Natural Convection Inside Square and Cubic Cavity with Left Wall Partially Heated

The numerical model is considered as two- (2-D) and three-dimensional (3-D), respectively, for 2-D and 3-D cases. Four heat parameters associated with the heat source are considered and defined as the heat source position (P), the heat source projection area (S), the heat source thickness (H), and the heat source distribution mode (W). For both 2-D and 3-D cases, the heat source is positioned along the left wall, which is also defined as the high-temperature boundary. The low-temperature boundary is partially distributed along the right wall, and the rest of the walls are defined as the adiabatic boundary. To describe the coupling effect between density and temperature fields, a coupled double distribution function model of lattice Boltzmann method is employed, indicating that, apart from the density distribution function, the temperature distribution function is considered as well, and the coupling effect is considered through the external force term added in the density distribution function. The numerical model is validated by using the classic natural convection inside a square cavity and followed by the grid convergence test. The numerical results of the 2-D and 3-D cases are compared and it is found that the 2-D results have a good agreement with the 3-D cases. The impact of each heat parameter on the properties of flow and heat transfer is regarded as new findings and revealed in detail. The comprehensive study of the different heat parameters presented in this study is aimed to propose more efficient strategies on heat source distributions for specific practical applications.