Résumé:
The works presented, focuses on the numerical simulation of laminar mixed convection flow in horizontal channel heated from below using the new Lattice Boltzmann method. First a detailed study of heat transfer by convection including mixed convection and convective thermal instability of Rayleigh Bénard and Rayleigh-Bénard-Poiseuille. A literature review was also presented on the most important works found about the configuration associated with this study. The work was continued by a presentation of the historical development of the new method of modeling and simulation used in this work, including the thermal lattice Boltzmann method with double populations, as well as fundamental theoretical basis for its application. The geometry chosen in this study is a two-dimensional horizontal duct heated from below, where the upper wall is considered cold. The calculation was performed for a laminar flow and an incompressible fluid with a Peclet number of Pe=20/3. A code was developed and tested during this work using MATLAB, by applying the thermal lattice Boltzmann method, with the D2Q9 lattice model for dynamic field, and the D2Q5 lattice for the thermal field. The validation of the results obtained with the lattice Boltzmann method are compared with those of the literature for an aspect ratio of B =H/L= 20, a Reynolds number of Re=10 and a Rayleigh number of Ra= 104, which shows that there are good agreements between the results of the program and the previous studies. The results of the CFD analysis where presented by plotting the streamlines, the isotherms, the profiles of velocity and the temperature in the middle of the duct. This analysis is completed by the study of the effect of non-dimensional parameters, in particular the Reynolds number, the Rayleigh number and the aspect ratio on the Nusselt number. This study made possible to evaluate the performance and the capacity of the lattice Boltzmann method to reproduce the physical phenomena of the mixed convection in a horizontal duct heated from below.
