Lattice Boltzmann Modelling of Natural Convection Problems in a Cavity with a Different Wall Temperature

In this study, the cyclic natural convection problem in a square enclosure is modeled using the Lattice Boltzmann Method (LBM) under laminar flow conditions. Four different combinations of boundary conditions are employed to create cases. These cases are denoted as HHHC (Horizontal Hot Horizontal Cold), HHVC (Horizontal Hot Vertical Cold), VHHC (Vertical Hot Horizontal Cold), and VHVC (Vertical Hot Vertical Cold). Four Rayleigh numbers have been utilized to represent laminar flow conditions, namely 𝑅𝑅𝑅𝑅=104 , 105 , 106 , and 107 . For validation purposes, the wellvalidated finite volume method-based commercial code Ansys-Fluent is employed. In the VHVC model and at the highest Rayleigh number, the results obtained with LBM were compared to and validated against the results obtained with the finite volume method. Nusselt numbers are compared for the four cases based on Rayleigh numbers, and the case with highest heat transfer identified. Cases of HHHC and VHVC have produced the lowest and highest Nusselt number, respectively.