Frost formation on evaporators negatively affects the cooling performance of refrigerators. It increases the thermal resistance between the refrigerant and air leading to a reduction in the system cooling capacity. In this study, the effect of frost accumulation over a bare and finned surface on the convective thermal resistances has been experimentally investigated under impinging flow conditions. The surfaces are vertically positioned in a horizontal wind tunnel. The convective resistances have been measured with an in-house developed heat flux measurement system. Finally, the effectiveness of the finned surface was derived from the measurements for dry, condensing flow and as well as for frosting conditions. Under frosting conditions, the effectiveness of the finned surface is measured as 1.4 that is by a factor of 2X lower compared to the effectiveness of the same finned surface operating under dry conditions. It has been observed that the frost accumulation initially takes place at the tip of the fins and leads to a 45% drop in the heat transfer rate when the fin tips are completely covered with frost. Further frost accumulation on the fin base does not result in an additional drop in the heat transfer rate. In this regard, the study emphasizes the importance of the fin tip design for the heat sinks operating under frosting conditions.