The complex dynamics of mixed convection circumstances, concentrating on two examples. In the first case, mixed convection was investigated in a single-sided lid-driven cavity with a top and bottom walls arrangement and the second scenario explores parallel and anti-parallel topologies, focusing on mixed convection in a double-sided lid-driven cavity. The main parameters in this study are the Reynolds, Rayleigh, Prandtl, Grashof, and Richardson numbers. Calculation of numerical solutions to the Navier-Stokes equations over wide ranges in parameters, 0 ≤ Gr ≤ 106, 0 ≤ Re ≤ 3000, Pr~O(1), and an aspect ratio approximately O(1). The study analyzes these results systematically to understand the relative importance of natural convection and forced convection. As a result of this study, a two-dimensional cavity with specific boundary conditions was created. In a square domain with adiabatic side walls, a top wall is maintained at a higher temperature than the bottom wall. The flow characteristics approach those of a typical driven-cavity of a non-stratified fluid when Gr/Re2 ≤ 1. There are low fluctuations in temperature and well-mixed fluids throughout the majority of the interior. Much of the inner cavity's middle and bottom are stationary when Gr/Re2≫1. Temperature patterns in these areas are vertically linear and isotherms are nearly horizontal. Lattice Boltzmann method considers the effect of gravity on mixed convection by adjusting the y-velocity using a temperature-dependent forcing factor. The calculation of the Nusselt number at the top wall reveals enhanced heat transfer, with the results suggesting increased intensity when Gr/Re2≪1.