**Multiple-relaxation-time Lattice Boltzmann approach for flow and convective heat transfer in open cavity with circular heat-generating obstacle**

Boutra Abdelkader$^{1,\star}$, Bourada Abderrahmane$^{2}$, Benkahla Youb Khaled$^{2}$

$^{\star}$ : aeknad@yahoo.fr

$^{1}$ Ecole Supérieure des Sciences Appliquées, Alger, 16001, Algérie

$^{2}$ Université des Sciences et de la Technologie Houari Boumediene USTHB

**Mots clés :** Volumetric Heat-generation, Mixed convection, Open cavity, Multiple-relaxation-time lattice Boltzmann method

**Résumé :**

In this research, mixed convection of Newtonian fluid in open square cavity, equipped with a circular heat-generating obstacle is studied numerically, using the multiple-relaxation-time lattice Boltzmann method. Mixed convection in ventilated cavity is applicable in many industrial transport processes such as, heat exchangers, pollution removal, thermal comforting of building spaces, food processing and solar systems [1], [2]. In this research, the MRT-LBM is used to solve the general equations governing the convective heat transfer of air in open square cavity, equipped with a circular volumetric heat-generating obstacle. The main aim of this study is to determine the effect of air injection, on cooling process of circular heat-generating obstacle. The lattice Boltzmann Method (LBM) may be applied to solve the problems of transfer phenomena. In this approach, the fluid is considered as a set of particles, which move (stream) with discrete velocity in specified directions, depending on the lattice structure, and collide (interact) with each other on lattice nodes. The distribution function f is the probability of finding a particle at a given node with a certain velocity. Collision and particle advection are driven by the LB equation, which reflects the development of these functions and external forces introduced by a source term [3]. The two-dimensional nine velocities model D2Q9 is used for flow field and the two-dimensional with five velocities D2Q5 model is used for temperature field. The cold fluid is injected through an opening at the bottom of the cavity, with a constant velocity and an isothermal cold temperature, to cool the obstacle, and exits from the top. The vertical walls are kept at constant hot temperature and the horizontal walls are adiabatic. The effect of Reynolds number, heat generation parameter, Prandtl number and the location of the heat-generating obstacle and the exit opening on hydrodynamic and heat transfer is studied. The obtained results show that these parameters have an important effect, on hydrodynamic and thermal transfer.

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[2] R. Nasrin and M. A. Alim, “Control volume finite element simulation of MHD forced and natural convection in a vertical channel with a heat-generating pipe,” Int. J. Heat Mass Transf., vol. 55, no. 11–12, pp. 2813–2821, 2012, doi: 10.1016/j.ijheatmasstransfer.2012.02.023.

[3] A. Boutra, Y. K. Benkahla, D. E. Ameziani, and R. Bennacer, “Lattice Boltzmann simulation of natural convection in cubical enclosures for the Bingham plastic fluid,” Heat Transf. Res., vol. 48, no. 7, pp. 607–624, 2017, doi: 10.1615/HeatTransRes.2016007507.

Work In Progress