In this study, we are interested in the two-dimensional numerical simulation of the turbulent mixed convection in the case of a square with two side lid-driven cavity containing a hot obstacle. The transfer equations coupled with those of the  K - ε closure model and the boundary conditions were presented and discretized using the finite volume method. The coupling between the velocity and pressure fields is achieved by the SIMPLE algorithm. The technique of line-by-line scanning with the Thomas algorithm (TDMA) is used for the iterative resolution of discretized equations. The control parameters of the present study are the temperature gradient between the hot walls and the cold walls, and the speed imposed on the mobile walls. Streamlines generally show flow characterized by the presence of two counter-rotating cells. The areas adjacent to the isothermal walls and to the moving walls are the site of the development of thermal and dynamic boundary layers, where significant temperature and velocity gradients have been observed, subsequently influencing the profiles of turbulent quantities such as turbulent viscosity, the production and dissipation of turbulent kinetic energy and the intensity of turbulence.