In this study, a square cavity with two ventilation ports in the presence of an adiabatic fin of different lengths placed on the walls of the cavity is numerically analyzed for the mixed convection case for a range of Richardson numbers (Ri = 0.1, 1, 10, 100) and at Reynolds number of 300. The effect of the fin height, placement of the fin on each of the four walls of the cavity and Richardson number on the heat transfer and fluid flow characteristics is numerically analyzed. The results are presented in terms of streamlines, isotherm plots, and averaged Nusselt number plots. It is observed that for the convection dominated case, fin length and its position on the one of the four walls of the cavity do not alter the thermal performance whereas when the buoyancy effects become important thermal performance increases for high fin length.