Journal of Thermal Analysis and Calorimetry

, Volume 135, Issue 6, pp 3197–3213 | Cite as

Numerical investigation of MHD effects on nanofluid heat transfer in a baffled U-shaped enclosure using lattice Boltzmann method

  • Yuan Ma
  • Rasul Mohebbi
  • M. M. Rashidi
  • O. MancaEmail author
  • Zhigang Yang


Lattice Boltzmann method (LBM) was carried out to investigate the effects of magnetic field and nanofluid on the natural convection heat transfer in a baffled U-shaped enclosure. The combination of different specifications of the baffle, LBM, nanofluid and magnetic field is the main innovation in the present study. In order to consider the effect of Brownian motion on the thermal conductivity, Koo–Kleinstreuer–Li model is used to define thermal conductivity and viscosity of nanofluid. Effects of Rayleigh number, Hartmann number, nanoparticle volume fraction, height and position of the baffle on the fluid flow and heat transfer characteristics have been examined. It was found that raising the Rayleigh number and nanoparticle solid volume fraction leads to increase the average Nusselt number irrespective of the position of the hot obstacle. However, the heat transfer rate is suppressed by the magnetic field. The heat transfer enhancement by introducing nanofluid decreases as increasing Rayleigh number, but it increases as increasing the Hartmann number. Moreover, the maximum heat transfer rate was observed when the enclosure equipped with a baffle with (s, h) = (0.2, 0.3) or (0.4, 0.3).


Magnetic field Nanofluid Natural convection Baffle LBM U-shaped Enclosure 

List of symbols


Position of the baffle


Length of the baffle


Discrete lattice velocity in direction


Density distribution function


Equilibrium density distribution function


Hartmann number


Nusselt number

U, V

Nondimensional velocity components


Prandtl number


Height of the enclosure


Weight of the enclosure


Speed of sound in Lattice scale


Energy distribution function


Equilibrium energy distribution function


Boltzmann constant


Fluid temperature


Thermal conductivity

Greek symbols


Weight function in direction i


Volume fraction


Relaxation time for temperature


Thermal diffusivity




Relaxation time for flow


Thermal expansion coefficient


Dynamic viscosity





Solid particles












Move direction of single particle



M. M. Rashidi extends his appreciation to the program: H2020 for supporting this work through the Research Project 701693.


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Shanghai Automotive Wind Tunnel Center, Tongji UniversityShanghaiChina
  2. 2.Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management SystemsShanghaiChina
  3. 3.School of EngineeringDamghan UniversityDamghanIran
  4. 4.Department of Civil Engineering, School of EngineeringUniversity of BirminghamBirminghamUK
  5. 5.Dipartimento di IngegneriaUniversità degli Studi della Campania “Luigi Vanvitelli”AversaItaly

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