Mixed convection characteristics in a baffled U-shaped lid-driven cavity in the presence of magnetic field

  • Yuan Ma
  • Rasul MohebbiEmail author
  • M. M. Rashidi
  • Zhigang Yang


The lattice Boltzmann method is utilized to investigate the mixed convection of a CuO/water nanofluid by magnetic field’s effect in a lid-driven U-shaped enclosure filled with a baffle. The bottom wall’s temperature is high. The Koo–Kleinstreuer–Li model, which considering the Brownian motion of nanoparticles, is adopted to obtain the thermophysical properties of the nanofluid. How the Hartmann number (Ha), Richardson number (Ri), Reynolds number (Re), and nanoparticle concentration (ϕ) affect streamlines, isotherms, and average Nusselt number (Nuave) is also examined. The results reveal that, at Re = 100 and for a large Ri, the nanofluid strategy degrades the Nu. The favorable effect of increasing the Re on the average Nu and adverse trends of the increment in the Ha on the heat transfer are the main highlights in this study. In addition, the increase in the Re more strongly affects the heat transfer rate at higher Ri.


Nanofluid KKL model Mixed convection MHD LBM U-shaped lid-driven cavity 

List of symbols


Baffle’s position (m)


Length of the baffle (m)


Lattice velocity’s direction (m s−1)


Density distribution function (kg m−3)


Equilibrium density distribution function (kg m−3)


Hartmann number


Richardson number


Nusselt number

U, V

Non-dimensional velocity components (m s−1)


Prandtl number


Height of the enclosure (m)


Mass of the enclosure (m)


Sound’s speed in lattice scale (m s−1)


Energy distribution function (K)


Equilibrium energy distribution function (K)


Boltzmann constant


Reynolds number


Fluid temperature (K)


Thermal conductivity (W K−1 m−1)

Greek symbols


Mass function in direction i


Volume fraction


Relaxation time for temperature


Thermal diffusivity (m2 s−1)


Density (kg m−3)


Relaxation time for flow


Thermal expansion coefficient (K−1)


Dynamic viscosity (kg m−1 s−1)





Solid particles












Move direction of single particle



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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2019

Authors and Affiliations

  • Yuan Ma
    • 1
    • 2
  • Rasul Mohebbi
    • 3
    Email author
  • M. M. Rashidi
    • 1
    • 2
  • Zhigang Yang
    • 1
    • 2
    • 4
  1. 1.Shanghai Automotive Wind Tunnel CenterTongji UniversityShanghaiChina
  2. 2.Shanghai Key Lab of Vehicle Aerodynamics and Vehicle Thermal Management SystemsShanghaiChina
  3. 3.School of EngineeringDamghan UniversityDamghanIran
  4. 4.Beijing Aeronautical Science and Technology Research InstituteBeijingChina

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