3D Numerical Investigation of Free Convection using Lattice Boltzmann and Finite Difference Methods

Numerical study of various physical phenomena in three dimensions has become a necessity to better understand the physical process than in two dimensions. Thus, in this paper, the code is elaborated to be adapted to the simulation of heat transfer in three dimensions. The numerical simulations are performed using a hybrid method. This method is based on the lattice Boltzmann approach for the computation of velocities, and on the finite difference technique for the calculation of temperature. The used numerical code is validated by examining the free convection in a cubic enclosure filled with air. Then, the analysis of the heat exchange between two cold vertical walls and a heated block located at the center of a cubic cavity is considered. The performed simulations showed that for a small value of the Rayleigh number (Ra=103 for example), the fluid exchanges its heat almost equally with all hot surfaces of the obstacle. However, for large values of Ra (Ra≥104), the numerical results found showed that the heat exchange rate is greater on the bottom face compared to the other faces of the obstacle.