heat transfer fluid c convection DPTC Double cavity parabolic trough collector l End of receiver CPTC Conventional parabolic trough collector g Glass Q Heat loss(w/m) b bellows REFERENCE [1] Sadaghiyani, O.K., Pourmahmoud, N. and Mirzaee, I. Numerical Simulation Coupled with MCRT Method to Study the Effect of Plug Diameter and Its Position on Outlet Temperature and the Efficiency of LS-2 Parabolic Trough Collector, Journal of Solar Energy Engineering, 135, 2013, pp [2] Jin, J., Ling, Y. and Hao, Y., Similarity analysis of parabolic-trough solar collectors, Applied Energy 204, 2017, pp [3] Bellos, E., Tzivanidis, C., Daniil, I. and Antonopoulos, K.A., The impact of internal longitudinal fins in parabolic trough collectors operating with gases, Energy Conversion and Management 135, 2017, pp [4] Mwesigye, A., Bello-Ochende, T. and Meyer J.P., Heat transfer and entropy generation in a parabolic trough receiver with wall-detached twisted tape inserts, International Journal of Thermal Sciences 99, 2016, pp [5] Cheng, Z.D., He Y.L. and Cui F.Q., Numerical study of heat transfer enhancement by unilateral longitudinal vortex generators inside parabolic trough solar receivers, International Journal of Heat and Mass Transfer 55, 2012, pp [6] Fuqiang W., Qingzhi L., Huaizhi H. and Jianyu T., Parabolic trough receiver with corrugated tube for improving heat transfer and thermal deformation characteristics, Applied Energy 164, 2016, pp [7] Mwesigye, A., Bello-Ochende, T. and Meyer, J.P., Heat transfer and thermodynamic performance of a parabolic trough receiver with centrally placed perforated plate inserts, Applied Energy 136, 2014, pp [8] Bellos, E., Tzivanidis, C. Investigation of a star flow insert in a parabolic trough solar collector, Applied Energy 224 (2018) [9] Huang, Z., Li, Zeng-Y., Yu, Guang-L. and Tao Wen-Q., Numerical investigations on fully-developed mixed turbulent convection in dimpled parabolic trough receiver tubes, Applied Thermal Engineering 114, 2017, pp [10] Bellos, E., Tzivanidis, C. and Tsimpoukis D., Optimum number of internal fins in parabolic trough collectors, Applied Thermal Engineering 137, 2018, pp [11] Dudley, V., Kolb, G., Sloan, M., and Kearney, D., 1994, SEGS LS2 Solar Collector Test Results, Report of Sandia National Laboratories, Report No. SANDIA [12] Bellos, E., and Trivanidis, C., A detailed exergetic analysis of parabolic trough collectors, Energy Conversion and Management 149, 2017, pp editor@iaeme.com