Laminar natural convection in vertical enclosures with conducting fins attached to the hot vertical wall has been studied numerically. Side vertical walls were kept at constant but different temperatures, while the horizontal top and bottom walls were kept adiabatically. A conjugate formulation was used for the mathematical formulation of the problem and a computer program based on the control volume approach and the SIMPLEC algorithm was used. The main aim of the current paper is to study numerically the effects of the number of fins and fins length as well as Rayleigh number on the flow pattern and heat transfer. It was observed that the heat transfer rate through an enclosure is affected greatly and hence can be controlled by the number of the attached fins to the vertical side wall of the enclosure as well as the fin lengths.