The formula for natural convection is Q=h*A(ΔT) and it is clear from this formula that the area of heat dissipation is a major factor in natural convection.
It may seem logical that the larger the area, the better the cooling effect, but when designing a heat sink in a limited space, it is not always the case that the larger the fin area, the better. The only way to achieve more heat dissipation area in a fixed space is to increase the number of fins, but increasing the number of fins also reduces the width of the airflow channel. As the fins create a thermal boundary layer as they are dissipating heat, there must be two cooling surfaces in an airflow channel. When both thermal surfaces create a thermal boundary layer, the airflow channel is shrunk and the airflow is diminished, weakening the heat dissipation effect. Therefore, in the natural convection regime, it is not the case that the larger the heat dissipation area, the better, but that there is an optimum value for each condition. The optimum values are generally obtained by parameterization using simulation software.