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This article presents a numerical simulation of the fully developed laminar free convection flow between vertical parallel plates with asymetric temperatures. The thermal boundary condition employed on the walls is of the type uniform wall temperature, with the left wall cooler and the right wall hotter. At the inlet, a uniform temperature is imposed, which is lower than or equal to the left wall temperature. The simulation tool used is OpenFOAM v12. Three successively refined meshes where used to perform mesh sensitivity analysis and to show mesh convergence. The numerical solutions obtained approach asymtotically the analytical solution. The temperature profile, as the analytical solution is linear, is exactly reproduced by the numerical method even in coarse meshes. The velocity profile, as the analytical solution is cubic, is progresively reproduced by the numerical method as the mesh is refined.