The design of finned surfaces is conventionally performed in two stages. First the fin efficiency is determined by simultaneously analyzing the conductive heat flow within the fin, and the convective heat dissipation from the surface of the fin. Then, the effects of the thermal interaction between the supporting interface and the fins and the convective heat exchange at the plain side of the supporting interface are incorporated by employing a technique based on electric circuit theory. In this study, it is shown that this technique in fact has a mathematically rigorous foundation. It is also shown that, for design purposes, there is a far superior alternative to the fin efficiency.