A CFD investigation of the effect of non-Newtonian behavior of Cu–water nanofluids on their heat transfer and flow friction characteristics

  • Qingang Xiong
  • Mehdi Vahabzadeh Bozorg
  • Mohammad Hossein Doranehgard
  • Kun HongEmail author
  • Giulio LorenziniEmail author


In the present study, a finite volume method is used to investigate heat transfer and flow friction behavior of non-Newtonian nanofluids. To study a practical application of the mentioned concept, a simple model of a parabolic trough solar receiver is simulated. The main objective of the present study is to investigate the effect of non-Newtonian behavior of the working fluid on the performance of a parabolic trough solar collector. The heat transfer fluid is assumed to be a non-Newtonian nanofluid, and the flow regime is considered to be laminar. The effect of Cu nanoparticle addition on heat transfer coefficient and flow friction of Newtonian, shear-thinning and shear-thickening nanofluids are studied. To comprehensively investigate the effect of buoyancy-driven secondary flows on the average Nusselt number and friction factor of the absorber tube, simulations are carried out for different Grashof numbers (Gr = 105, 106, 107), Reynolds numbers (Re = 200, 500, 1000), Cu nanoparticle volume fractions (φ = 0, 0.01, 0.03) and non-Newtonian power-law indexes (n = 0.25, 0.75, 1, 1.25, 1.75). It is concluded that when shear-thickening nanofluids are utilized as the working fluid, nanoparticle addition makes no sensible changes in the average Nusselt number. Besides, for all values of non-Newtonian power-law index, variations in volume fraction values do not have any significant effect on the friction factor. Furthermore, it is shown that when the working fluid is shear-thinning, nanoparticle addition triggers to considerable increment in Nusselt number. At high Grashof and Reynolds numbers, the ratios of Nusselt number and friction factor of shear-thinning nanofluids (n = 0.25) to those of shear-thickening nanofluids are up to 3.57 and 0.08, respectively.


CFD Nanofluid Non-Newtonian fluid Laminar flow Heat transfer coefficient Pressure drop 

List of symbols


Specific heat (J kg−1 K−1)


Diameter of the base fluid molecule (m)


Diameter of the nanoparticle (m)


Rate of deformation tensor


Secondary flow


Gravitational acceleration (m s−2)


Receiver tube length (m)


Receiver tube diameter (m)


Boltzmann constant (J K−1)


Power-law index


Nusselt number


Pressure (Pa)


Consistency index


Grashof number


Reynolds number


Dimensionless friction factor


Streamwise velocity (m s−1)


Parabolic trough collector


Heat transfer fluid


Concentration of the receiver tube


Temperature (K)


Heat flux (W m−2)


Velocity field (m s−1)


Brownian velocity











Base fluid






Mixture (nanofluid)



x, y, z

Cartesian coordinates (m)



Greek letters


Thermal diffusivity (m2 s−1)


Thermal expansion coefficient (K−1)


Dimensionless temperature


Nanoparticle volume fraction


Dynamic viscosity (kg m−1 s−1)


Density (kg m−3)


Shear stress (Pa)

\(\dot{\gamma }\)

Effective strain rate


Thermal conductivity (W m−1 K−1)



  1. 1.
    Shahsavani E, Afrand M, Kalbasi R. Using experimental data to estimate the heat transfer and pressure drop of non-Newtonian nanofluid flow through a circular tube: applicable for use in heat exchangers. Appl Therm Eng. 2018;129:1573–81.CrossRefGoogle Scholar
  2. 2.
    Mwesigye A, Huan Z, Meyer JP. Thermodynamic optimisation of the performance of a parabolic trough receiver using synthetic oil–Al2O3 nanofluid. Appl Energy. 2015;156:398–412.CrossRefGoogle Scholar
  3. 3.
    Okafor IF, Dirker J, Meyer JP. 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. Renew Energy. 2017;108:287–302.CrossRefGoogle Scholar
  4. 4.
    Mwesigye A, Meyer JP. Optimal thermal and thermodynamic performance of a solar parabolic trough receiver with different nanofluids and at different concentration ratios. Appl Energy. 2017;193:393–413.CrossRefGoogle Scholar
  5. 5.
    Bozorg MV, Siavashi M. Two-phase mixed convection heat transfer and entropy generation analysis of a non-Newtonian nanofluid inside a cavity with internal rotating heater and cooler. Int J Mech Sci. 2019;151:842–57.CrossRefGoogle Scholar
  6. 6.
    Salari E, Peyghambarzadeh SM, Sarafraz MM, Hormozi F, Nikkhah V. Thermal behavior of aqueous iron oxide nano-fluid as a coolant on a flat disc heater under the pool boiling condition. Heat Mass Transf. 2017;53:265–75.CrossRefGoogle Scholar
  7. 7.
    Sarafraz MM, Arya A, Nikkhah V, Hormozi F. Thermal performance and viscosity of biologically produced silver/coconut oil nanofluids. Chem Biochem Eng Q. 2016;30:489–500.CrossRefGoogle Scholar
  8. 8.
    Sarafraz MM, Safaei MR, Tian Z, Goodarzi M, Bandarra Filho EP, Arjomandi M. Thermal assessment of nano-particulate graphene-water/ethylene glycol (WEG 60: 40) nano-suspension in a compact heat exchanger. Energies. 2019;12:1929.CrossRefGoogle Scholar
  9. 9.
    Sarafraz MM, Arya H, Saeedi M, Ahmadi D. Flow boiling heat transfer to MgO-therminol 66 heat transfer fluid: experimental assessment and correlation development. Appl Therm Eng. 2018;138:552–62.CrossRefGoogle Scholar
  10. 10.
    Sarafraz MM, Nikkhah V, Nakhjavani M, Arya A. Thermal performance of a heat sink microchannel working with biologically produced silver-water nanofluid: experimental assessment. Exp Therm Fluid Sci. 2018;91:509–19.CrossRefGoogle Scholar
  11. 11.
    Sarafraz MM, Arjomandi M. Thermal performance analysis of a microchannel heat sink cooling with Copper Oxide-Indium (CuO/In) nano-suspensions at high-temperatures. Appl Therm Eng. 2018;137:700–9.CrossRefGoogle Scholar
  12. 12.
    Arya A, Sarafraz MM, Shahmiri S, Madani SAH, Nikkhah V, Nakhjavani SM. Thermal performance analysis of a flat heat pipe working with carbon nanotube-water nanofluid for cooling of a high heat flux heater. Heat Mass Transf. 2018;54:985–97.CrossRefGoogle Scholar
  13. 13.
    Salari E, Peyghambarzadeh M, Sarafraz MM, Hormozi F. Boiling heat transfer of alumina nano-fluids: role of nanoparticle deposition on the boiling heat transfer coefficient. Period Polytech Chem Eng. 2016;60:252–8.CrossRefGoogle Scholar
  14. 14.
    Kole M, Dey TK. Effect of aggregation on the viscosity of copper oxide–gear oil nanofluids. Int J Therm Sci. 2011;50:1741–7.CrossRefGoogle Scholar
  15. 15.
    Behroyan I, Vanaki SM, Ganesan P, Saidur R. A comprehensive comparison of various CFD models for convective heat transfer of Al2O3 nanofluid inside a heated tube. Int Commun Heat Mass Transf. 2016;70:27–37.CrossRefGoogle Scholar
  16. 16.
    Siavashi M, Karimi K, Xiong Q, Doranehgard MH. Numerical analysis of mixed convection of two-phase non-Newtonian nanofluid flow inside a partially porous square enclosure with a rotating cylinder. J Therm Anal Calorim. 2019;137(1):267–87.CrossRefGoogle Scholar
  17. 17.
    Gasljevic K, Aguilar G, Matthys EF. Buoyancy effects on heat transfer and temperature profiles in horizontal pipe flow of drag-reducing fluids. Int J Heat Mass Transf. 2000;43:4267–74.CrossRefGoogle Scholar
  18. 18.
    Duffie JA, Beckman WA. Solar engineering of thermal processes. New York: Wiley; 2013.CrossRefGoogle Scholar
  19. 19.
    Zeitoun O. Heat transfer for laminar flow in partially heated tubes. Alex Eng J. 2002;41:205–12.Google Scholar
  20. 20.
    Hewitt GF, Shires GL, Polezhaev YV, Devahastin S. International encyclopedia of heat and mass transfer. Dry Technol. 1998;16:1521–2.CrossRefGoogle Scholar
  21. 21.
    Ede AJ. The heat transfer coefficient for flow in a pipe. Int J Heat Mass Transf. 1961;4:105–10.CrossRefGoogle Scholar
  22. 22.
    Barozzi GS, Zanchini E, Mariotti M. Experimental investigation of combined forced and free convection in horizontal and inclined tubes. Meccanica. 1985;20:18–27.CrossRefGoogle Scholar
  23. 23.
    Yasuo M, Kozo F, Shinobu T, Masakuni N. Forced convective heat transfer in uniformly heated horizontal tubes 1st report—experimental study on the effect of Buoyancy. Int J Heat Mass Transf. 1966;9:453–63.CrossRefGoogle Scholar
  24. 24.
    Xiong Q, Yeganeh MM, Yaghoubi E, Asadi A, Doranehgard MH, Hong K. Parametric investigation on biomass gasification in a fluidized bed gasifier and conceptual design of gasifier. Chem Eng Process Intensif. 2018;127:271–91.CrossRefGoogle Scholar
  25. 25.
    Asadi A, Zhang Y, Mohammadi H, Khorand H, Rui Z, Doranehgard MH, et al. Combustion and emission characteristics of biomass derived biofuel, premixed in a diesel engine: a CFD study. Renew Energy. 2019;138:79–89.CrossRefGoogle Scholar
  26. 26.
    Bidabadi M, Bozorg MV, Bordbar V. A three-dimensional simulation of discrete combustion of randomly dispersed micron-aluminum particle dust cloud and applying genetic algorithm to obtain the flame front. Energy. 2017;140:804–17.CrossRefGoogle Scholar
  27. 27.
    Vahabzadeh Bozorg M, Bidabadi M, Bordbar V. Numerical investigation of flame behavior and quenching distance in randomly distributed poly-dispersed iron dust cloud combustion within a narrow channel. J Hazard Mater. 2019;367:482–91.CrossRefGoogle Scholar
  28. 28.
    Mahian O, Kianifar A, Sahin AZ, Wongwises S. Heat transfer, pressure drop, and entropy generation in a solar collector using SiO2/water nanofluids: effects of nanoparticle size and pH. J Heat Transf. 2015;137:61011.CrossRefGoogle Scholar
  29. 29.
    Goudarzi K, Shojaeizadeh E, Nejati F. An experimental investigation on the simultaneous effect of CuO–H2O nanofluid and receiver helical pipe on the thermal efficiency of a cylindrical solar collector. Appl Therm Eng. 2014;73:1236–43.CrossRefGoogle Scholar
  30. 30.
    Sarafraz MM, Safaei MR. Diurnal thermal evaluation of an evacuated tube solar collector (ETSC) charged with graphene nanoplatelets-methanol nano-suspension. Renew Energy. 2019;142:364–72.CrossRefGoogle Scholar
  31. 31.
    Eastman JA, Choi SUS, Li S, Yu W, Thompson LJ. Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Appl Phys Lett. 2001;78:718–20.CrossRefGoogle Scholar
  32. 32.
    Wang Y, Xu J, Liu Q, Chen Y, Liu H. Performance analysis of a parabolic trough solar collector using Al2O3/synthetic oil nanofluid. Appl Therm Eng. 2016;107:469–78.CrossRefGoogle Scholar
  33. 33.
    Bozorg MV, Hossein Doranehgard M, Hong K, Xiong Q. CFD study of heat transfer and fluid flow in a parabolic trough solar receiver with internal annular porous structure and synthetic oil–Al2O3 nanofluid. Renew Energy. 2019;145:2598–614.CrossRefGoogle Scholar
  34. 34.
    Li Z-Y, Huang Z, Tao W-Q. Three-dimensional numerical study on fully-developed mixed laminar convection in parabolic trough solar receiver tube. Energy. 2016;113:1288–303.CrossRefGoogle Scholar
  35. 35.
    Khanafer K, Vafai K. A critical synthesis of thermophysical characteristics of nanofluids. Int J Heat Mass Transf. 2011;54:4410–28.CrossRefGoogle Scholar
  36. 36.
    Haddad Z, Oztop HF, Abu-Nada E, Mataoui A. A review on natural convective heat transfer of nanofluids. Renew Sustain Energy Rev. 2012;16:5363–78.CrossRefGoogle Scholar
  37. 37.
    Zhou S-Q, Ni R. Measurement of the specific heat capacity of water-based Al2O3 nanofluid. Appl Phys Lett. 2008;92:93123.CrossRefGoogle Scholar
  38. 38.
    Morais AF, Seybold H, Herrmann HJ, Andrade JS Jr. Non-Newtonian fluid flow through three-dimensional disordered porous media. Phys Rev Lett. 2009;103:194502.CrossRefGoogle Scholar
  39. 39.
    Corcione M. Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids. Energy Convers Manag. 2011;52:789–93.CrossRefGoogle Scholar
  40. 40.
    Bergman TL, Incropera FP, DeWitt DP, Lavine AS. Fundamentals of heat and mass transfer. New York: Wiley; 2011.Google Scholar
  41. 41.
    Ghasemi SE, Ranjbar AA. Effect of using nanofluids on efficiency of parabolic trough collectors in solar thermal electric power plants. Int J Hydrog Energy. 2017;42:21626–34.CrossRefGoogle Scholar
  42. 42.
    Mahian O, Kolsi L, Amani M, Estellé P, Ahmadi G, Kleinstreuer C, et al. Recent advances in modeling and simulation of nanofluid flows-part II: Applications. Phys Rep. 2018;791:1–59.CrossRefGoogle Scholar
  43. 43.
    Patankar S. Numerical heat transfer and fluid flow. Cambridge: CRC Press; 1980.Google Scholar
  44. 44.
    Spalding DB. A novel finite difference formulation for differential expressions involving both first and second derivatives. Int J Numer Methods Eng. 1972;4:551–9.CrossRefGoogle Scholar
  45. 45.
    Minea AA, El-Maghlany WM. Influence of hybrid nanofluids on the performance of parabolic trough collectors in solar thermal systems: recent findings and numerical comparison. Renew Energy. 2018;120:350–64.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.National & Local Joint Engineering Research Center for Mineral Salt Deep Utilization, Key Laboratory for Palygorskite Science and Applied Technology of Jiangsu ProvinceHuaiyin Institute of TechnologyHuaianChina
  2. 2.Department of Energy Conversion, Combustion Research Laboratory, School of Mechanical EngineeringIran University of Science and TechnologyTehranIran
  3. 3.Department of Civil and Environmental Engineering, School of Mining and Petroleum EngineeringUniversity of AlbertaEdmontonCanada
  4. 4.IT Innovation Center, General MotorsWarrenUSA
  5. 5.Department of Engineering and ArchitectureUniversity of ParmaParmaItaly

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