Free convection about a single vertically orientated square fin on a horizontal plate has been investigated numerically. Fluid is drawn towards the fin from the far field which cools the fin and finally leaves through the top. For short fins, convection rather than the conduction is the controlling mechanism and this renders the fin thermal conductivity a parameter of little importance for such fins. Heat flux at the base of the fin decreases with increasing width of the fin confirming the benefits of large number of slender fins. A correlation has been developed to evaluate the heat flux at fin base which may be used to predict the upper bound of free convection heat transfer from any heat sink with square fins on a horizontal base. Rate of heat transfer so calculated has been compared with experimental data published recently. The study also reveals the advantage of the cylindrical fins over square fins.