Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 3, pp 1629–1641 | Cite as

Analytical investigation of nanoparticle migration in a duct considering thermal radiation

  • Zhixiong LiEmail author
  • S. Saleem
  • Ahmad Shafee
  • Ali J. Chamkha
  • Sunwen Du


Buongiorno model is applied to investigate nanofluid migration through a permeable duct in the presence of external forces. Influences of radiation and Joule heating on first law equation are added. Final formulas are solved via differential transform method. Roles of suction, thermophoretic, radiation and Brownian motion parameters, Schmidt number, Hartmann number, Eckert number were presented. Results show that temperature gradient improves with the enhancement of Reynolds number, suction and Radiation parameters. Nu augments with the augmentation of Hartmann and Eckert numbers, while reverse behavior is seen for skin friction coefficient. Also, it can be concluded that Nusselt number enhances with the increase in radiation parameter but it decreases with the increase in Brownian motion.


Differential transform method Porous duct Nanoparticle Lorentz forces Buongiorno model 

List of symbols


Magnetic induction (Tesla)


Prandtl number


Radiation parameter


Hartmann number


Specific heat capacity (J/kgK)


Vertical and horizontal velocities (m/s)


Thermal radiation (W)


Fluid temperature (K)

Greek symbols


Stefan–Boltzmann constant


Dynamic viscosity (Pa s)


Volume fraction of nanofluid


Thermal diffusivity (m2 s−1)


Similarity-independent variable


Mean absorption coefficient


Electrical conductivity



Thermal quantity


Base fluid



Authors would like to express their gratitude to King Khalid University, Abha 61413, Saudi Arabia, for providing administrative and technical support.


  1. 1.
    Karimipour A, D’Orazio A, Shadloo MS. The effects of different nano particles of Al2O3 and Ag on the MHD nano fluid flow and heat transfer in a microchannel including slip velocity and temperature jump. Physica E. 2017;86:146–53.CrossRefGoogle Scholar
  2. 2.
    Maleki H, Safaei MR, Abdullah AA, Alrashed A, Kasaeian A. Flow and heat transfer in non-Newtonian nanofluids over porous surfaces. J Therm Anal Calorim. 2018. Scholar
  3. 3.
    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.CrossRefGoogle Scholar
  4. 4.
    Hosseini SM, Safaei MR, Goodarzi M, Abdullah AA, Alrashed A, Nguyen TK. New temperature, interfacial shell dependent dimensionless model for thermal conductivity of nanofluids. Int J Heat Mass Transf. 2017;114:207–10.CrossRefGoogle Scholar
  5. 5.
    Esfahani JA, Safaei MR, Goharimanesh M, Oliveira LR, Goodarzi M, Shamshirband S, Filho EPB. Comparison of experimental data, modelling and non-linear regression on transport properties of mineral oil based nanofluids. Powder Techno. 2017;317:458–70.CrossRefGoogle Scholar
  6. 6.
    Sheikholeslami M, Rokni HB. Simulation of nanofluid heat transfer in presence of magnetic field: a review. Int J Heat Mass Transf. 2017;115:1203–33.CrossRefGoogle Scholar
  7. 7.
    Sheikholeslami M, Ganji DD. Nanofluid convective heat transfer using semi analytical and numerical approaches: a review. J Taiwan Inst Chem Eng. 2016;65:43–77.CrossRefGoogle Scholar
  8. 8.
    Rizwan UH, Shahzad F, Al-Mdallal QM. MHD pulsatile flow of engine oil based carbon nanotubes between two concentric cylinders. Results Phys. 2017;7:57–68.CrossRefGoogle Scholar
  9. 9.
    Sheikholeslami M. Finite element method for PCM solidification in existence of CuO nanoparticles. J Mol Liq. 2018;265:347–55.CrossRefGoogle Scholar
  10. 10.
    Arani AAA, AliAkbari O, Safaei MR, Marzban A, Alrashed AAAA, Ahmadi GR, Nguyen TK. Heat transfer improvement of water/single-wall carbon nanotubes (SWCNT) nanofluid in a novel design of a truncated double-layered microchannel heat sink. Int J Heat Mass Transf. 2017;113:780–95.CrossRefGoogle Scholar
  11. 11.
    Sheikholeslami M, Jafaryar M, Saleem S, Li Z, Shafee A, Jiang Y. Nanofluid heat transfer augmentation and exergy loss inside a pipe equipped with innovative turbulators. Int J Heat Mass Transf. 2018;126:156–63.CrossRefGoogle Scholar
  12. 12.
    Khodabandeh E, Safaei MR, Akbari S, AliAkbari O, Alrashed AAAA. Application of nanofluid to improve the thermal performance of horizontal spiral coil utilized in solar ponds: geometric study. Renew Energy. 2018;122:1–16.CrossRefGoogle Scholar
  13. 13.
    Tao YB, He YL. Effects of natural convection on latent heat storage performance of salt in a horizontal concentric tube. Appl Energy. 2015;143(1):38–46.CrossRefGoogle Scholar
  14. 14.
    Ahmed N, Adnan, Khan U, Mohyud-Din ST. Unsteady radiative flow of chemically reacting fluid over a convectively heated stretchable surface with cross-diffusion gradients. Int J Therm Sci. 2017;121:182–91.CrossRefGoogle Scholar
  15. 15.
    Sheikholeslami M, Ghasemi A, Li Z, Shafee A, Saleem S. Influence of CuO nanoparticles on heat transfer behavior of PCM in solidification process considering radiative source term. Int J Heat Mass Transf. 2018;126:1252–64.CrossRefGoogle Scholar
  16. 16.
    Alrashed AAAA, Gharibdousti MS, Goodarzi M, Oliveira LR, Safaei MR, Filho EPB. Effects on thermophysical properties of carbon based nanofluids: experimental data, modelling using regression, ANFIS and ANN. Int J Heat Mass Transf. 2018;125:920–32.CrossRefGoogle Scholar
  17. 17.
    Jafaryar M, Sheikholeslami M, Li Z, Moradi R. Nanofluid turbulent flow in a pipe under the effect of twisted tape with alternate axis. J Therm Anal Calorim. 2018. Scholar
  18. 18.
    Nasiri H, Abdollahzadeh Jamalabadi MY, Sadeghi R, Safaei MR, Nguyen TK, Shadloo MS. A smoothed particle hydrodynamics approach for numerical simulation of nano-fluid flows. J Therm Anal Calorim. 2018. Scholar
  19. 19.
    Sheikholeslami M. Solidification of NEPCM under the effect of magnetic field in a porous thermal energy storage enclosure using CuO nanoparticles. J Mol Liq. 2018;263:303–15.CrossRefGoogle Scholar
  20. 20.
    Goodarzi M, Safaei MR, Vafai K, Ahmadi G. Investigation of nanofluid mixed convection in a shallow cavity using a two-phase mixture model. Int J Therm Sci. 2014;75:204–20.CrossRefGoogle Scholar
  21. 21.
    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.CrossRefGoogle Scholar
  22. 22.
    Kandelousi MS. KKL correlation for simulation of nanofluid flow and heat transfer in a permeable channel. Phys Lett A. 2014;378(45):3331–9.CrossRefGoogle Scholar
  23. 23.
    Sheikholeslami M, Ganji DD. Nanofluid flow and heat transfer between parallel plates considering Brownian motion using DTM. Comput Methods Appl Mech Engrg. 2015;283:651–63.CrossRefGoogle Scholar
  24. 24.
    Sheikholeslami M, Shehzad SA, Abbasi FM, Li Z. Nanofluid flow and forced convection heat transfer due to Lorentz forces in a porous lid driven cubic enclosure with hot obstacle. Comput Methods Appl Mech Eng. 2018;338:491–505.CrossRefGoogle Scholar
  25. 25.
    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.CrossRefGoogle Scholar
  26. 26.
    Sheikholeslami M, Shehzad SA, Li Z. Nanofluid heat transfer intensification in a permeable channel due to magnetic field using Lattice Boltzmann method. Physica B: Condens Matter. 2018;542:51–8.CrossRefGoogle Scholar
  27. 27.
    Sheikholeslami M. Numerical simulation for solidification in a LHTESS by means of Nano-enhanced PCM. J Taiwan Inst Chem Eng. 2018;86:25–41.CrossRefGoogle Scholar
  28. 28.
    Jafaryar M, Sheikholeslami M, Li Z. CuO-water nanofluid flow and heat transfer in a heat exchanger tube with twisted tape turbulator. Powder Technol. 2018;336:131–43.CrossRefGoogle Scholar
  29. 29.
    Safaei MR, Shadloo MS, 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(10):1–14.CrossRefGoogle Scholar
  30. 30.
    Sheikholeslami M. Numerical modeling of Nano enhanced PCM solidification in an enclosure with metallic fin. J Mol Liq. 2018;259:424–38.CrossRefGoogle Scholar
  31. 31.
    Sheikholeslami M, Ghasemi A. Solidification heat transfer of nanofluid in existence of thermal radiation by means of FEM. Int J Heat Mass Transf. 2018;123:418–31.CrossRefGoogle Scholar
  32. 32.
    Sheikholeslami M, Shehzad SA. CVFEM simulation for nanofluid migration in a porous medium using Darcy model. Int J Heat Mass Transf. 2018;122:1264–71.CrossRefGoogle Scholar
  33. 33.
    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.CrossRefGoogle Scholar
  34. 34.
    Sheikholeslami M, Rokni HB. CVFEM for effect of Lorentz forces on nanofluid flow in a porous complex shaped enclosure by means of Non-equilibrium model. J Mol Liquids. 2018;254:446–62.CrossRefGoogle Scholar
  35. 35.
    Sheikholeslami M. Magnetohydrodynamic nanofluid forced convection in a porous lid driven cubic cavity using Lattice Boltzmann Method. J Mol Liq. 2017;231:555–65.CrossRefGoogle Scholar
  36. 36.
    Sheikholeslami M, Bhatti MM. Active method for nanofluid heat transfer enhancement by means of EHD. Int J Heat Mass Transf. 2017;109:115–22.CrossRefGoogle Scholar
  37. 37.
    Sheikholeslami M, Shehzad SA. Thermal radiation of ferrofluid in existence of Lorentz forces considering variable viscosity. Int J Heat Mass Transf. 2017;109:82–92.CrossRefGoogle Scholar
  38. 38.
    Sheikholeslami M, Rokni HB. Magnetic nanofluid flow and convective heat transfer in a porous cavity considering Brownian motion effects. Phys Fluids. 2018;10(1063/1):5012517.Google Scholar
  39. 39.
    Sheikholeslami M, Shehzad SA. Simulation of water based nanofluid convective flow inside a porous enclosure via Non-equilibrium model. Int J Heat Mass Transf. 2018;120:1200–12.CrossRefGoogle Scholar
  40. 40.
    Sheikholeslami M, Seyednezhad M. Simulation of nanofluid flow and natural convection in a porous media under the influence of electric field using CVFEM. Int J Heat Mass Transf. 2018;120:772–81.CrossRefGoogle Scholar
  41. 41.
    Sheikholeslami M, Hayat T, Muhammad T, Alsaedi A. MHD forced convection flow of nanofluid in a porous cavity with hot elliptic obstacle by means of Lattice Boltzmann method. Int J Mech Sci. 2018;135:532–40.CrossRefGoogle Scholar
  42. 42.
    Sheikholeslami M. Numerical investigation of nanofluid free convection under the influence of electric field in a porous enclosure. J Mol Liq. 2018;249:1212–21.CrossRefGoogle Scholar
  43. 43.
    Rashidi MM, Nasiri M, Shadloo MS, Yang Z. Entropy generation in a circular tube heat exchanger using nanofluids: Effects of different modeling approaches. Heat Transf Eng. 2017;38(9):853–66.CrossRefGoogle Scholar
  44. 44.
    Shadloo MS, Hadjadj A, Hussain F. Statistical behavior of supersonic turbulent boundary layers with heat transfer at M∞ = 2. Int J Heat Fluid Flow. 2015;53:113–34.CrossRefGoogle Scholar
  45. 45.
    Sheikholeslami M. CuO-water nanofluid flow due to magnetic field inside a porous media considering Brownian motion. J Mol Liq. 2018;249:921–9.CrossRefGoogle Scholar
  46. 46.
    Sheikholeslami M, Rokni HB. Numerical simulation for impact of Coulomb force on nanofluid heat transfer in a porous enclosure in presence of thermal radiation. Int J Heat Mass Transf. 2018;118(2018):823–31.CrossRefGoogle Scholar
  47. 47.
    Sheikholeslami M. Numerical investigation for CuO-H2O nanofluid flow in a porous channel with magnetic field using mesoscopic method. J Mol Liq. 2018;249:739–46.CrossRefGoogle Scholar
  48. 48.
    Sheikholeslami M, Shehzad SA. Numerical analysis of Fe3O4–H2O nanofluid flow in permeable media under the effect of external magnetic source. Int J Heat Mass Transf. 2018;118:182–92.CrossRefGoogle Scholar
  49. 49.
    Sheikholeslami M, Sadoughi MK. Simulation of CuO-water nanofluid heat transfer enhancement in presence of melting surface. Int J Heat Mass Transf. 2018;116:909–19.CrossRefGoogle Scholar
  50. 50.
    Sheikholeslami M, Seyednezhad M. Lattice Boltzmann method simulation for CuO-water nanofluid flow in a porous enclosure with hot obstacle. J Mol Liq. 2017;243:249–56.CrossRefGoogle Scholar
  51. 51.
    Sheikholeslami M, Hayat T, Alsaedi A. On simulation of nanofluid radiation and natural convection in an enclosure with elliptical cylinders. Int J Heat Mass Transf. 2017;115:981–91.CrossRefGoogle Scholar
  52. 52.
    Sheikholeslami M. Influence of magnetic field on nanofluid free convection in an open porous cavity by means of Lattice Boltzmann Method. J Mol Liq. 2017;234:364–74.CrossRefGoogle Scholar
  53. 53.
    Goodarzi M, Kherbeet AS, Afrand M, Sadeghinezhad E. Investigation of heat transfer performance and friction factor of a counter-flow double-pipe heat exchanger using nitrogen-doped, graphene-based nanofluids. Int Commun Heat Mass Transf. 2016;76:16–23.CrossRefGoogle Scholar
  54. 54.
    Safaei MR, Gooarzi M, Akbari OA, Shadloo MS, Dahari M, Book CH, Performance evaluation of nanofluids in a rib-microchannel for electronics cooling application. In: The book: electronics cooling. InTech Publications; 2016.Google Scholar
  55. 55.
    Sheikholeslami M, Shehzad SA. CVFEM for influence of external magnetic source on Fe3O4–H2O nanofluid behavior in a permeable cavity considering shape effect. Int J Heat Mass Transf. 2017;115:180–91.CrossRefGoogle Scholar
  56. 56.
    Sheikholeslami M, Seyednezhad M. Nanofluid heat transfer in a permeable enclosure in presence of variable magnetic field by means of CVFEM. Int J Heat Mass Transf. 2017;114:1169–80.CrossRefGoogle Scholar
  57. 57.
    Sheikholeslami M, Rokni HB. Melting heat transfer influence on nanofluid flow inside a cavity in existence of magnetic field. Int J Heat Mass Transf. 2017;114:517–26.CrossRefGoogle Scholar
  58. 58.
    Sheikholeslami M. Magnetic field influence on CuO -H2O nanofluid convective flow in a permeable cavity considering various shapes for nanoparticles. Int J Hydrogen Energy. 2017;42:19611–21.CrossRefGoogle Scholar
  59. 59.
    Sheikholeslami M. Influence of Lorentz forces on nanofluid flow in a porous cavity by means of non-darcy model. Eng Comput. 2017;34(8):2651–67.CrossRefGoogle Scholar
  60. 60.
    Sheikholeslami M, Shehzad SA. Magnetohydrodynamic nanofluid convective flow in a porous enclosure by means of LBM. Int J Heat Mass Transf. 2017;113:796–805.CrossRefGoogle Scholar
  61. 61.
    Sheikholeslami M, Sadoughi M. Mesoscopic method for MHD nanofluid flow inside a porous cavity considering various shapes of nanoparticles. Int J Heat Mass Transf. 2017;113:106–14.CrossRefGoogle Scholar
  62. 62.
    Sheikholeslami M. Lattice Boltzmann method simulation of MHD non-darcy nanofluid free convection. Phys B. 2017;516:55–71.CrossRefGoogle Scholar
  63. 63.
    Sheikholeslami M, Bhatti MM. Forced convection of nanofluid in presence of constant magnetic field considering shape effects of nanoparticles. Int J Heat Mass Transf. 2017;111:1039–49.CrossRefGoogle Scholar
  64. 64.
    Sheikholeslami M. CuO-water nanofluid free convection in a porous cavity considering Darcy law. Eur Phys J Plus. 2017;132:55. Scholar
  65. 65.
    Sheikholeslami M. Numerical investigation of MHD nanofluid free convective heat transfer in a porous tilted enclosure. Eng Comput. 2017;34(6):1939–55.CrossRefGoogle Scholar
  66. 66.
    Sheikholeslami M. Magnetic field influence on nanofluid thermal radiation in a cavity with tilted elliptic inner cylinder. J Mol Liq. 2017;229:137–47.CrossRefGoogle Scholar
  67. 67.
    Sheikholeslami M. Numerical simulation of magnetic nanofluid natural convection in porous media. Phys Lett A. 2017;381:494–503.CrossRefGoogle Scholar
  68. 68.
    Sheikholeslami M. Influence of Lorentz forces on nanofluid flow in a porous cylinder considering Darcy model. J Mol Liq. 2017;225:903–12.CrossRefGoogle Scholar
  69. 69.
    Sheikholeslami M. CVFEM for magnetic nanofluid convective heat transfer in a porous curved enclosure. Eur Phys J Plus. 2016;131:413. Scholar
  70. 70.
    Sheikholeslami M, Rokni HB. Nanofluid two phase model analysis in existence of induced magnetic field. Int J Heat Mass Transf. 2017;107:288–99.CrossRefGoogle Scholar
  71. 71.
    Sheikholeslami M, Chamkha AJ. Influence of Lorentz forces on nanofluid forced convection considering Marangoni convection. J Mol Liq. 2017;225:750–7.CrossRefGoogle Scholar
  72. 72.
    Sheikholeslami M. Influence of Coulomb forces on Fe3O4-H2O nanofluid thermal improvement. Int J Hydrogen Energy. 2017;42:821–9.CrossRefGoogle Scholar
  73. 73.
    Sheikholeslami M, Vajravelu K, Rashidi MM. Forced convection heat transfer in a semi annulus under the influence of a variable magnetic field. Int J Heat Mass Transf. 2016;92:339–48.CrossRefGoogle Scholar
  74. 74.
    Sheikholeslami M, Li Z, Shamlooei M. Nanofluid MHD natural convection through a porous complex shaped cavity considering thermal radiation. Phys Lett A. 2018;382:1615–32.CrossRefGoogle Scholar
  75. 75.
    Shadloo MS, Hadjadj A. Laminar-turbulent transition in supersonic boundary layers with surface heat transfer: a numerical study. Numer Heat Transf Part A: Appl. 2017. Scholar
  76. 76.
    Raptis A. Radiation and free convection flow through a porous medium. Int Commun Heat Mass Transf. 1998;25:289–95.CrossRefGoogle Scholar
  77. 77.
    Vajravelu K, Kumar BVR. Analytic and numerical solutions of coupled nonlinear system arising in three-dimensional rotating flow. Int J Non-Linear Mech. 2004;39:13–24.CrossRefGoogle Scholar
  78. 78.
    Mehmood A, Ali A. Analytic solution of three-dimensional viscous flow and heat transfer over a stretching flat surface by homotopy analysis method. ASME J Heat Trans. 2008;130:12701-1–7.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  • Zhixiong Li
    • 1
    • 2
    Email author
  • S. Saleem
    • 3
  • Ahmad Shafee
    • 4
  • Ali J. Chamkha
    • 5
    • 6
  • Sunwen Du
    • 7
  1. 1.School of EngineeringOcean University of ChinaQingdaoChina
  2. 2.School of Mechanical, Materials, Mechatronic and Biomedical EngineeringUniversity of WollongongWollongongAustralia
  3. 3.Department of Mathematics, College of ScienceKing Khalid UniversityAbhaSaudi Arabia
  4. 4.Public Authority of Applied Education & Training, College of Technological StudiesApplied Science DepartmentShuwaikhKuwait
  5. 5.Mechanical Engineering Department, Prince Sultan Endowment for Energy and EnvironmentPrince Mohammad Bin Fahd UniversityAl-KhobarSaudi Arabia
  6. 6.RAK Research and Innovation CenterAmerican University of Ras Al KhaimahRas Al KhaimahUnited Arab Emirates
  7. 7.College of Mining TechnologyTaiyuan University of TechnologyTaiyuanP. R. China

Personalised recommendations