Skip to main content
SpringerLink
Log in

Evaluating energy efficiency and economic effect of heat transfer in copper tube for small solar linear Fresnel reflector

  • Published:
Journal of Thermal Analysis and Calorimetry Aims and scope Submit manuscript

Abstract

An experimental and numerical investigation of a small linear Fresnel for water heating application has been carried out in Blida, Algeria. The numerical simulation with a 1D modeling in transient mode was performed by using the finite difference method. The thermal evaluation is based on the energy assessments characterized by the differential equations of pure water with a flow mass rate equal to 0.015 kg s−1 and copper absorber tube temperature. Moreover, the Fluent code has been developed in order to conduct the CFD modeling at the absorber tube of the solar collector. SolTrace software has been used to determine the optical behavior of the linear reflector. The average optical efficiency of the device is about 42.97%, but the average value of the experimental thermal efficiency reached 29.21% for 22/01/2015 and 29.20% for 19/02/2015. The average value of pure water temperature for 22/01/2015 is 67.28 °C, while its value for 19/02/2015 is 70.99 °C. This solar experimental setup will reduce the consumption of liquefied natural gas by 88.9 m3, which will reduce the CO2 emission by 187.93 kg. In addition, its manufacturing cost will be recovered 16 years from the date of use of this heater.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Abbreviations

A A,ext :

Exterior surface of the receiver tube (m²)

CpF :

Water specific heat capacity (J kg−1 °C−1)

D A,ext :

Outer diameter of the copper pipe (m)

D A,int :

Inner diameter of the copper pipe (m)

DNI:

Solar direct beam radiation (W m−2)

F :

Focal distance (m)

h F :

Convection coefficient between the water and the receiver tube (W m−2 °C−1)

h w :

Heat transfer coefficient of wind (W m−2 °C−1)

K l (θ l):

Longitudinal coefficient of incidence angle modifier (–)

K t (θ t):

Transverse coefficient of incidence angle modifier (–)

L Ab :

Receiver tube length (m)

L m :

Flat mirror length (m)

\(\dot{m}\) :

Water mass flow rate inside the receiver tube (Kg s−1)

q absorbed :

Thermal power received by the receiver tube (W)

q gain :

Energy gained by the water (W)

S e :

Effective surface of the flat mirrors (m²)

S T :

Total area of reflective mirrors (m²)

T Ab :

Temperature of copper tube (°C)

T amb :

Air temperature (°C)

T fi :

Water temperature entering the absorber tube (°C)

T fo :

Water outside temperature (°C)

U L :

Global coefficient of heat loss (W m−2 °C−1)

\(\dot{V}\) :

Volumetric flow rate of water inside the absorber tube (m3 s−1)

W :

Mirror width (m)

γ :

Intercept factor (–)

α obp :

Ordinary black paint absorptivity (–)

α Ab :

Receiver tube absorptivity (–)

α ss :

Suitable selective surface absorptivity (–)

∆X :

Length element (m)

ε Ab :

Receiver tube emissivity (–)

ε obp :

Ordinary black paint emissivity (–)

ε ss :

Emissivity coefficient of suitable selective surface (–)

θ i :

Incidence angle (°)

ρ F :

Water density (Kg m−3)

ρ m :

Mirror reflection coefficient (–)

σ :

Stefan–Boltzmann constant (W m−2 °C−4)

BDLFRs:

Beam-down linear Fresnel reflectors (–)

CFD:

Computational fluid dynamics (–)

CLFRs:

Compact linear Fresnel reflectors (–)

HTF:

Heat transfer fluid (–)

LFR:

Linear Fresnel reflector (–)

SPLFRs:

Stretched parabolic linear Fresnel reflectors (–)

References

  1. Kalogirou SA. Solar thermal collectors and applications. Prog Energy Combust Sci. 2004;30(3):231–95. https://doi.org/10.1016/j.pecs.2004.02.001.

    Article  CAS  Google Scholar 

  2. Ammar AA, et al. Performance study on photovoltaic/thermal solar-assisted heat pump system. J Therm Anal Calorim. 2019;136(1):79–87. https://doi.org/10.1007/s10973-018-7741-6.

    Article  CAS  Google Scholar 

  3. Al-Musawi AIA, et al. Numerical study of the effects of nanofluids and phase-change materials in photovoltaic thermal (PVT) systems. J Therm Anal Calorim. 2019;137(2):623–36. https://doi.org/10.1007/s10973-018-7972-6.

    Article  CAS  Google Scholar 

  4. Raj AK, et al. Performance analysis of a double-pass solar air heater system with asymmetric channel flow passages. J Therm Anal Calorim. 2019;136(1):21–38. https://doi.org/10.1007/s10973-018-7762-1.

    Article  CAS  Google Scholar 

  5. Ngo TT, Phu NM. Computational fluid dynamics analysis of the heat transfer and pressure drop of solar air heater with conic-curve profile ribs. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08709-4.

    Article  Google Scholar 

  6. Tyagi VV, et al. Thermal performance evaluation of a solar air heater with and without thermal energy storage: an experimental study. J Therm Anal Calorim. 2012;107(3):1345–52. https://doi.org/10.1007/s10973-011-1617-3.

    Article  CAS  Google Scholar 

  7. Ghodbane M, et al. Study and numerical simulation of solar system for air heating. J Fund Appl Sci. 2016;8(1):41–60. https://doi.org/10.4314/jfas.v8i1.3.

    Article  Google Scholar 

  8. Seyednezhad M, et al. Nanoparticles for water desalination in solar heat exchanger. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08634-6.

    Article  Google Scholar 

  9. Kariman H, et al. Energy and economic analysis of evaporative vacuum easy desalination system with brine tank. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08945-8.

    Article  Google Scholar 

  10. Tlili I, et al. Water management and desalination in KSA view 2030. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08700-z.

    Article  Google Scholar 

  11. Sheikhani H, et al. A review of solar absorption cooling systems combined with various auxiliary energy devices. J Therm Anal Calorim. 2018;134(3):2197–212. https://doi.org/10.1007/s10973-018-7423-4.

    Article  CAS  Google Scholar 

  12. Mahesh A, Kaushik SC. Solar adsorption refrigeration system using different mass of adsorbents. J Therm Anal Calorim. 2013;111(1):897–903. https://doi.org/10.1007/s10973-012-2264-z.

    Article  CAS  Google Scholar 

  13. Sarbu I, Sebarchievici C. Review of solar refrigeration and cooling systems. Energy Build. 2013;67:286–97. https://doi.org/10.1016/j.enbuild.2013.08.022.

    Article  Google Scholar 

  14. Rahman S, et al. Performance enhancement of a solar powered air conditioning system using passive techniques and SWCNT/R-407c nano refrigerant. Case Stud Therm Eng. 2019;16:100565. https://doi.org/10.1016/j.csite.2019.100565.

    Article  Google Scholar 

  15. Pandey AK, et al. Thermal performance evaluation of direct flow solar water heating system using exergetic approach. J Therm Anal Calorim. 2015;121(3):1365–73. https://doi.org/10.1007/s10973-015-4566-4.

    Article  CAS  Google Scholar 

  16. Shukla R, Sumathy K. Design approach of a density-driven solar water heater system: a study in North Dakota. J Therm Anal Calorim. 2019;136(1):113–20. https://doi.org/10.1007/s10973-018-7723-8.

    Article  CAS  Google Scholar 

  17. Mehmood A, et al. Performance evaluation of solar water heating system with heat pipe evacuated tubes provided with natural gas backup. Energy Rep. 2019;5:1432–44. https://doi.org/10.1016/j.egyr.2019.10.002.

    Article  Google Scholar 

  18. Kalogirou SA. Performance of solar collectors. Solar energy engineering: processes and systems. Cambridge: Academic Press; 2009. p. 219–50.

    Chapter  Google Scholar 

  19. Kalogirou SA. Solar energy engineering: processes and systems. 1st ed. Cambridge: Academic Press; 2009.

    Google Scholar 

  20. Bellos E, Tzivanidis C. A review of concentrating solar thermal collectors with and without nanofluids. J Therm Anal Calorim. 2019;135(1):763–86. https://doi.org/10.1007/s10973-018-7183-1.

    Article  CAS  Google Scholar 

  21. Rajendran DR, et al. Review on influencing parameters in the performance of concentrated solar power collector based on materials, heat transfer fluids and design. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08759-8.

    Article  Google Scholar 

  22. Said Z, et al. Fuzzy modeling and optimization for experimental thermophysical properties of water and ethylene glycol mixture for Al2O3 and TiO2 based nanofluids. Powder Technol. 2019;353:345–58.

    Article  CAS  Google Scholar 

  23. Said Z, et al. Enhancing the performance of automotive radiators using nanofluids. Renew Sustain Energy Rev. 2019;112:183–94.

    Article  CAS  Google Scholar 

  24. Sheikholeslami M, Darzi M, Li Z. Experimental investigation for entropy generation and exergy loss of nano-refrigerant condensation process. Int J Heat Mass Transf. 2018;125:1087–95. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.155.

    Article  CAS  Google Scholar 

  25. Sheikholeslami M, Shehzad SA, Li Z. Water based nanofluid free convection heat transfer in a three dimensional porous cavity with hot sphere obstacle in existence of Lorenz forces. Int J Heat Mass Transf. 2018;125:375–86. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.076.

    Article  CAS  Google Scholar 

  26. Hussein AK. Applications of nanotechnology to improve the performance of solar collectors—recent advances and overview. Renew Sustain Energy Rev. 2016;62:767–92. https://doi.org/10.1016/j.rser.2016.04.050.

    Article  Google Scholar 

  27. Hussein AK. Applications of nanotechnology in renewable energies—a comprehensive overview and understanding. Renew Sustain Energy Rev. 2015;42:460–76. https://doi.org/10.1016/j.rser.2014.10.027.

    Article  CAS  Google Scholar 

  28. Bellos E, Said Z, Tzivanidis C. The use of nanofluids in solar concentrating technologies: a comprehensive review. J Clean Prod. 2018;196:84–99. https://doi.org/10.1016/j.jclepro.2018.06.048.

    Article  CAS  Google Scholar 

  29. Stalin PMJ, et al. Experimental and theoretical investigation on the effects of lower concentration CeO2/water nanofluid in flat-plate solar collector. J Therm Anal Calorim. 2019;135(1):29–44. https://doi.org/10.1007/s10973-017-6865-4.

    Article  CAS  Google Scholar 

  30. Sheikholeslami M, Darzi M, Sadoughi MK. Heat transfer improvement and pressure drop during condensation of refrigerant-based nanofluid; an experimental procedure. Int J Heat Mass Transf. 2018;122:643–50. https://doi.org/10.1016/j.ijheatmasstransfer.2018.02.015.

    Article  CAS  Google Scholar 

  31. Sheikholeslami M, Jafaryar M, Li Z. Nanofluid turbulent convective flow in a circular duct with helical turbulators considering CuO nanoparticles. Int J Heat Mass Transf. 2018;124:980–9. https://doi.org/10.1016/j.ijheatmasstransfer.2018.04.022.

    Article  CAS  Google Scholar 

  32. Sheikholeslami M, et al. Nanofluid heat transfer augmentation and exergy loss inside a pipe equipped with innovative turbulators. Int J Heat Mass Transf. 2018;126:156–63. https://doi.org/10.1016/j.ijheatmasstransfer.2018.05.128.

    Article  CAS  Google Scholar 

  33. Hachicha AA, et al. A review study on the modeling of high-temperature solar thermal collector systems. Renew Sustain Energy Rev. 2019;112:280–98. https://doi.org/10.1016/j.rser.2019.05.056.

    Article  Google Scholar 

  34. Said Z, Arora S, Bellos E. A review on performance and environmental effects of conventional and nanofluid-based thermal photovoltaics. Renew Sustain Energy Rev. 2018;94:302–16. https://doi.org/10.1016/j.rser.2018.06.010.

    Article  CAS  Google Scholar 

  35. Loni R, et al. Energy and exergy investigation of alumina/oil and silica/oil nanofluids in hemispherical cavity receiver: experimental Study. Energy. 2018;164:275–87. https://doi.org/10.1016/j.energy.2018.08.174.

    Article  CAS  Google Scholar 

  36. Loni R, et al. GMDH modeling and experimental investigation of thermal performance enhancement of hemispherical cavity receiver using MWCNT/oil nanofluid. Sol Energy. 2018;171:790–803. https://doi.org/10.1016/j.solener.2018.07.003.

    Article  CAS  Google Scholar 

  37. Loni R, et al. Thermal performance comparison between Al2O3/oil and SiO2/oil nanofluids in cylindrical cavity receiver based on experimental study. Renew Energy. 2018;129:652–65. https://doi.org/10.1016/j.renene.2018.06.029.

    Article  CAS  Google Scholar 

  38. Sheikholeslami M, et al. Heat transfer of nanoparticles employing innovative turbulator considering entropy generation. Int J Heat Mass Transf. 2019;136:1233–40. https://doi.org/10.1016/j.ijheatmasstransfer.2019.03.091.

    Article  CAS  Google Scholar 

  39. Alkanhal TA, et al. Simulation of convection heat transfer of magnetic nanoparticles including entropy generation using CVFEM. Int J Heat Mass Transf. 2019;136:146–56. https://doi.org/10.1016/j.ijheatmasstransfer.2019.02.095.

    Article  CAS  Google Scholar 

  40. Sheikholeslami M, Arabkoohsar A, Jafaryar M. Impact of a helical-twisting device on the thermal–hydraulic performance of a nanofluid flow through a tube. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08683-x.

    Article  Google Scholar 

  41. Ghodbane M, et al. A numerical simulation of a linear Fresnel solar reflector directed to produce steam for the power plant. J Clean Prod. 2019;231:494–508. https://doi.org/10.1016/j.jclepro.2019.05.201.

    Article  Google Scholar 

  42. Villarini M, et al. Influence of the incident radiation on the energy performance of two small-scale solar organic rankine cycle trigenerative systems: a simulation analysis. Appl Energy. 2019;242:1176–88. https://doi.org/10.1016/j.apenergy.2019.03.066.

    Article  Google Scholar 

  43. Barba FJ, et al. Solar radiation as a prospective energy source for green and economic processes in the food industry: from waste biomass valorization to dehydration, cooking, and baking. J Clean Prod. 2019;220:1121–30. https://doi.org/10.1016/j.jclepro.2019.02.175.

    Article  CAS  Google Scholar 

  44. Hachicha AA, Al-Sawafta I, Said Z. Impact of dust on the performance of solar photovoltaic (PV) systems under United Arab Emirates weather conditions. Renew Energy. 2019;141:287–97. https://doi.org/10.1016/j.renene.2019.04.004.

    Article  Google Scholar 

  45. Hohne PA, Kusakana K, Numbi BP. Optimal energy management and economic analysis of a grid-connected hybrid solar water heating system: a case of Bloemfontein, South Africa. Sustain Energy Technol Assess. 2019;31:273–91. https://doi.org/10.1016/j.seta.2018.12.027.

    Article  Google Scholar 

  46. Hohne PA, Kusakana K, Numbi BP. A review of water heating technologies: an application to the South African context. Energy Rep. 2019;5:1–19. https://doi.org/10.1016/j.egyr.2018.10.013.

    Article  Google Scholar 

  47. Kumar PM, Mylsamy K. Experimental investigation of solar water heater integrated with a nanocomposite phase change material: energetic and exergetic approach. J Therm Anal Calorim. 2019;136(1):121–32. https://doi.org/10.1007/s10973-018-7937-9.

    Article  CAS  Google Scholar 

  48. Sheikholeslami M, et al. Hybrid nanoparticles dispersion into water inside a porous wavy tank involving magnetic force. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08858-6.

    Article  Google Scholar 

  49. Sheikholeslami M, et al. Second law analysis of a porous structured enclosure with nano-enhanced phase change material and under magnetic force. J Therm Anal Calorim. 2019. https://doi.org/10.1007/s10973-019-08979-y.

    Article  Google Scholar 

  50. Shafieian A, Khiadani M, Nosrati A. Thermal performance of an evacuated tube heat pipe solar water heating system in cold season. Appl Therm Eng. 2019;149:644–57. https://doi.org/10.1016/j.applthermaleng.2018.12.078.

    Article  Google Scholar 

  51. Karki S, Haapala KR, Fronk BM. Investigation of the combined efficiency of a solar/gas hybrid water heating system. Appl Therm Eng. 2019;149:1035–43. https://doi.org/10.1016/j.applthermaleng.2018.12.086.

    Article  Google Scholar 

  52. Daniels JW, Heymsfield E, Kuss M. Hydronic heated pavement system performance using a solar water heating system with heat pipe evacuated tube solar collectors. Sol Energy. 2019;179:343–51. https://doi.org/10.1016/j.solener.2019.01.006.

    Article  Google Scholar 

  53. Ghodbane M, Boumeddane B, Said N. Design and experimental study of a solar system for heating water utilizing a linear Fresnel reflector. J Fund Appl Sci. 2016;8(3):804–25. https://doi.org/10.4314/jfas.v8i3.8.

    Article  Google Scholar 

  54. Ghodbane M, Boumeddane B, Said N. A linear Fresnel reflector as a solar system for heating water: theoretical and experimental study. Case Stud Therm Eng. 2016;8(C):176–86. https://doi.org/10.1016/j.csite.2016.06.006.

    Article  Google Scholar 

  55. Ghodbane M, et al. Performance assessment of linear Fresnel solar reflector using MWCNTs/DW nanofluids. Renew Energy. 2019. https://doi.org/10.1016/j.renene.2019.10.137.

    Article  Google Scholar 

  56. Barbón A, et al. Optimization of the distribution of small scale linear Fresnel reflectors on roofs of urban buildings. Appl Math Model. 2018;2018(59):233–50. https://doi.org/10.1016/j.apm.2018.01.040.

    Article  Google Scholar 

  57. Barbón A, et al. Parametric study of the small scale linear Fresnel reflector. Renew Energy. 2018;2018(116):64–74. https://doi.org/10.1016/j.renene.2017.09.066.

    Article  Google Scholar 

  58. Barbón A, et al. Theoretical elements for the design of a small scale linear Fresnel reflector: frontal and lateral views. Sol Energy. 2016;2016(132):188–202. https://doi.org/10.1016/j.solener.2016.02.054.

    Article  Google Scholar 

  59. Bellos E, Tzivanidis C, Papadopoulos A. Daily, monthly and yearly performance of a linear Fresnel reflector. Sol Energy. 2018;173:517–29. https://doi.org/10.1016/j.solener.2018.08.008).

    Article  Google Scholar 

  60. Bellos E, Tzivanidis C, Papadopoulos A. Secondary concentrator optimization of a linear Fresnel reflector using Bezier polynomial parametrization. Sol Energy. 2018;171:716–27. https://doi.org/10.1016/j.solener.2018.07.025.

    Article  Google Scholar 

  61. Bellos E, Tzivanidis C. Development of analytical expressions for the incident angle modifiers of a linear Fresnel reflector. Sol Energy. 2018;173:769–79. https://doi.org/10.1016/j.solener.2018.08.019.

    Article  Google Scholar 

  62. Bellos E, Tzivanidis C. Assessment of linear solar concentrating technologies for Greek climate. Energy Convers Manag. 2018;171:1502–13. https://doi.org/10.1016/j.enconman.2018.06.076.

    Article  Google Scholar 

  63. Bellos E, et al. Experimental and numerical investigation of a linear Fresnel solar collector with flat plate receiver. Energy Convers Manag. 2016;130:44–59. https://doi.org/10.1016/j.enconman.2016.10.041.

    Article  CAS  Google Scholar 

  64. Bellos E. Progress in the design and the applications of linear Fresnel reflectors—a critical review. Therm Sci Eng Prog. 2019;2019(10):112–37. https://doi.org/10.1016/j.tsep.2019.01.014.

    Article  Google Scholar 

  65. Bellos E, Tzivanidis C, Papadopoulos A. Enhancing the performance of a linear Fresnel reflector using nanofluids and internal finned absorber. J Therm Anal Calorim. 2019;135(1):237–55. https://doi.org/10.1007/s10973-018-6989-1.

    Article  CAS  Google Scholar 

  66. Pulido-Iparraguirre D, et al. Optimized design of a linear Fresnel reflector for solar process heat applications. Renew Energy. 2019;131:1089–106. https://doi.org/10.1016/j.renene.2018.08.018.

    Article  Google Scholar 

  67. Dabwan YN, et al. Performance analysis of integrated linear fresnel reflector with a conventional cooling, heat, and power tri-generation plant. Renew Energy. 2019;138:639–50. https://doi.org/10.1016/j.renene.2019.01.098.

    Article  Google Scholar 

  68. Wang G, et al. Experimental and optical performances of a solar CPV device using a linear Fresnel reflector concentrator. Renew Energy. 2020;146:2351–61. https://doi.org/10.1016/j.renene.2019.08.090.

    Article  Google Scholar 

  69. Marefati M, Mehrpooya M. Introducing and investigation of a combined molten carbonate fuel cell, thermoelectric generator, linear fresnel solar reflector and power turbine combined heating and power process. J Clean Prod. 2019;240:118247. https://doi.org/10.1016/j.jclepro.2019.118247.

    Article  Google Scholar 

  70. Gang W, et al. Direct utilization of solar linear Fresnel reflector on multi-effect eccentric horizontal tubular still with falling film. Energy. 2019;170:170–84. https://doi.org/10.1016/j.energy.2018.12.150.

    Article  Google Scholar 

  71. Zhu J, Chen Z. Optical design of compact linear fresnel reflector systems. Sol Energy Mater Sol Cells. 2018;176:239–50. https://doi.org/10.1016/j.solmat.2017.12.016.

    Article  CAS  Google Scholar 

  72. Rungasamy AE, Craig KJ, Meyer JP. Comparative study of the optical and economic performance of etendue-conserving compact linear Fresnel reflector concepts. Sol Energy. 2019;181:95–107. https://doi.org/10.1016/j.solener.2019.01.081.

    Article  Google Scholar 

  73. Sánchez-González A, Gómez-Hernández J. Beam-down linear Fresnel reflector: BDLFR. Renew Energy. 2020;146:802–15. https://doi.org/10.1016/j.renene.2019.07.017.

    Article  Google Scholar 

  74. Zhu Y, et al. Design and experimental investigation of a stretched parabolic linear Fresnel reflector collecting system. Energy Convers Manag. 2016;126:89–98. https://doi.org/10.1016/j.enconman.2016.07.073.

    Article  Google Scholar 

  75. Said Z, et al. Optical performance assessment of a small experimental prototype of linear Fresnel reflector. Case Stud Therm Eng. 2019. https://doi.org/10.1016/j.csite.2019.100541.

    Article  Google Scholar 

  76. Bellos E, et al. Energy and financial investigation of a cogeneration system based on linear Fresnel reflectors. Energy Convers Manag. 2019;198:111821. https://doi.org/10.1016/j.enconman.2019.111821.

    Article  CAS  Google Scholar 

  77. Bellos E, Tzivanidis C, Papadopoulos A. Optical and thermal analysis of a linear Fresnel reflector operating with thermal oil, molten salt and liquid sodium. Appl Therm Eng. 2018;133:70–80. https://doi.org/10.1016/j.applthermaleng.2018.01.038.

    Article  CAS  Google Scholar 

  78. Ghodbane M, Boumeddane B. Estimating solar radiation according to semi empirical approach of PERRIN DE BRICHAMBAUT: application on several areas with different climate in Algeria. Int J Energ. 2016;1(1):20–9.

    Article  Google Scholar 

  79. Ghodbane M. Étude et optimisation des performances d’une machine de climatisation a éjecteur reliée à un concentrateur solaire. Blida 1: Département de génie Mécanique, Université Saad Dahleb; 2017. p. 200.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mechanical Engineering Department, Saad Dahlab University, Blida 1, Algeria

    Mokhtar Ghodbane & Boussad Boumeddane

  2. Thermal Department, School of Mechanical Engineering, National Technical University of Athens, Athens, Greece

    Evangelos Bellos

  3. Department of Sustainable and Renewable Energy Engineering, University of Sharjah, P.O. Box, 27272, Sharjah, United Arab Emirates

    Zafar Said

  4. Mechanical Engineering Department, College of Engineering, University of Babylon, Babylon City, Hilla, Iraq

    Ahmed Kadhim Hussein

  5. Department of Mechanical Engineering, College of Engineering, Haïl University, Haïl City, 2440, Saudi Arabia

    Lioua Kolsi

  6. Research Unit of Metrology and Energy Systems, Energy Engineering Department, National Engineering School, University of Monastir, 5000, Monastir, Tunisia

    Lioua Kolsi

Authors
  1. Mokhtar Ghodbane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Evangelos Bellos
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zafar Said
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Boussad Boumeddane
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Ahmed Kadhim Hussein
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Lioua Kolsi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zafar Said.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Appendix

Appendix

  1. (a)

    Flowchart for numerical simulation by Matlab

figure a
  1. (b)

    Flowchart for CFD modeling by Fluent

figure b

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghodbane, M., Bellos, E., Said, Z. et al. Evaluating energy efficiency and economic effect of heat transfer in copper tube for small solar linear Fresnel reflector. J Therm Anal Calorim 143, 4197–4215 (2021). https://doi.org/10.1007/s10973-020-09384-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10973-020-09384-6

Keywords

Search

Navigation