Résumé:
The work presented focuses on the numerical simulation of laminar natural convection in a closed square cavity, with a partially heated wall using the new method of lattice Boltzmann (LBM). First, a detailed study of the general heat transfer by convection including natural convection and a literature review of the most important works found in the literature. The work was followed by the presentation of different conventional modeling methods including finite volumes method with the theory of the new method used, especially the thermal lattice Boltzmann method with double population. The geometry chosen in this study is a two-dimensional square where the length of the heated wall part of the cavity at a constant temperature, is varied from 20% to 80 % of the total width, while the opposite wall is completely cooled. The walls of the top and bottom are assumed adiabatic. The calculation was performed for a laminar flow and an incompressible fluid with a Prandtl number is Pr=0.71. The calculations are carried out by two methods: the thermal lattice Boltzmann method with double population where the code was developed and tested during this work with MATLAB editor. And the finite volume method using the Fluent code. The validation of results is presented for both methods and compared with those of the literature for the classical case of a square cavity differentially heated. The results of the CFD analysis and comparison between the two methods were presented by plotting the streamlines, the isotherms, the profiles of velocity and temperature in the middle of the cavity. This analysis is completed by calculating the Nusselt number with the two methods. These results revealed that there's a good agreement between the two methods and the lattice Boltzmann method can perfectly reproduce the natural convection phenomenon in a cavity.
