Skip to main content

Numerical study of flow and heat transfer of water-Al2O3 nanofluid inside a channel with an inner cylinder using Eulerian–Lagrangian approach


The present paper is a numerical study on heat transfer and pressure drop of a nanofluid including water as base fluid with Al2O3 nanoparticles inside a square channel having an inner cylinder, with and without fin under constant heat flux condition using two-phase Euler–Lagrange approach. Numerical investigation has been carried out for various combinations of base fluid, nanoparticle size and concentration through a straight cylinder. Simulation has been performed in a laminar flow regime using finite volume method. Besides, the thermal boundary condition of constant uniform heat flux on the channel wall was applied. The results show that the increase in Reynolds number and nanoparticle volume concentration have considerable effects on heat transfer coefficient enhancement. The heat transfer coefficient decreases when nanoparticles diameter increases. The passive way used in this study, leads to higher pressure drops. For all fluids under consideration, pressure drop escalates with Reynolds number. Adding nanoparticles to the base fluid leads to rise in pressure drop, and this effect is more intensive for higher concentrations.

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
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18


A :

Particle surface area, m2

B :

Channel height/m

C c :

Cunningham correction factor to Stokes’ drag law

C p :

Specific heat/J kg−1 K−1

D :

Rigid cylinder diameter

\(d_{\text{p}}\) :

Particle diameter/nm

\(d_{\text{ij}}\) :

Deformation tensor

\(F_{\text{D}}\) :

Drag force/N kg−1

\(F_{\text{L}}\) :

Lift force/N kg−1

\(F_{\text{V}}\) :

Virtual mass force/N kg−1

\(F_{\text{G}}\) :

Gravity force/N kg−1

\(F_{\text{P}}\) :

Pressure gradient force/N kg−1

\(F_{\text{B}}\) :

Brownian force/N kg−1

g :

Gravity acceleration/m s−2

h :

Convective heat transfer coefficient/W m−2 K

k :

Thermal conductivity for fluid/W m−1 K−1

\(k_{\text{B}}\) :

Boltzmann constant (= \(1.3807 \times 10^{23}\)) J K-1

L :

Axial length/m

\(m_{\text{p}}\) :

Mass of particle/kg

\(n_{\text{p}}\) :

Number of solid particle in cell volume

\(Nu\) :

Nusselt number

P :

Pressure/N m−2

Q :

Heat flux/W m−2

Re :

Reynolds number

S p,e :

Energy transfer between fluid and particle

S 0 :

Spectral intensity basis

\(S_{\text{n,ij}}\) :

Spectral intensity

t :


T :


v :

Velocity/m s−1

μ :

Dynamic viscosity/N sm−2

\(\delta_{\text{ij}}\) :

Kronecker delta function



\(\zeta_{i}\) :

Zero-mean, unit-variance-independent

λ :

Molecular free path/m

ν :

Kinematic viscosity/m s−2

ρ :

Density/kg m−3






  1. 1.

    Alipour H, Karimipour A, Safaei MR, Toghraie Semiromi D, Akbari OA. Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver–water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel. Phys E: Low-Dimens Syst Nanostruct. 2017;88:60–76.

    CAS  Article  Google Scholar 

  2. 2.

    Gravndyan Q, Akbari OA, Toghraie D, Marzban A, Mashayekhi R, Karimi R, Pourfattah F. The effect of aspect ratios of rib on the heat transfer and laminar water/Tio2 nanofluid flow in a two-dimensional rectangular microchannel. J Mol Liq. 2017;236:254–65.

    CAS  Article  Google Scholar 

  3. 3.

    Mushtaq Ismael H. Investigation of flow and heat transfer characteristics in micro pin fin heat sink with nanofluids. Appl Therm Eng. 2014;63:598–607.

    Article  Google Scholar 

  4. 4.

    Dardan E, Afrand M, Isfahani AM. Effect of suspending hybrid nano-additives on rheological behavior of engine oil and pumping power. Appl Ther Eng. 2016;109:524–34.

    CAS  Article  Google Scholar 

  5. 5.

    Vafaei M, Afrand M, Sina N, Kalbasi R, Sourani F, Teimouri H. Evaluation of thermal conductivity of MgO-MWCNTs/EG hybrid nanofluids based on experimental data by selecting optimal artificial neural networks. Phys E. 2017;85:90–6.

    CAS  Article  Google Scholar 

  6. 6.

    Afrand M, Najafabadi KN, Sina N, Safaei MR, Kherbeet AS, Wongwises S, Dahari M. Prediction of dynamic viscosity of a hybrid nano-lubricant by an optimal artificial neural network. Int Communic Heat Mass Transf. 2016;76:209–14.

    CAS  Article  Google Scholar 

  7. 7.

    Toghraie D, Mokhtari M, Afrand M. Molecular dynamic simulation of copper and platinum nanoparticles Poiseuille flow in a nanochannels. Phys E. 2016;84:152–61.

    CAS  Article  Google Scholar 

  8. 8.

    Esfe MH, Motahari K, Sanatizadeh E, Afrand M, Rostamian H, Ahangar MR. Estimation of thermal conductivity of CNTs-water in low temperature by artificial neural network and correlation. Int Communic Heat Mass Transf. 2016;76:376–81.

    Article  Google Scholar 

  9. 9.

    Afrand M, Nadooshan AA, Hassani M, Yarmand H, Dahari M. Predicting the viscosity of multi-walled carbon nanotubes/water nanofluid by developing an optimal artificial neural network based on experimental data. Int Communic Heat Mass Transf. 2016;77:49–53.

    CAS  Article  Google Scholar 

  10. 10.

    Afrand M. Experimental study on thermal conductivity of ethylene glycol containing hybrid nano-additives and development of a new correlation. Appl Therm Eng. 2017;110:1111–9.

    CAS  Article  Google Scholar 

  11. 11.

    Goodarzi M, Kherbeet AS, Afrand M, Sadeghinezhad E, Mehrali M, Zahedi P, Wongwises S, Dahari M. Investigation of heat transfer performance and friction factor of a counter-flow double-pipe heat exchanger using nitrogen-doped, graphene-based nanofluids. Int Communic Heat Mass Transf. 2016;76:16–23.

    CAS  Article  Google Scholar 

  12. 12.

    Chengara A, Nikolov AD, Wasan DT, Trokhymchuk A, Henderson D. Spreading of nanofluids driven by the structural disjoining pressure gradient. J Coll Interface Sci. 2004;280:192–201.

    CAS  Article  Google Scholar 

  13. 13.

    Bahiraei M. Effect of particle migration on flow and heat transfer characteristics of magnetic nanoparticle suspensions. J Mol Liq. 2015;209:531–8.

    CAS  Article  Google Scholar 

  14. 14.

    Bahiraei M. A numerical study of heat transfer characteristics of CuO–water nanofluid by Euler–Lagrange approach. J Therm Anal Calorim. 2016;123:–9.

  15. 15.

    Bahiraei M, Rahim Mashaei P. Using nanofluid as a smart suspension in cooling channels with discrete heat sources: numerical investigation and modeling. J Therm Anal Calorim. 2015;119:–91.

  16. 16.

    Goudarzi K, Jamali H. Heat transfer enhancement of Al2O3-EG nanofluid in a car radiator with wire coil inserts. Appl Therm Eng. 2017;118:510–7.

    CAS  Article  Google Scholar 

  17. 17.

    Ding ZW, Cheah SC, Saeid NH. Parametric study of heat transfer enhancement using nanofluids, In: Energy and Environment, ICEE 2009, 3rd International Conference, IEEE, 2009:294–298.

  18. 18.

    Sohel MR, Khaleduzzaman SS, Saidur R, Hepbasli A, Sabri MFM, Mahbubul IM. An experimental investigation of heat transfer enhancement of a mini-channel heat sink using Al2O3–H2O nanofluids. Int J Heat Mass Transf. 2014;74:164–72.

    CAS  Article  Google Scholar 

  19. 19.

    Ho C, Wei LC, Li ZW. An experimental investigation of forced convective cooling performance of a microchannel heat sink with Al2O3/water nanofluids. Appl Therm Eng. 2010;30:96–103.

    CAS  Article  Google Scholar 

  20. 20.

    Akbarzadeh S, Farhadi M, Sedighi K, Ebrahimi M. Experimental investigation on the thermal conductivity and viscosity of ZnO nanofluid and development of new correlations. Transp Phenom Nano Micro Scale. 2014;2:149–60.

    Google Scholar 

  21. 21.

    Nguyen CT, Roy G, Gauthier C, Galanis N. Heat transfer enhancement using Al2O3–water nanofluid for an electronic liquid cooling system. Appl Therm Eng. 2017;27:1501–6.

    Article  Google Scholar 

  22. 22.

    Zhang J, Diao Y, Zhao Y, Zhang Y. An experimental investigation of heat transfer enhancement in mini-channel: combination of nanofluid and micro fin structure techniques. Exp Therm Fluid Sci. 2017;81:21–32.

    CAS  Article  Google Scholar 

  23. 23.

    Shi S, Yan C, Niu G. Numerical study of heat transfer and pressure drop of integral pin-fin tubes. In: Proceedings of the Power and Energy Engineering Conference (APPEEC), Asia-Pacific, IEEE, 2011:1–4.

  24. 24.

    Mir NA, Syed KS, Iqbal M. Numerical solution of fluid flow and heat transfer in the finned double pipe. J Res Sci. 2004;15:253–62.

    Google Scholar 

  25. 25.

    Akbari OA, Safaei MR, Goodarzi M, Noreen SA, Zarringhalam M, Ahmadi Sheikh Shabani G, Dahari M. A modified two-phase mixture model of nanofluid flow and heat transfer in a 3-D curved micro-tube. Adv Powder Technol. 2016;27:2175–85.

    CAS  Article  Google Scholar 

  26. 26.

    Moshizi SA, Malvandi A, Ganji DD, Pop I. A two-phase theoretical study ofAl2O3–water nanofluid flow inside a concentric pipe with heat generation/absorption. Int J Therm Sci. 2014;84:347–57.

    CAS  Article  Google Scholar 

  27. 27.

    Esmaeilnejad A, Aminfar H, Shafiee Neistanak M. Numerical investigation of forced convection heat transfer through micro-channels with non-Newtonian nanofluids. Int J Therm Sci. 2014;75:76–86.

    CAS  Article  Google Scholar 

  28. 28.

    Bahiraei M. A comprehensive review on different numerical approaches for simulation in nanofluids: traditional and novel techniques. J Dispersion Sci Technol. 2014;35:984–96.

    CAS  Article  Google Scholar 

  29. 29.

    Bahiraei M. Particle migration in nanofluids: a critical review. Int J Therm Sci. 2016;109:90–113.

    CAS  Article  Google Scholar 

  30. 30.

    Behnampour A, Akbari OA, Safaei MR, Ghavami M, Marzban A, Shabani GA, Mashayekhi R. Analysis of heat transfer and nanofluid fluid flow in microchannels with trapezoidal, rectangular and triangular shaped ribs. Phys E: Low-Dimens Sys Nanostr. 2017;91:15–31.

    CAS  Article  Google Scholar 

  31. 31.

    Buongiorno J, Hu LW, Kim SJ, Hannink R, Truong BA, Forrest E. Nanofluids for enhanced economics and safety of nuclear reactors: an evaluation of the potential features, issues, and research gaps. Nucl Technol. 2008;162:80–91.

    CAS  Article  Google Scholar 

  32. 32.

    Bahiraei M. Studying nanoparticle distribution in nanofluids considering the effective factors on particle migration and determination of phenomenological constants by Eulerian–Lagrangian simulation. Adv Powder Technol. 2015;26:802–10.

    Article  Google Scholar 

  33. 33.

    Li A, Ahmadi G. Dispersion and deposition of spherical particles from point sources in a turbulent channel flow. Aerosol Sci Technol. 1992;16:209–26.

    CAS  Article  Google Scholar 

  34. 34.

    Bazdidi-Tehrani F, Sedaghatnejad M, Vasefi SI, Ekrami Jolandan N. Investigation of mixed convection and particle dispersion of nanofluids in a vertical duct. Proc Inst Mech Eng, Part C: J Mech Eng Sci. 2016;230:3691–705.

    CAS  Article  Google Scholar 

  35. 35.

    Ranz WE, Marshall WR. Evaporation from drops. Chem Eng Prog. 1952;48:141446.

    Google Scholar 

  36. 36.

    Saffman PG. The lift on a small sphere in a slow shear flow. J Fluid Mech. 1965;22:385–400.

    Article  Google Scholar 

  37. 37.

    Crowe CT, Schwarzkopf JD, Sommerfeld M, Tsuji Y. Multiphase flows with droplets and particles. Boca Raton: CRC Press; 2011.

    Book  Google Scholar 

  38. 38.

    Murthy JY, Minkowycz WJ, Sparrow EM, Mathur SR, Pletcher RH, Heinrich JC, Kassab AJ, Wrobel LC, Bialecki RA, Divo EA, Madnia CK. Handbook of numerical heat transfer.

  39. 39.

    Akbari OA, Toghraie D, Karimipour A. Impact of ribs on flow parameters and laminar heat transfer of water-aluminum oxide nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel. Adv Mech Eng. 2015;7:1–11.

    CAS  Article  Google Scholar 

  40. 40.

    Bergman TL, Incropera FP. Fundamentals of heat and mass transfer. New York: Wiley; 2011.

    Google Scholar 

  41. 41.

    White FM. Fluid mechanics, vol. WCB. Boston: McGraw-Hill; 1999.

    Google Scholar 

  42. 42.

    Afrand M. Using a magnetic field to reduce natural convection in a vertical cylindrical annulus. Int J Therm Sci. 2107;118:12–23.

  43. 43.

    Afrand M, Toghraie D, Karimipour A, Wongwises S. A numerical study of natural convection in a vertical annulus filled with gallium in the presence of magnetic field. J Magn Magn Mater. 2017;430:22–8.

    CAS  Article  Google Scholar 

  44. 44.

    Afrand M, Farahat S, Hossein Nezhad A, Sheikhzadeh GA, Sarhaddi F, Wongwises S. Multi-objective optimization of natural convection in a cylindrical annulus mold under magnetic field using particle swarm algorithm. Int Commun Heat Mass Transf. 2015;60:13–20.

    Article  Google Scholar 

  45. 45.

    Afrand M, Farahat S, Nezhad AH, Ali Sheikhzadeh G, Sarhaddi F. 3-D numerical investigation of natural convection in a tilted cylindrical annulus containing molten potassium and controlling it using various magnetic fields. Int J Appl Electromagn Mech. 2014;46:809–21.

    Google Scholar 

  46. 46.

    Afrand M, Farahat S, Nezhad AH, Sheikhzadeh GA, Sarhaddi F. Numerical simulation of electrically conducting fluid flow and free convective heat transfer in an annulus on applying a magnetic field. Heat Transf Res. 2014;45:8.

    Article  Google Scholar 

  47. 47.

    Afrand M, Rostami S, Akbari M, Wongwises S, Esfe MH, Karimipour A. Effect of induced electric field on magneto-natural convection in a vertical cylindrical annulus filled with liquid potassium. Int J Heat Mass Transf. 2015;90:418–26.

    CAS  Article  Google Scholar 

  48. 48.

    Akbari OA, Toghraie D, Karimipour A, Marzban A, Ahmadi GR. The effect of velocity and dimension of solid nanoparticles on heat transfer in non-Newtonian nanofluids. Phys E: Low-Dimens Sys Nanostruct. 2017;86:68–75.

    CAS  Article  Google Scholar 

  49. 49.

    Akbari OA, Toghraie D, Karimipour A, Safaei MR, Goodarzi M, Alipour H, Dahari M. Investigation of rib’s height effect on heat transfer and flow parameters of laminar water–Al2O3 nanofluid in a rib-microchannel. Appl Math Comput. 2016;290:135–53.

    Google Scholar 

  50. 50.

    Saeedan M, Bahiraei M. Effects of geometrical parameters on hydrothermal characteristics of shell-and-tube heat exchanger with helical baffles: numerical investigation, modeling and optimization. Chem Eng Res Des. 2015;96:43–53.

    CAS  Article  Google Scholar 

  51. 51.

    Nazari S, Toghraie D. Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium. Phys E: Low-Dimens Sys Nanostruct. 2107;87:134–40.

  52. 52.

    Karimipour A, Alipour H, Akbari OA, Semiromi DT, Esfe MH. Studying the effect of indentation on flow parameters and slow heat transfer of water-silver nano-fluid with varying volume fraction in a rectangular two-dimensional micro channel. Indian J Sci Technol. 2015;8:51707.

    Article  Google Scholar 

  53. 53.

    Safaei MR, Gooarzi M, Akbari OA, Shadloo MS, Dahari M. Performance evaluation of nanofluids in an inclined ribbed microchannel for electronic cooling applications. In: Electronic Cooling, INTECH Publication; 2016.

  54. 54.

    Akbari OA, Afrouzi HH, Marzban A, Toghraie D, Malekzade H, Arabpour A. Investigation of volume fraction of nanoparticles effect and aspect ratio of the twisted tape in the tube. J Therm Anal Calorim. in press (2017).

  55. 55.

    Akbari OA, Toghraie D, Karimipour A. Numerical simulation of heat transfer and turbulent flow of water nanofluids copper oxide in rectangular microchannel with semi attached rib. Adv Mech Eng. 2016;8:1–25.

    CAS  Article  Google Scholar 

  56. 56.

    Mashayekhi R, Khodabandeh E, Bahiraei M, Bahrami L, Toghraie D, Akbari OA. Application of a novel conical strip insert to improve the efficacy of water–Ag nanofluid for utilization in thermal systems: a two-phase simulation. Energy Convers Manage. 2017;151:573–86.

    CAS  Article  Google Scholar 

  57. 57.

    Khodabandeh E, Rahbari A, Rosen MA, Ashrafi ZN, Akbari OA, Anvari AM. Experimental and numerical investigations on heat transfer of a water-cooled lance for blowing oxidizing gas in an electrical arc furnace. Energy Convers Manage. 2017;148:43–56.

    CAS  Article  Google Scholar 

  58. 58.

    Khodabandeh E, Pourramezan M, Pakravan MH. Effects of excess air and preheating on the flow pattern and efficiency of the radiative section of a fired heater. Appl Therm Eng. 2016;105:537–48.

    Article  Google Scholar 

  59. 59.

    Khodabandeh E, Ghaderi M, Afzalabadi A, Rouboa A, Salarifard A. Parametric study of heat transfer in an electric arc furnace and cooling system. Appl Therm Eng. 2017;123:1190–200.

    Article  Google Scholar 

  60. 60.

    Kim D, Kwon Y, Cho Y, Li C, Cheong S, Hwang Y, Lee J, Hong D, Moon S. Convective heat transfer characteristics of nanofluids under laminar and turbulent flow conditions. Curr Appl Phys. 2009;9:119–23.

    Article  Google Scholar 

  61. 61.

    Garoosi F, Talebi F. Numerical analysis of conjugate natural and mixed convection heat transfer of nanofluids in a square cavity using the two-phase method. Adv Powder Technol. 2017;28:1668–95.

    CAS  Article  Google Scholar 

  62. 62.

    Garoosi F, Talebi F. Numerical simulation of conjugate conduction and natural convection heat transfer of nanofluid inside a square enclosure containing a conductive partition and several disconnected conducting solid blocks using the Buongiorno’s two phase model. Powder Technol. 2017;317:48–71.

    CAS  Article  Google Scholar 

  63. 63.

    Garoosi F, Rashidi MM. Two phase flow simulation of conjugate natural convection of the nanofluid in a partitioned heat exchanger containing several conducting obstacles. Int J Mech Sci. 2017;160:282–306.

    Article  Google Scholar 

  64. 64.

    Garoosi F, Shakibaeinia A, Bagheri G. Eulerian–Lagrangian modeling of solid particle behavior in a square cavity with several pairs of heaters and coolers inside. Powder Technol. 2015;280:239–55.

    CAS  Article  Google Scholar 

  65. 65.

    Garoosi F, Safaei MR, Dahari M, Hooman K. Eulerian–Lagrangian analysis of solid particle distribution in an internally heated and cooled air-filled cavity. Appl Math Comput. 2015;250:28–46.

    Google Scholar 

  66. 66.

    Garoosi F, Hoseininejad F, Rashidi MM. Numerical study of heat transfer performance of nanofluids in a heat exchanger. Appl Therm Eng. 2016;105:436–55.

    Article  Google Scholar 

  67. 67.

    Garoosi F, Hoseininejad F, Rashidi MM. Numerical study of natural convection heat transfer in a heat exchanger filled with nanofluids. Energy. 2016;109:664–78.

    CAS  Article  Google Scholar 

  68. 68.

    Garoosi F, Hoseininejad F. Numerical study of natural and mixed convection heat transfer between differentially heated cylinders in an adiabatic enclosure filled with nanofluid. J Mol Liq. 2016;215:1–7.

    CAS  Article  Google Scholar 

  69. 69.

    Garoosi F, Jahanshaloo L, Garoosi S. Numerical simulation of mixed convection of the nanofluid in heat exchangers using a Buongiorno model. Powder Technol. 2015;269:296–311.

    CAS  Article  Google Scholar 

  70. 70.

    Garoosi F, Garoosi S, Hooman K. Numerical simulation of natural convection and mixed convection of the nanofluid in a square cavity using Buongiorno model. Powder Technol. 2014;268:279–92.

    CAS  Article  Google Scholar 

  71. 71.

    Goodarzi M, Safaei MR, Vafai K, Ahmadi G, Dahari M, Kazi SN, Jomhari N. Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model. Int J Therm Sci. 2014;75:204–20.

    CAS  Article  Google Scholar 

  72. 72.

    Safaei MR, Togun H, Vafai K, Kazi SN, Badarudin A. Investigation of heat transfer enhancement in a forward-facing contracting channel using FMWCNT nanofluids. Numer Heat Transf, Part A: Appl. 2014;66:1321–40.

    CAS  Article  Google Scholar 

  73. 73.

    Goshayeshi HR, Goodarzi M, Safaei MR, Dahari M. Experimental study on the effect of inclination angle on heat transfer enhancement of a ferrofluid in a closed loop oscillating heat pipe under magnetic field. Exp Therm Fluid Sci. 2016;74:265–70.

    CAS  Article  Google Scholar 

  74. 74.

    Goodarzi M, Amiri A, Goodarzi MS, Safaei MR, Karimipour A, Languri EM, Dahari M. Investigation of heat transfer and pressure drop of a counter flow corrugated plate heat exchanger using MWCNT based nanofluids. Int Commun Heat Mass Transf. 2015;66:172–9.

    CAS  Article  Google Scholar 

  75. 75.

    Goshayeshi HR, Safaei MR, Goodarzi M, Dahari M. Particle size and type effects on heat transfer enhancement of Ferro-nanofluids in a pulsating heat pipe. Powder Technol. 2016;301:1218–26.

    CAS  Article  Google Scholar 

  76. 76.

    Safaei MR, Ahmadi G, Goodarzi MS, Safdari Shadloo M, Goshayeshi HR, Dahari M. Heat transfer and pressure drop in fully developed turbulent flows of graphene nanoplatelets–silver/water nanofluids. Fluids. 2016;1:20.

    Article  Google Scholar 

  77. 77.

    Safaei MR, Safdari Shadloo M, Goodarzi MS, Hadjadj A, Goshayeshi HR, Afrand M, Kazi SN. A survey on experimental and numerical studies of convection heat transfer of nanofluids inside closed conduits. Adv Mech Eng. 2016;8:1687814016673569.

    Article  Google Scholar 

  78. 78.

    Esfahani JA, Safaei MR, Goharimanesh M, De Oliveira LR, Goodarzi M, Shamshirband S, Bandarra Filho EP. Comparison of experimental data, modelling and non-linear regression on transport properties of mineral oil based nanofluids. Powder Technol. 2017;317:458–70.

    CAS  Article  Google Scholar 

  79. 79.

    Safaei MR, Jahanbin A, Kianifar A, Gharehkhani S, Kherbeet AS, Goodarzi M, Dahari M. Mathematical modeling for nanofluids simulation: a review of the latest works. In: Modeling and Simulation in Engineering Sciences 2016. InTech.

  80. 80.

    Hosseini SM, Safaei MR, Goodarzi M, Alrashed AA, Nguyen TK. New temperature, interfacial shell dependent dimensionless model for thermal conductivity of nanofluids. Int J Heat Mass Transf. 2017;114:207–10.

    CAS  Article  Google Scholar 

  81. 81.

    Rezaei O, Akbari OA, Marzban A, Toghraie D, Pourfattah F, Mashayekhi R. The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel. Phys E. 2017;93:179–89.

    CAS  Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Mehdi Bahiraei.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ahmadi, A.A., Khodabandeh, E., Moghadasi, H. et al. Numerical study of flow and heat transfer of water-Al2O3 nanofluid inside a channel with an inner cylinder using Eulerian–Lagrangian approach. J Therm Anal Calorim 132, 651–665 (2018).

Download citation


  • Convection heat transfer
  • Nanofluid
  • Two-phase
  • Euler–Lagrange method
  • Separation sheet