In the present study, a 3D steady-state numerical analysis was performed to investigate forced convection heat transfer within a horizontal smooth tube carrying a heat transfer fluid (HTF) (a thermal oil, in this analysis) with turbulent flow and azimuthally non-uniform heat flux (NUHF). The effect of heat flux non-uniformity on the average Nusselt number, in relation to tube material conductivity and thickness, was examined through a conjugate heat transfer analysis. The analysis was conducted using the SST $ k-\omega $ turbulence model for a Reynolds number ranges from 10,000 to 110,000, and fluid Prandtl numbers of 7.25, 0.3566, and 15.74, reflecting possible operating temperatures, in ANSYS Fluent software 18.2. A comparison was made between the average Nusselt number for various azimuthally NUHF distributions and for an azimuthally uniform heat flux (UHF). Subsequently, the effect of tube material conductivity and thickness on the average Nusselt number under azimuthally NUHF distribution was numerically investigated. The results show that the deviation of the Nusselt number with NUHF from that with UHF can exceed 84%. The findings specifically prove and highlight that the assumption of azimuthal heat flux uniformity on an absorber tube of a parabolic trough solar collector, made by many researchers, may lead to significant inaccuracies.
Citation: Hamzeh Jamali. Numerical analysis of how azimuthally non-uniform heat flux influences turbulent convective heat transfer in parabolic trough solar collector[J]. AIMS Energy, 2025, 13(6): 1391-1416. doi: 10.3934/energy.2025052
In the present study, a 3D steady-state numerical analysis was performed to investigate forced convection heat transfer within a horizontal smooth tube carrying a heat transfer fluid (HTF) (a thermal oil, in this analysis) with turbulent flow and azimuthally non-uniform heat flux (NUHF). The effect of heat flux non-uniformity on the average Nusselt number, in relation to tube material conductivity and thickness, was examined through a conjugate heat transfer analysis. The analysis was conducted using the SST $ k-\omega $ turbulence model for a Reynolds number ranges from 10,000 to 110,000, and fluid Prandtl numbers of 7.25, 0.3566, and 15.74, reflecting possible operating temperatures, in ANSYS Fluent software 18.2. A comparison was made between the average Nusselt number for various azimuthally NUHF distributions and for an azimuthally uniform heat flux (UHF). Subsequently, the effect of tube material conductivity and thickness on the average Nusselt number under azimuthally NUHF distribution was numerically investigated. The results show that the deviation of the Nusselt number with NUHF from that with UHF can exceed 84%. The findings specifically prove and highlight that the assumption of azimuthal heat flux uniformity on an absorber tube of a parabolic trough solar collector, made by many researchers, may lead to significant inaccuracies.
| [1] |
Jamali H (2019) Investigation and review of mirrors reflectance in parabolic trough solar collectors (PTSCs). Energy Rep 5: 145–158. https://doi.org/10.1016/j.egyr.2019.01.006 doi: 10.1016/j.egyr.2019.01.006
|
| [2] |
Hadi Attia ME, Abdel-Aziz MM, Khelifa A (2025) A numerical approach to enhance the performance of double-pass solar collectors with finned photovoltaic/thermal integration. Appl Therm Eng 268: 125974. https://doi.org/10.1016/j.applthermaleng.2025.125974 doi: 10.1016/j.applthermaleng.2025.125974
|
| [3] |
Cheng ZD, He YL, Cui FQ, et al. (2012) Numerical simulation of a parabolic trough solar collector with nonuniform solar flux conditions by coupling FVM and MCRT method. Sol Energy 86: 1770–1784. https://doi.org/10.1016/j.solener.2012.02.039 doi: 10.1016/j.solener.2012.02.039
|
| [4] |
Cheng ZD, He YL, Qiu Y (2015) A detailed nonuniform thermal model of a parabolic trough solar receiver with two halves and two inactive ends. Renewable Energy 74: 139–147. https://doi.org/10.1016/j.renene.2014.07.060 doi: 10.1016/j.renene.2014.07.060
|
| [5] |
Bellos E, Tzivanidis CN, Antonopoulos KA, et al. (2016) Thermal enhancement of solar parabolic trough collectors by using nanofluids and converging—diverging absorber tube. Renewable Energy 94: 213–222. https://doi.org/10.1016/j.renene.2016.03.062 doi: 10.1016/j.renene.2016.03.062
|
| [6] |
Bellos E, Tzivanidis CN (2017) Parametric analysis and optimization of an Organic Rankine Cycle with nanofluid based solar parabolic trough collectors. Renewable Energy 114: 1376–1393. https://doi.org/10.1016/j.renene.2017.06.055 doi: 10.1016/j.renene.2017.06.055
|
| [7] |
Dirker J, Meyer JP, Reid W (2018) Experimental investigation of circumferentially non-uniform heat flux on the heat transfer coefficient in a smooth horizontal tube with buoyancy driven secondary flow. Exp Therm Fluid Sci 98: 480–496. https://doi.org/10.1016/j.expthermflusci.2018.06.017 doi: 10.1016/j.expthermflusci.2018.06.017
|
| [8] |
Bellos E, Tzivanidis C (2018) Analytical expression of parabolic trough solar collector performance. Designs 2: 9. https://doi.org/10.3390/designs2010009 doi: 10.3390/designs2010009
|
| [9] |
Bellos E, Tzivanidis C, Said Z (2020) A systematic parametric thermal analysis of nanofluid-based parabolic trough solar collectors. Sustainable Energy Technol Assess 39: 100714. https://doi.org/10.1016/j.seta.2020.100714 doi: 10.1016/j.seta.2020.100714
|
| [10] |
Lu J, Ding J, Yang J, et al. (2013) Nonuniform heat transfer model and performance of parabolic trough solar receiver. Energy 59: 666–675. https://doi.org/10.1016/j.energy.2013.07.052 doi: 10.1016/j.energy.2013.07.052
|
| [11] |
Faheem A, Ranzi G, Fiorito F, et al. (2016) A numerical study of turbulent mixed convection in a smooth horizontal pipe. J Heat Transfer 138: 012501. https://doi.org/10.1115/1.4031112 doi: 10.1115/1.4031112
|
| [12] |
Hachicha AA, Rodríguez I, Capdevila R, et al. (2013) Heat transfer analysis and numerical simulation of a parabolic trough solar collector. Appl Energy 111: 581–592. https://doi.org/10.1016/j.apenergy.2013.04.067 doi: 10.1016/j.apenergy.2013.04.067
|
| [13] |
Wang Y, Liu Q, Lei J, et al. (2014) A three-dimensional simulation of a parabolic trough solar collector system using molten salt as heat transfer fluid. Appl Therm Eng 70: 462–476. https://doi.org/10.1016/j.applthermaleng.2014.05.051 doi: 10.1016/j.applthermaleng.2014.05.051
|
| [14] |
Bellos E, Tzivanidis C, Tsimpoukis D (2018) Thermal, hydraulic and exergetic evaluation of a parabolic trough collector operating with thermal oil and molten salt based nanofluids. Energy Convers Manage 156: 388–402. https://doi.org/10.1016/j.enconman.2017.11.051 doi: 10.1016/j.enconman.2017.11.051
|
| [15] |
Marefati M, Mehrpooya M, Shafii MB (2018) Optical and thermal analysis of a parabolic trough solar collector for production of thermal energy in different climates in Iran with comparison between the conventional nanofluids. J Cleaner Prod 175: 294–313. https://doi.org/10.1016/j.jclepro.2017.12.080 doi: 10.1016/j.jclepro.2017.12.080
|
| [16] |
Quezada-García S, Sánchez-Mora H, Polo-Labarrios MA, et al. (2019) Modeling and simulation to determine the thermal efficiency of a parabolic solar trough collector system. Case Stud Therm Eng 16: 100523. https://doi.org/10.1016/j.csite.2019.100523 doi: 10.1016/j.csite.2019.100523
|
| [17] | Bergman TL, Lavine AS, Incropera FP, et al. (2011) Fundamentals of heat and mass transfer (7th ed.). Wiley. Available from: https://bcs.wiley.com/he-bcs/Books?action=index&itemId=0470501979&bcsId=6563. |
| [18] |
Norouzi AM, Siavashi M, Ahmadi R, et al. (2021) Experimental study of a parabolic trough solar collector with rotating absorber tube. Renewable Energy 168: 734–749. https://doi.org/10.1016/j.renene.2020.12.088 doi: 10.1016/j.renene.2020.12.088
|
| [19] |
Norouzi AM, Siavashi M, Oskouei MK (2020) Efficiency enhancement of the parabolic trough solar collector using the rotating absorber tube and nanoparticles. Renewable Energy 145: 569–584. https://doi.org/10.1016/j.renene.2019.06.027 doi: 10.1016/j.renene.2019.06.027
|
| [20] |
Bezaatpour M, Rostamzadeh H, Bezaatpour J (2021) Hybridization of rotary absorber tube and magnetic field inducer with nanofluid for performance enhancement of parabolic trough solar collector. J Cleaner Prod 283: 124565. https://doi.org/10.1016/j.jclepro.2020.124565 doi: 10.1016/j.jclepro.2020.124565
|
| [21] |
Khanna S, Singh S, Kedare SB (2015) Explicit expressions for temperature distribution and deflection in absorber tube of solar parabolic trough concentrator. Sol Energy 114: 289–302. https://doi.org/10.1016/j.solener.2015.01.044 doi: 10.1016/j.solener.2015.01.044
|
| [22] |
Adebiyi GA, Hall W (1976) Experimental investigation of heat transfer to supercritical pressure carbon dioxide in a horizontal pipe. Int J Heat Mass Transfer 19: 715–720. https://doi.org/10.1016/0017-9310(76)90123-X doi: 10.1016/0017-9310(76)90123-X
|
| [23] |
Ghajar AJ, Tam LM (1994) Heat transfer measurements and correlations in the transition region for a circular tube with three different inlet configurations. Exp Therm Fluid Sci 8: 79–90. https://doi.org/10.1016/0894-1777(94)90075-2 doi: 10.1016/0894-1777(94)90075-2
|
| [24] | Gnielinski V (1976) New equations for heat and mass transfer in turbulent pipe and channel flow. Int Chem En 16: 359–368. |
| [25] |
Churchill SW (1977) Comprehensive correlating equations for heat, mass and momentum transfer in fully developed flow in smooth tubes. Ind Eng Chem Fundam 16: 109–116. https://doi.org/10.1021/i160061a021 doi: 10.1021/i160061a021
|
| [26] | Boufendi T, Afrid M (2004) The physical aspect of three-dimensional mixed convection in a uniformly heated horizontal pipe. Sci Technol, 39–52. Available from: https://www.academia.edu/98296662/The_Physical_Aspect_of_Three_Dimensional_Mixed_Convection_in_a_Uniformly_Heated_Horizontal_Pipe. |
| [27] |
Mohammed HA, Salman YK (2007) Experimental investigation of mixed convection heat transfer for thermally developing flow in a horizontal circular cylinder. Appl Therm Eng 27: 1522–1533. https://doi.org/10.1016/j.applthermaleng.2006.09.023 doi: 10.1016/j.applthermaleng.2006.09.023
|
| [28] |
Grassi W, Testi D (2006) Heat transfer correlations for turbulent mixed convection in the entrance region of a uniformly heated horizontal tube. J Heat Transfer 128: 1103–1107. https://doi.org/10.1115/1.2345436 doi: 10.1115/1.2345436
|
| [29] |
Mohammed HA, Salman YK (2007) The effects of different entrance sections lengths and heating on free and forced convective heat transfer inside a horizontal circular tube. Int Commun Heat Mass Transfer 34: 769–784. https://doi.org/10.1016/j.icheatmasstransfer.2007.03.005 doi: 10.1016/j.icheatmasstransfer.2007.03.005
|
| [30] |
Testi D (2013) A novel correlation for azimuthal and longitudinal distributions of heat transfer coefficients in developing horizontal pipe flow under transitional mixed convection. Int J Heat Mass Transfe 60: 221–229. https://doi.org/10.1016/j.ijheatmasstransfer.2013.01.003 doi: 10.1016/j.ijheatmasstransfer.2013.01.003
|
| [31] |
Chae MS, Chung BJ (2014) Laminar mixed-convection experiments in horizontal pipes and derivation of a semi-empirical buoyancy coefficient. Int J Therm Sci 84: 335–346. https://doi.org/10.1016/j.ijthermalsci.2014.06.007 doi: 10.1016/j.ijthermalsci.2014.06.007
|
| [32] |
Reynolds WC (1963) Turbulent heat transfer in a circular tube with variable circumferential heat flux. Inter J Heat Mass Transfer 6: 445–454. https://doi.org/10.1016/0017-9310(63)90119-4 doi: 10.1016/0017-9310(63)90119-4
|
| [33] |
Black A, Sparrow EM (1967) Experiments on turbulent heat transfer in a tube with circumferentially varying thermal boundary conditions. J Heat Transfer 89: 258–268. https://doi.org/10.1115/1.3614375 doi: 10.1115/1.3614375
|
| [34] |
Schmidt RR, Sparrow EM (1978) Turbulent flow of water in a tube with circumferentially nonuniform heating, with or without buoyancy. J Heat Transfer 100: 403–409. https://doi.org/10.1115/1.3450822 doi: 10.1115/1.3450822
|
| [35] |
Knowles GR, Sparrow EM (1979) Local and average heat transfer characteristics for turbulent airflow in an asymmetrically heated tube. J Heat Transfer 101: 635–641. https://doi.org/10.1115/1.3451049 doi: 10.1115/1.3451049
|
| [36] |
Chieng CC, Launder BE (2007) On the calculation of turbulent transport in flow through an asymmetrically heated pipe. Numer Heat Transfer 2: 359–371. https://doi.org/10.1080/10407787908913419 doi: 10.1080/10407787908913419
|
| [37] | Zeitoun O (2002) Heat transfer for laminar flow in partially heated tubes. Alexandria Eng J 41: 205–212. Available from: https://www.researchgate.net/publication/255618364. |
| [38] |
Shen X, Lu J, Ding J, et al. (2014) Convective heat transfer of molten salt in circular tube with nonuniform heat flux. Exp Therm fluid Sci 55: 6–11. https://doi.org/10.1016/j.expthermflusci.2014.02.015 doi: 10.1016/j.expthermflusci.2014.02.015
|
| [39] |
Okafor IF, Dirker J, Meyer JP (2014) Influence of circumferential solar heat flux distribution on the heat transfer coefficients of linear Fresnel collector absorber tubes. Sol Energy 107: 381–397. https://doi.org/10.1016/j.solener.2014.05.011 doi: 10.1016/j.solener.2014.05.011
|
| [40] | Zeitoun O, Conjugate Laminar forced convection in partially heated tubes. Available from: https://www.researchgate.net/publication/267948343. |
| [41] |
Okafor IF, Dirker J, Meyer JP (2017) Influence of non-uniform heat flux distributions on the secondary flow, convective heat transfer and friction factors for a parabolic trough solar collector type absorber tube. Renewable Energy 108: 287–302. https://doi.org/10.1016/j.renene.2017.02.053 doi: 10.1016/j.renene.2017.02.053
|
| [42] |
Huang Z, Li ZY, Tao WQ (2017) Numerical study on combined natural and forced convection in the fully-developed turbulent region for a horizontal circular tube heated by non-uniform heat flux. Appl Energy 185: 2194–2208. https://doi.org/10.1016/j.apenergy.2015.11.066 doi: 10.1016/j.apenergy.2015.11.066
|
| [43] | Okafor IF, Dirker J, Meyer JP (2016) Turbulent mixed convection heat transfer for non-uniform heat flux distributions on a horizontal circular tube. Proceedings of the 12th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics (HEFAT 2016), 993–998. Available from: https://www.researchgate.net/publication/305496420. |
| [44] |
Okafor IF, Dirker J, Meyer JP (2019) Asymmetrical non-uniform heat flux distributions for laminar flow heat transfer with mixed convection in a horizontal circular tube. Heat Transfer Eng 40: 109–127. https://doi.org/10.1080/01457632.2017.1421055 doi: 10.1080/01457632.2017.1421055
|
| [45] |
Seco-Nicolás M, Alarcón M, Luna-Abad JP (2021) 3D numerical simulation of laminar forced-convection flow subjected to asymmetric thermal conditions. An application to solar thermal collectors. Sol Energy 220: 230–245. https://doi.org/10.1016/j.solener.2021.02.022 doi: 10.1016/j.solener.2021.02.022
|
| [46] |
Laube T, Dietrich B, Marocco L, et al. (2022) Turbulent heat transfer in a liquid metal tube flow with azimuthally inhomogeneous heat flux. Int J Heat Mass Transfer 189: 122734. https://doi.org/10.1016/j.ijheatmasstransfer.2022.122734 doi: 10.1016/j.ijheatmasstransfer.2022.122734
|
| [47] |
Vahidinia F, Khorasanizadeh H, Aghaei A (2021) Comparative energy, exergy and CO2 emission evaluations of a LS-2 parabolic trough solar collector using Al2O3/SiO2-Syltherm 800 hybrid nanofluid. Energy Convers Manage 245: 114596. https://doi.org/10.1016/j.enconman.2021.114596 doi: 10.1016/j.enconman.2021.114596
|
| [48] |
Abed N, Afgan I, Iacovides H, et al. (2021) Thermal-hydraulic analysis of parabolic trough collectors using straight conical strip inserts with nanofluids. Nanomaterials 11: 853. https://doi.org/10.3390/nano11040853 doi: 10.3390/nano11040853
|
| [49] |
Fahim T, Laouedj S, Abderrahmane A, et al. (2022) Heat transfer enhancement in parabolic through solar receiver: a three-dimensional numerical investigation. Nanomaterials 12: 419. https://doi.org/10.3390/nano12030419 doi: 10.3390/nano12030419
|
| [50] |
Enciso Contreras E, de la Cruz Alejo J, Alcocer GI, et al. (2020) Thermal analysis of a parabolic trough solar collector with synthetic oil as working fluid using a computational tool. J Technol Prototypes 6: 1–9. https://doi.org/10.35429/JTP.2020.17.6.1.9 doi: 10.35429/JTP.2020.17.6.1.9
|
| [51] |
Wang Y, Xu J, Liu Q, et al. (2016) Performance analysis of a parabolic trough solar collector using Al2O3/synthetic oil nanofluid. Appl Therm Eng 107: 469–478. https://doi.org/10.1016/j.applthermaleng.2016.06.170 doi: 10.1016/j.applthermaleng.2016.06.170
|
| [52] |
Abubakr M, Amein H, Akoush BM, et al. (2020) An intuitive framework for optimizing energetic and exergetic performances of parabolic trough solar collectors operating with nanofluids. Renewable Energy 157: 130–149. https://doi.org/10.1016/j.renene.2020.04.160 doi: 10.1016/j.renene.2020.04.160
|
| [53] |
Akbarimoosavi S, Yaghoubi M (2014) 3D thermal-structural analysis of an absorber tube of a parabolic trough collector and the effect of tube deflection on optical efficiency. Energy Procedia 49: 2433–2443. https://doi.org/10.1016/j.egypro.2014.03.258 doi: 10.1016/j.egypro.2014.03.258
|
| [54] |
Yaghoubi M, Ahmadi F, Bandehee M (2013) Analysis of heat losses of absorber tubes of parabolic through collector of Shiraz (Iran) solar power plant. J Clean Energy Technol 1: 33–37. https://doi.org/10.7763/JOCET.2013.V1.8 doi: 10.7763/JOCET.2013.V1.8
|
| [55] |
Fornarelli F, Lippolis A, Oresta P (2017) Buoyancy effect on the flow pattern and the thermal performance of an array of circular cylinders. J Heat Transfer 139: 022501. https://doi.org/10.1115/1.4034794 doi: 10.1115/1.4034794
|
| [56] |
Chang C, Li X, Zhang Q (2014) Experimental and numerical study of the heat transfer characteristics in solar thermal absorber tubes with circumferentially non-uniform heat flux. Energy Procedia 49: 305–313. https://doi.org/10.1016/j.egypro.2014.03.033 doi: 10.1016/j.egypro.2014.03.033
|
| [57] | White FM, Corfield I (2006) Viscous Fluid Flow. Vol. 3, McGraw-Hill, New York. |
| [58] |
Menter FR (2009) Review of the shear-stress transport turbulence model experience from an industrial perspective. In J Comput Fluid Dyn. 23: 305–316. https://doi.org/10.1080/10618560902773387 doi: 10.1080/10618560902773387
|
| [59] |
Malekan M, Khosravi A, Syri S (2019) Heat transfer modeling of a parabolic trough solar collector with working fluid of Fe3O4 and CuO/Therminol 66 nanofluids under magnetic field. Appl Thermal Eng 163: 114435. https://doi.org/10.1016/j.applthermaleng.2019.114435 doi: 10.1016/j.applthermaleng.2019.114435
|
| [60] |
Hoseinzadeh H, Kasaeian A, Shafii MB (2018) Geometric optimization of parabolic trough solar collector based on the local concentration ratio using the Monte Carlo method. Energy Convers Manage 175: 278–287. https://doi.org/10.1016/j.enconman.2018.09.001 doi: 10.1016/j.enconman.2018.09.001
|
| [61] |
He YL, Xiao J, Cheng Z, et al. (2011) A MCRT and FVM coupled simulation method for energy conversion process in parabolic trough solar collector. Renewable Energy 36: 976–985. https://doi.org/10.1016/j.renene.2010.07.017 doi: 10.1016/j.renene.2010.07.017
|
| [62] | Agagna B, Smaili A (2021) Effects of rim angle on performance predictions of a parabolic trough solar collector. Advances in Green Energies and Materials Technology: Selected Articles from the Algerian Symposium on Renewable Energy and Materials (ASREM-2020), 375–382. Springer. https://doi.org/10.1007/978-981-16-0378-5_49 |
| [63] | Mohammed, AK, Talabani ZJ (2013) Study of forced convection heat transfer from horizontal and vertical tubes. Int J Eng Res Techno 2: 2011–2017. Available from: https://www.ijert.org/research/study-of-forced-convection-heat-transfer-from-horizontal-and-vertical-tubes-IJERTV2IS100645.pdf. |
| [64] |
Patankar SV, Spalding DB (1983) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. Numer Predict Flow Heat Transf Turbul Combust, 54–73. https://doi.org/10.1016/B978-0-08-030937-8.50013-1 doi: 10.1016/B978-0-08-030937-8.50013-1
|
| [65] | Jamali H (2016) Analyses of absorber tube of parabolic trough solar collector (PTSC) based on convective heat transfer coefficient of fluid. Int Energy J 16: 73–86. Available from: https://www.thaiscience.info/Journals/Article/RIEJ/10992364.pdf. |
| [66] |
Almanza R, Lentz A, Jimenez G (1997) Receiver behavior in direct steam generation with parabolic troughs. Sol Energy 61: 275–278. https://doi.org/10.1016/S0038-092X(97)88854-8 doi: 10.1016/S0038-092X(97)88854-8
|
| [67] |
Flores V, Almanza R (2004) Behavior of the compound wall copper—steel receiver with stratified two-phase flow regimen in transient states when solar irradiance is arriving on one side of receiver. Sol Energy 76: 195–198. https://doi.org/10.1016/j.solener.2003.08.015 doi: 10.1016/j.solener.2003.08.015
|
| [68] |
Wang F, Shuai Y, Yuan Y, et al. (2012) Effects of material selection on the thermal stresses of tube receiver under concentrated solar irradiation. Mater Des 33: 284–291. https://doi.org/10.1016/j.matdes.2011.07.048 doi: 10.1016/j.matdes.2011.07.048
|
| [69] |
Jamali H (2019) Optimization of thermal efficiency of a parabolic trough solar collector (PTSC) based on new materials application for the absorber tube selective coating and glass cover. J Appl Res Technol 16: 384–393. https://doi.org/10.22201/icat.16656423.2018.16.5.742 doi: 10.22201/icat.16656423.2018.16.5.742
|
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Hamzeh Jamali. Numerical analysis of how azimuthally non-uniform heat flux influences turbulent convective heat transfer in parabolic trough solar collector[J]. AIMS Energy, 2025, 13(6): 1391-1416. doi: 10.3934/energy.2025052
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