Numerical investigation of nanofluid convection heat transfer in a microchannel using two-phase lattice Boltzmann method

  • Amir Hossein Saberi
  • Mohammad KaltehEmail author


In this study, the laminar forced convection heat transfer of copper–water nanofluid in a 2D microchannel with one wall insulated and the other with constant heat flux is simulated numerically. In this paper, two-phase lattice Boltzmann method is used for simulation of the problem considering the intermolecular forces such as drag, buoyancy, Brownian, van der Waals and Born forces. The collision and streaming equations are used for both phases separately, and the effect of nanoparticles volume fraction on the velocity and temperature profiles is examined. It is observed that velocity decreases with increasing the nanoparticles volume fraction. Moreover, an increase in nanoparticles volume fraction raises the mean fluid temperature and increases the heat transfer rate. Further, the effect of an increase in nanoparticles volume fraction and their diameter changes on the Nusselt number variations in the microchannel is investigated. Also, the effect of considering viscous dissipation on the Nusselt number in different nanoparticle volume fractions is compared to the state without considering it. Finally, the effect of Reynolds number on Nusselt number is investigated.


Forced convection Nanofluid Two-phase Lattice Boltzmann method Viscous dissipation 

List of symbols


Hamaker coefficient


Radius of nanoparticles (m)


Mass coefficient


Lattice velocity


Cunningham correction


Nanoparticles diameter (m)


Hydraulic diameter (m)


Direction of lattice velocity


Brownian force (N)


Mass fraction of the σth component


Specific heat capacity (J kg−1 K−1)


Born force (N)


Buoyancy force (N)


Summation of forces acting on the base fluid (N)


Drag force (N)


Summation of forces acting on the nanoparticle (N)


Van Der Waals force (N)


Density distribution function


Density equilibrium distribution function


Temperature distribution function


Equilibrium temperature distribution function


Convective heat transfer coefficient (W m−2 K)


Thermal conductivity (W m−1 K−1)


Boltzmann constant (J K−1)


Center-to-center distance between particles (m)


Number of lattices in X-direction


Number of lattices in Y-direction


Mass of nanoparticle (kg)


Number of particle in the Lattice


Power of Lennard-Jones potential


Number of the particles


Nusselt number


Gas constant (J K−1 mol−1)


Reynolds number


Specific surface area (m2 kg−1)


Time (s)


Temperature (K)


Volume of a lattice


Macroscopic velocity (m s−1)

X, Y

Axial and vertical Cartesian coordinates

Greek symbols


Thermal diffusivity (m2 s−1)


Average thermal diffusivity (m2 s−1)


Dimensionless temperature


Mean free path (m)


Collision diameter (m)


Dynamic viscosity (kg m−1 s−1)


Kinematic viscosity (m2 s−1)


Average kinematic viscosity (m2 s−1)


Density (kg m−3)


Collision relaxation time for flow


Collision relaxation time for temperature


Nanoparticle volume fraction


Energy exchange between nanoparticles and base fluid


Mass coefficient



Base fluid


Discrete lattice directions







X, Y

X and Y directions





Fluid or solid phase



  1. 1.
    Florio LA, Harnoy A. Combination technique for improving natural convection cooling in electronics. Int J Therm Sci. 2007;46:76–92.CrossRefGoogle Scholar
  2. 2.
    Mahian O, Kolsi L, Amani M, Estelle P, Ahmadi G, Kleinstreuer C, Marshall JS, Siavashi M, Taylor RA, Niazmand H, Wongwises S, Hayat T, Kolanjiyil A, Kasaeian A, Pop I. Recent advances in modeling and simulation of nanofluid flows—part I: fundamental and theory. Phys Rep. 2018;790:1–48.CrossRefGoogle Scholar
  3. 3.
    Anoop K, Sadr R, Yu J, Kang S, Jeon S, Banerjee D. Experimental study of forced convective heat transfer of nanofluids in a microchannel. Int Commun Heat Mass Transf. 2012;39:1325–30.CrossRefGoogle Scholar
  4. 4.
    Rashidi F, Nezamabad NM. Experimental investigation of convective heat transfer coefficient of CNTs nanofluid under constant heat flux. In: Proceedings of the world congress on engineering; 2011.Google Scholar
  5. 5.
    Qiang L, Yimin X. Convective heat transfer and flow characteristics of Cu–water nanofluid. Sci China Ser E. 2002;45:408–16.Google Scholar
  6. 6.
    Lai F-H, Yang Y-T. Lattice Boltzmann simulation of natural convection heat transfer of Al2O3/water nanofluids in a square enclosure. Int J Therm Sci. 2011;50:1930–41.CrossRefGoogle Scholar
  7. 7.
    Mohebbi R, Lakzayi H, Sidik NAC, Japar WMAA. Lattice Boltzmann method based study of the heat transfer augmentation associated with Cu/water nanofluid in a channel with surface mounted blocks. Int J Heat Mass Transf. 2018;117:425–35.CrossRefGoogle Scholar
  8. 8.
    Mohamad AA, Kuzmin A. A critical evaluation of force term in lattice Boltzmann method, natural convection problem. Int J Heat Mass Transf. 2010;53:990–6.CrossRefGoogle Scholar
  9. 9.
    Saberi AH, Kalteh M. Numerical investigation of nanofluid flow and conjugated heat transfer in a micro-heat-exchanger using the lattice Boltzmann method. Numer Heat Transf Part A. 2016;70(12):1390–401.CrossRefGoogle Scholar
  10. 10.
    Yousofvand R, Derakhshan S, Ghasemi K, Siavashi M. MHD transverse mixed convection and entropy generation study of electromagnetic pump including a nanofluid using 3D LBM simulation. Int J Mech Sci. 2017;133:73–90.CrossRefGoogle Scholar
  11. 11.
    Siavashi M, Ghasemi K, Yousofvand R, Derakhshan S. Computational analysis of SWCNH nanofluid-based direct absorption solar collector with a metal sheet. Sol Energy. 2018;170:252–62.CrossRefGoogle Scholar
  12. 12.
    Ghasemi K, Siavashi M. Lattice Boltzmann numerical simulation and entropy generation analysis of natural convection of nanofluid in a porous cavity with different linear temperature distributions on side walls. J Mol Liq. 2017;233:415–30.CrossRefGoogle Scholar
  13. 13.
    Ghasemi K, Siavashi M. MHD nanofluid free convection and entropy generation in porous enclosures with different conductivity ratios. J Magn Magn Mater. 2017;442:474–90.CrossRefGoogle Scholar
  14. 14.
    Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Phys Rev E. 1815;47(3):1993.Google Scholar
  15. 15.
    Shan X, Doolen G. Multicomponent lattice Boltzmann model with interparticle interaction. J Stat Phys. 1995;81(1–2):79–393.Google Scholar
  16. 16.
    Qi C, He Y, Yan S, Tian F, Hu Y. Numerical simulation of natural convection in a square enclosure filled with nanofluid using the two-phase lattice Boltzmann method. Nanoscale Res Lett. 2013;8:56.CrossRefGoogle Scholar
  17. 17.
    Xuan Y, Yao Z. Lattice Boltzmann model for nanofluids. Heat Mass Transf. 2005;41:199–205.Google Scholar
  18. 18.
    Joshi AS, Sun Y. Multiphase lattice Boltzmann method for particle suspensions. Phys Rev E. 2009;79:066703.CrossRefGoogle Scholar
  19. 19.
    Liu X, Liu H, Liu Y. Simulation of magnetorheological fluids based on lattice Boltzmann method with double meshes. J Appl Math. 2012;2012:16.Google Scholar
  20. 20.
    Zhou L, Xuan Y, Li Q. Multiscale simulation of flow and heat transfer of nanofluid with lattice Boltzmann method. Int J Multiph Flow. 2010;36(5):364–74.CrossRefGoogle Scholar
  21. 21.
    Nishiyama T, Yasuda S, Inamuro T. Lattice Boltzmann simulation of the dispersion of aggregated brownian particles under shear flows. Eur Phys J Spec Top. 2009;171(1):145–9.CrossRefGoogle Scholar
  22. 22.
    Inamuro T, Ii T. Lattice Boltzmann simulation of the dispersion of aggregated particles under shear flows. Math Comput Simul. 2006;72(2–6):141–6.CrossRefGoogle Scholar
  23. 23.
    Guo Y, Qin D, Shen S, Bennacer R. Nanofluid multi-phase convective heat transfer in closed domain: simulation with lattice Boltzmann method. Int Commun Heat Mass Transf. 2012;39(3):350–4.CrossRefGoogle Scholar
  24. 24.
    Qi C, Liang L, Rao Z. Study on the flow and heat transfer of liquid metal based nanofluid with different nanoparticle radiuses using two-phase lattice Boltzmann method. Int J Heat Mass Transf. 2016;94:316–26.CrossRefGoogle Scholar
  25. 25.
    Ahmed M, Eslamian M. Numerical simulation of natural convection of a nanofluid in an inclined heated enclosure using two-phase lattice Boltzmann method: accurate effects of thermophoresis and Brownian forces. Nanoscale Res Lett. 2015;10:296.CrossRefGoogle Scholar
  26. 26.
    Wu X, Kumar R. Lattice Boltzmann model for flow and heat transfer of nanofluids in a microchannel. In: 3rd International conference on microchannels and minichannels; 2005.Google Scholar
  27. 27.
    Avelino M, Kakac S. Convective heat transfer in microchannels: a review. In: Proceedings of the 10 Brazilian congress of thermal sciences and engineering; 2004.Google Scholar
  28. 28.
    Fani B, Kalteh M, Abbassi A. Investigating the effect of Brownian motion and viscous dissipation on the nanofluid heat transfer in a trapezoidal microchannel heat sink. Adv Powder Technol. 2015;26:83–90.CrossRefGoogle Scholar
  29. 29.
    Tian ZW, Zou C, Liu HJ, Guo ZL, Liu ZH, Zheng CG. Lattice Boltzmann scheme for simulating thermal micro-flow. Physica A. 2007;385:59–68.CrossRefGoogle Scholar
  30. 30.
    Feke DL, Prabhu ND, Mann JA Jr, Mann JA III. A formulation of the short-range repulsion between spherical colloidal particles. J Phys Chem. 1984;88:5735–9.CrossRefGoogle Scholar
  31. 31.
    Sun W. Interaction forces between a spherical nanoparticle and a flat surface. Phys Chem Chem Phys. 2014;16:5846–54.CrossRefGoogle Scholar
  32. 32.
    Shi Y, Zhao TS, Guo ZL. Thermal lattice Bhatnagar–Gross–Krook model for flows with viscous heat dissipation in the incompressible limit. Phys Rev E. 2004;70:066310.CrossRefGoogle Scholar
  33. 33.
    Kalteh M, Abbassi A, Saffar-Avval M, Frijns A, Darhuber A, Harting J. Experimental and numerical investigation of nanofluid forced convection inside a wide microchannel heat sink. Appl Therm Eng. 2012;36:260–8.CrossRefGoogle Scholar
  34. 34.
    Das SK, Choi SU, Pradeep T, Yu W. Nanofluids: science and technology. New York: Wiley; 2007.CrossRefGoogle Scholar
  35. 35.
    Yu J, Kang SW, Jeong RG, Banerjee D. Experimental validation of numerical predictions for forced convective heat transfer of nanofluids in a microchannel. Int J Heat Fluid Flow. 2016;62:203–12.CrossRefGoogle Scholar
  36. 36.
    Nelson IC, Banerjee D. Flow loop experiments using polyalphaolefin nanofluids. J Thermophys Heat Transf. 2009;23(4):752–61.CrossRefGoogle Scholar
  37. 37.
    Ebadian MA, Dong ZF. Forced convection, internal flow in ducts. In: Rohsenow WM, Hartnett JP, Cho YI, editors. Handbook of heat transfer. New York: McGraw-Hill; 1998. p. 51–5137.Google Scholar
  38. 38.
    Mahian O, Kolsi L, Amani M, Estelle P, Ahmadi G, Kleinstreuer C, Marshall JS, Taylor RA, Abu-nada E, Rashidi S, Niazmand H, Wongwises S, Hayat T, Kasaeian A, Pop I. Recent advances in modeling and simulation of nanofluid flows—part II: fundamental and theory. Phys Rep. 2018;791:1–59.CrossRefGoogle Scholar
  39. 39.
    Keblinski P, Phillpot SR, Choi SUS, Eastman JA. Mechanisms of heat flow in suspensions of nano-sized particles (nanofluid). Int J Heat Mass Transf. 2002;45:855–63.CrossRefGoogle Scholar
  40. 40.
    Chon CH, Kihm KD, Lee SP, Choi SUS. Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett. 2005;87:153107.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of GuilanRashtIran

Personalised recommendations