Journal of Statistical Physics

, Volume 174, Issue 5, pp 972–991 | Cite as

Multiple-Relaxation-Time Lattice Boltzmann Model for Flow and Convective Heat Transfer in Channel with Porous Media

  • Kaoutar BouarnounaEmail author
  • Abdelkader Boutra
  • Karim Ragui
  • Nabila Labsi
  • Youb Khaled Benkahla


In this paper, we investigate numerically the flow field and heat transfer of a Newtonian fluid flowing within a horizontal channel, partially filled with a porous medium. A thin deflector, considered as adiabatic, is inserted inside the channel to control the flow of the convective fluid. This numerical study is based on the multiple-relaxation-time Lattice Boltzmann method (MRT-LBM). The two-dimensional nine-velocity (D2Q9) model is adopted to solve the flow field, while the two-dimensional five-velocity (D2Q5) model is developed to solve the temperature field. A parametric study is carried out according to the Darcy number (10−1 ≤ Da ≤ 10−5), the Reynolds number (20 ≤ Re ≤ 600), the thickness of the porous substrate (0.1 ≤ S ≤ 0.8),the thickness of the deflector and its location (0.1 ≤ D ≤ 0.8 and L/4 ≤ xi ≤ 3L/4). The obtained results show the important effect of these parameters, which cannot be neglected, on both flow and the heat transfer structure, within this kind of channels.


Fluid flow and heat transfer Porous blocks Channel Deflector Lattice Boltzmann method (MRT-LBM) 

List of Symbols


Specific heat of fluid


Dimensional thickness of deflector substrate, [m]


Dimensionless thickness of deflector substrate, (= d/H)


Darcy number (= K/H2)


Discrete particle velocity


Density distribution function


Acceleration of gravity [m s−2]


Channel height [m]


Channel length [m]


Local Nusselt number


Prandtl number (= ν/α)


Thermal conductivity


Permeability of the porous medium (m2)


Reynolds number (= u0H/ν)


Dimensional thickness of porous substrate, [m]


Dimensionless thickness of porous substrate (= s/H)


Time [s]


Temperature [K]


x-velocity component [m s−1]


y-velocity component [m s−1]


Uniform velocity at the channel inlet [m s−1]

x, y

Cartesian coordinates [m]


Distance of the deflector from the inlet [m]

Greek Symbols


Thermal diffusivity (= k/ρCp)


Porosity of porous medium


Fluid dynamic viscosity [kg m−1 s−1]


Kinematic viscosity [m2 s−1]


Dimensionless temperature \( ( = \,(T\, - \,T_{h} )/(Tm\, - \,T_{h} )) \)


Fluid density [kg m−3]









Direction Index


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Kaoutar Bouarnouna
    • 1
    Email author
  • Abdelkader Boutra
    • 1
    • 2
  • Karim Ragui
    • 1
  • Nabila Labsi
    • 1
  • Youb Khaled Benkahla
    • 1
  1. 1.Laboratory of Transfer phenomenaUSTHBAlgiersAlgeria
  2. 2.Ecole Supérieure des Sciences Appliquées d’AlgerCasbahAlgeria

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