Skip to main content

Application of copper oxide–thermal oil (CuO-HTO) nanofluid on convective heat transfer enhancement in inclined circular tube


The influence of using copper oxide–thermal oil on convective heat transfer and pressure drop in an upward flow in an inclined smooth tube is studied experimentally in this paper. The flow regime and wall temperature are laminar and constant, respectively. The effects of nanofluid, Graetz number, Prandtl number, negative inclination angle on convective heat transfer rate rise moderately with the augmentation of nanoparticles mass concentration. Both correlations are recommended to evaluate Nusselt number and Darcy friction factor in an upward flow under constant wall temperature and laminar flow in smooth pipe. The maximum deviations are 19% and 21%, respectively, which are acceptable for scientific research to be used in industrial applications. Accompaniment of heat transfer ratio with pumping power ratio is presented in this paper. If the increment of pressure drop is more than heat transfer enhancement, it will not be appropriate to use CuO–thermal oil, negative inclination angles and smooth tube. The figure of merit increases up to 1.58% which is calculated with 1.5% nanoparticle mass concentration and inclination angle of 30° at Prandtl number of 387. The results show that most of the values are more than unity, so the heat transfer enhancement is more than increment of pressure drop.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


C p :

Specific heat capacity/kJ kg−1 K−1

f :

Darcy friction factor/\(\pi^{2} \rho D^{5} \Delta P\, 2L\dot{m}^{2}\)

Gz :

Graetz number/Re Pr D/L

h :

Convection coefficient/W/m2 K


Thermal conductivity/W/m K

\(\dot{m}\) :

Mass flow rate/kg s

N :

Number of fins


Nusselt number/h k

Pr :

Prandtl number/μCp k

\(\dot{Q}\) :

Flow rate/m3 s

Re :

Reynolds number/ρuD μ

T :


\(\Delta P\) :

Pressure drop/Pa

U :


z :

The height of fin/m

ϑ :

Dynamic viscosity/m3 s


Figure of merit

ρ :

Density/kg m3

\(\Delta \rho\) :

Density difference/kg m3

θ :

Inclination of tubes/°

φ :

Nanoparticles mass concentration/%


Pumping power/W


Characteristics of fluid at average bulk temperature

bf :

Base fluid

b, o:

Bulk outlet

b, i:

Bulk inlet


Experimental values

nf :



Appraised at the wall conditions


  1. Asadi A, Asadi M, Rezaniakolaei A, Rosendahl LA, Afrand M, Wongwises S. Heat transfer efficiency of Al2O3-MWCNT/thermal oil hybrid nanofluid as cooling fluid in thermal and energy management applications: an experimental and theoretical investigation. Int J Heat Mass Transf. 2018;117:474–86.

    Article  CAS  Google Scholar 

  2. Wei B, Zou C, Yuan X, Li X. Thermo-physical properties evaluation of diathermic oil based hybrid nanofluids for heat transfer application. Int J Heat Mass Transf. 2017;107:281–7.

    Article  CAS  Google Scholar 

  3. Amir A, Shanbedi M, Yamand H, Azani HK, Gharehkhani S, Montazer E, Sadri R, Sarsam W, Chew BT, Kazi SN. Laminar convective heat transfer of hexylamine-treated MWCNTs-based turbine oil nanofluid. Energy Convers Manag. 2015;105:355–67.

    Article  CAS  Google Scholar 

  4. Dastmalchi M, Arefmanesh A, Sheikhzadeh GA. Numerical investigation of heat transfer and pressure drop of heat transfer oil in smooth and micro-finned tubes. Int J Therm Sci. 2017;121:294–304.

    Article  Google Scholar 

  5. Li W, Zou C, Li X. Thermo-physical properties of waste cooking oil-based nanofluid. Appl Therm Eng. 2016;112:784–92.

    Article  CAS  Google Scholar 

  6. Asadi A, Asadi M, Rezaniakolaei A, Rosendahi LA. An experimental and theoretical investigation on heat transfer capability of Mg (OH)/MWCNT-engine oil hybrid nano-lubricant adopted as a coolant and lubricant fluid. Appl Therm Eng. 2018;129:577–86.

    Article  CAS  Google Scholar 

  7. Ilyas SU, Pendyala R, Narahari M. Rheological behaviour of mechanically stabilized and surfactant-free MWCNT-thermal oil-based nanofluid. Int Commun Heat Mass Transfer. 2017;87:250–5.

    Article  CAS  Google Scholar 

  8. Ambreen T, Kim M-H. Heat transfer and pressure drop correlation of nanofluid: a state of art of art review. Renew Sustain Energy Rev. 2018;91:564–83.

    Article  CAS  Google Scholar 

  9. Ilyas SU, Pendyala R, Narahri M. Experimental investigation of natural convection heat transfer characteristics in MWCNT-thermal oil nanofluid. J Therm Anal Calorim. 2018.

    Article  Google Scholar 

  10. Rashidi S, Eskandarian M, Mahian O, Poncet S. Combination of nanofluid and inserts for heat transfer enhancement. J Therm Anal Calorim. 2018.

    Article  Google Scholar 

  11. Jafaryar M, Sheikholeslami M, Li Z. Nanofluid turbulent flow in a pipe under the effect of twisted tape with alternate axis. J Therm Anal Calorim. 2018.

    Article  Google Scholar 

  12. Akbari OA, Hassanzadeh Afrouzi H, Marzban A, Toghraie D. Investigation of volume fraction of nanoparticles effect and aspect ratio of the twisted tape in the tube. J Therm Anal Calorim. 2017;129(3):1911–22.

    Article  CAS  Google Scholar 

  13. Hashemi SM, Akhavan-Behabadi MA. An empirical study on heat transfer and pressure drop characteristics of CuO-base oil nanofluid flow in a horizontal helically coiled tube under constant. Int Commun Heat Mass Transf. 2012;39(1):144–51.

    Article  CAS  Google Scholar 

  14. Mirfendereski S, Abbassi A, Saffar-avval M. Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall heat flux. Adv Powder Technol. 2015;26(5):1483–94.

    Article  CAS  Google Scholar 

  15. Fakoor Pakdaman M, Akhavan-Behabadi MA, Razi P. An experimental investigation on thermos-physical properties and overall performance of MWCNT/heat transfer oil nanofluid flow inside vertical helically coiled tubes. Exp Therm Fluid Sci. 2012;40:103–11.

    Article  CAS  Google Scholar 

  16. Hekmatipour F, Jalali M, Hekmatipour F, Akhavan-Behabadi MA, Sajadi B. On the convection heat transfer and pressure drop of copper oxide-heat transfer oil nanofluid in inclined microfin tube. Heat Mass Transf. 2018.

    Article  Google Scholar 

  17. Zeinali Heris S, Hassan TH, Noie SH, Sardarabadi H, Sardarabadi M. Laminar convective heat transfer of Al2O3/water nanofluid through square cross-sectional duct. Int J Heat Fluid Flow. 2013;44:375–82.

    Article  CAS  Google Scholar 

  18. Razi P, Akavan-Behabadi MA, Saeedinia M. Pressure drop and thermal characteristics of CuO-base oil nanofluid laminar flow in flattened tubes under constant heat flux. Int Commun Heat Mass Transf. 2011;38(7):964–71.

    Article  CAS  Google Scholar 

  19. Ashtiani D, Akhavan-Behabadi MA, Fakoor Pakdaman M. An experimental investigation on heat transfer characteristics of multi-walled CNT-heat transfer oil nanofluid flow inside flattened tubes under uniform wall temperature condition. Int Commun Heat Mass Transf. 2012;39(9):1404–9.

    Article  CAS  Google Scholar 

  20. Jafarimoghaddam A, Aberoumand S, Javaherdeh K, Abbassian Arani AA. Al/oil nanofluid inside annular tube: an experimental study on convective heat transfer and pressure drop. Heat Mass Transf. 2018;54(4):1053–67.

    Article  CAS  Google Scholar 

  21. Jafarimoghaddam A, Aberoumand S, Aberouman H, Javaherdeh K. Experimental study on Cu/Oil nanofluids through concentric annular tube: a correlation. Heat Transf Asian Res. 2017;46(3):251–60.

    Article  Google Scholar 

  22. Akhavan-Behabadi MA, Hekmatipour F, Sajadi B. An empirical study on the mixed convection transfer and pressure drop of HTO/CuO nanofluid in inclined tube. Exp Therm Fluid Sci. 2016;78:10–7.

    Article  CAS  Google Scholar 

  23. Hekmatipour F, Akhavan-Behabadi MA, Sajadi B, Fkoor-Pakdaman M. Mixed convection heat transfer and pressure drop characteristics of the copper oxide-heat transfer oil (CuO-HTO) nanofluid in vertical tube. Case Stud Therm Eng. 2017;10:532–40.

    Article  Google Scholar 

  24. Derakhshan MM, Akhavan-Behabadi MA. Mixed convection of MWCNT-heat transfer oil nanofluid inside inclined plain and microfin tubes under laminar assisted flow. Int J Therm Sci. 2016;99:1–8.

    Article  CAS  Google Scholar 

  25. Ben Mansour R, Galanis N, Nguyen CT. Experimental study of mixed convection with water-Al2O3 nanofluid in inclined tube with uniform wall heat flux. Int J Therm Sci. 2011;50(3):403–10.

    Article  CAS  Google Scholar 

  26. Derakhshan MM, Akhavan-Behabadi MA, Mohseni SG. Experimental on mixed convection heat transfer and performance evaluation of MWCNT-Oil nanofluid flow in horizontal and vertical microfin tubes. Exp Therm Fluid Sci. 2015;61:241–8.

    Article  CAS  Google Scholar 

  27. Zeinali Heris S, Farzin F, Sardarabadi H. Experimental comparison among thermal characteristics of three metal oxide nanoparticles/turbine oil-based nanofluids under laminar flow regime. Int J Thermophys. 2015;36(4):760–82.

    Article  CAS  Google Scholar 

  28. Zeinali Heris S, Nasr Esfahany M, Etemad G. Investigation of CuO/water nanofluid laminar convective heat transfer through a circular tube. J Enhanc Heat Transf. 2006;13(4):279–89.

    Article  Google Scholar 

  29. Farzin F, Zeinali Heris S, Rahimi S. laminar convective heat transfer and pressure drop of TiO2/Turbine oil nanofluid. J Thermophys Heat Transf. 2013;27(1):127–33.

    Article  CAS  Google Scholar 

  30. Zeniali Heris S, Gh Etemad S, Esfahany MN. Convective heat transfer of Cu/Water nanofluid flowing through a circular tube. Exp Heat Transf. 2009;22:217–27.

    Article  CAS  Google Scholar 

  31. Ben Mansour R, Galanis N, Nguyen CT. Developing laminar mixed convection of nanofluids inclined tube with uniform wall heat flux. Int J Numer Methods Heat Fluid Flow. 2009;19(2):146–64.

    Article  CAS  Google Scholar 

  32. Mansour RB, Galanis N, Nguyen CT. Experimental study on mixed convection with water–Al2O3 nanofluid in inclined tube with uniform wall heat flux. Int J Therm Sci. 2011;50(3):403–10.

    Article  CAS  Google Scholar 

  33. Akhavan- Behabadi MA, Hekmatipour F, Mirhabibi SM, Sajadi B. Experimental investigation of thermal-rheological properties and heat transfer behaviour of the heat transfer oil-copper oxide (HTO- CuO) nanofluid in smooth tubes. Exp Therm Fluid Sci. 2015;68:681–8.

    Article  CAS  Google Scholar 

  34. Lorenzini M, Morini GL, Henning T, Brandnet J. Uncertainty assessment in friction factor measurements as a tool to design experimental set-ups. Int J Therm Sci. 2008;48:282–9.

    Article  CAS  Google Scholar 

  35. Holman JP, Heat Transfer, Tenth Edition, McGraw Hill, 2010.,_Tenth_Edition_(

  36. Rea U, McKrell T, Hu L-W, Buongiorno J. Laminar convective heat transfer and viscous pressure loss of alumina–water nanofluids. Int J Heat Mass Transf. 2009;52:2042–8.

    Article  CAS  Google Scholar 

  37. Ranjbarzadeh R, Karimipour A, Afrand M, Isfahani AHM, Shirneshan A. Empirical analysis of heat transfer and friction factor of water/graphene oxide nanofluid flow in turbulent regime through an isothermal pipe. Appl Therm Eng. 2017;126:538–47.

    Article  CAS  Google Scholar 

  38. Meyer JP, McKrell TJ, Grote K. The influence of multi-walled carbon nanotubes on single heat transfer and pressure drop characteristics in the transitional flow regime of smooth tubes. Int J Heat Mass Transf. 2013;58:597–609.

    Article  CAS  Google Scholar 

  39. Ferrouillat S, Bontemps A, Ribeiro J-P, Gruss J-A, Soriano O. Hydraulic and heat transfer study of SiO2/water nanofluids in horizontal tubes with imposed wall temperature boundary conditions. Int J Heat Fluid Flow. 2011;32:424–39.

    Article  CAS  Google Scholar 

  40. Sarkar JA. Critical review on convective heat transfer correlations of nanofluids. Renew Sustain Energy Rev. 2011;15:3271–7.

    Article  CAS  Google Scholar 

  41. Bergman TL, Lavine AS, Incropera FP, Dewitt DP. Fundamentals of heat and mass transfer. 7th ed. Hoboken: Willey; 2011.

    Google Scholar 

  42. Saeedinia M, Akhavan-Behabadi MA, Nasr M. Experimental study on heat transfer and pressure drop of nanofluid flow in horizontal coiled wire inserted tube under constant heat flux. Exp Therm Fluid Sci. 2012;36:158–68.

    Article  CAS  Google Scholar 

  43. Feng Z-Z, Li W. Laminar mixed convection of large-Prandtl-number in-tube nanofluid flow, Part I: experimental study. Int J Heat Mass Transf. 2013;65:919–27.

    Article  CAS  Google Scholar 

  44. Li W, Feng Z-Z. Laminar mixed convection of large-Prandtl-number in-tube nanofluid flow, Part II: correlations. Int J Heat Mass Transf. 2013;65:928–35.

    Article  CAS  Google Scholar 

  45. Brown AR, Thomas MA. Combined free and forced convection heat transfer for laminar flow in horizontal tubes. Ins Mech Eng. 1965;7(4):440.

    Article  Google Scholar 

  46. Anoop KB, Sundararajn T, Das SK. Effect of particle size on the convection heat transfer in nanofluid in the developing region. Int J Heat Mass Transf. 2009;52:2189–95.

    Article  CAS  Google Scholar 

  47. Moffat RJ. Describing the uncertainties in experimental result. Exp Therm Fluid Sci. 1988;1(1):3–17.

    Article  Google Scholar 

  48. Gupta M, Arora N, Kumar R, Kumar S, Dilbaghi N. A comprehensive review of experimental investigations of forced convective heat transfer characteristics for various nanofluid. Int J Mech Mater Eng. 2014;9:11–32.

    Article  Google Scholar 

  49. Kahani M, Zeinali Heris S, Mousavi SM. Comparative study between metal oxide nanoparticles on thermal characteristics of nanofluid flow through helical coils. Powder Technol. 2013;246:82–92.

    Article  CAS  Google Scholar 

  50. Wongcharee K, Eiamsa-ard S. Enhancement of heat transfer using CuO/water nanofluid and twisted tape with alternative axis. Int Commun Heat Mass Transf. 2011;38:742–8.

    Article  CAS  Google Scholar 

  51. Ho CJ, Chen WC, Yan WM. Experimental study on cooling performance of minichannel heat sink using water-based MEPCM particle. Int Commun Heat Mass Transf. 2013;48:67–72.

    Article  CAS  Google Scholar 

  52. Routbort JL, Singh D, Timofeeva EV, France DM. Pumping power of nanofluid in flowing system. J Nanopart Res. 2011;13:931–7.

    Article  CAS  Google Scholar 

  53. Choudhury D, Pantakar SV. Combined forced and free laminar convection in the entrance region of an inclined isothermal tube. J Heat Transfer. 1988;110(4a):901–9.

    Article  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Farhad Hekmatipour.



Based on the literature [28, 29], if the parameter of R depends on V1 to Vn variables which can be gauged with an uncertainty of UV1 to UVn, the overall uncertainty of R is:

$$U_{R} = \left[ {\mathop \sum \limits_{i = 1}^{n} \left( {\frac{\partial R}{{\partial V_{\text{i}} }} U_{{V_{\text{i}} }} } \right)^{2} } \right]^{1/2}$$

Based on the definition of the Darcy friction factor, Eq. (1):

$$U_{f} = \left[ { \left( {\frac{{\pi^{2} D^{5} }}{{L\rho \dot{Q}^{3} }}\Delta pU_{{{\dot{\text{Q}}}}} } \right)^{2} + \left( {\frac{{\pi^{2} D^{5} }}{{L\rho \dot{Q}^{2} }}U_{{\Delta {\text{p}}}} } \right)^{2} + \left( {\frac{{\pi^{2} D^{5} }}{{L\rho^{2} \dot{Q}^{2} }}\Delta pU_{\uprho} } \right)^{2} } \right]^{1/2}$$

Moreover, for the Nusselt number, Eq. (2):

$$ \begin{aligned} U_{\text{Nu}} & = \left\{ {\left[ {\frac{{\rho c_{\text{p}} }}{\pi Lk}\ln \left( {\frac{{T_{w} - T_{\text{b,i}} }}{{T_{w} - T_{\text{b,o}} }}} \right)U_{{{\dot{\text{Q}}}}} } \right]^{2} + \left[ {\frac{{\rho c_{p} \dot{Q}}}{\pi Lk}\frac{{T_{\text{b,o}} - T_{\text{b,i}} }}{{\left( {T_{\text{w}} - T_{\text{b,i}} } \right)\left( {T_{\text{w}} - T_{\text{b,o}} } \right)}}U_{{{\text{T}}_{\text{w}} }} } \right]^{2} + \left[ {\frac{{\rho c_{\text{p}} \dot{Q}}}{\pi Lk}\frac{1}{{T_{\text{w}} - T_{\text{b,i}} }}U_{{{\text{T}}_{\text{b,i}} }} } \right]^{2} } \right. \\ & \quad \left. { + \,\left[ {\frac{{\rho c_{\text{p}} \dot{Q}}}{\pi Lk}\frac{1}{{T_{\text{w}} - T_{\text{b,o}} }}U_{{{\text{T}}_{{{\text{b}} . {\text{o}}}} }} } \right]^{2} + \left[ {\frac{{c_{\text{p}} \dot{Q}}}{\pi Lk}\ln \left( {\frac{{T_{\text{w}} - T_{\text{b,i}} }}{{T_{\text{w}} - T_{\text{b,o}} }}} \right)U_{\rho } } \right]^{2} + \left[ {\frac{{\rho \dot{Q}}}{\pi Lk}\ln \left( {\frac{{T_{w} - T_{\text{b,i}} }}{{T_{\text{w}} - T_{\text{b,o}} }}} \right)U_{{{\text{c}}_{\text{p}} }} } \right]^{2} } \right\}^{1/2} \\ \end{aligned} $$

From the definition of the performance index, Eq. (8), it can be concluded that:

$$U_{\eta } = \left[ { \left( {\frac{{1/h_{{{\text{b}}_{\text{f}} }} }}{{\varOmega_{{{\text{n}}_{\text{f}} }} /\varOmega_{{{\text{b}}_{\text{f}} }} }}U_{{{\text{h}}_{{{\text{n}}_{\text{f}} }} }} } \right)^{2} + \left( {\frac{{h_{{{\text{n}}_{\text{f}} }} /h_{{{\text{b}}_{\text{f}} }}^{2} }}{{\varOmega_{{{\text{n}}_{\text{f}} }} /\Delta p_{{{\text{b}}_{\text{f}} }} }}U_{{{\text{h}}_{{{\text{b}}_{\text{f}} }} }} } \right)^{2} + \left( {\frac{{h_{{{\text{n}}_{\text{f}} }} /h_{{{\text{b}}_{\text{f}} }} }}{{\varOmega_{{{\text{n}}_{\text{f}} }}^{2} /\varOmega_{{{\text{b}}_{\text{f}} }} }}U_{{\Delta {\text{p}}_{{{\text{n}}_{\text{f}} }} }} } \right)^{2} + \left( {\frac{{h_{{{\text{n}}_{\text{f}} }} /h_{{{\text{b}}_{\text{f}} }} }}{{\varOmega_{{{\text{n}}_{\text{f}} }} }}U_{{\Delta {\text{p}}_{{{\text{n}}_{\text{f}} }} }} } \right)^{2} } \right]^{1/2}$$

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Hekmatipour, F., Jalali, M. Application of copper oxide–thermal oil (CuO-HTO) nanofluid on convective heat transfer enhancement in inclined circular tube. J Therm Anal Calorim 136, 2449–2459 (2019).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Nanofluid
  • Pressure drop
  • Convective heat transfer
  • Upward flow
  • Laminar flow