Earlier papers by the authors developed a new set of parameters for characterizing heat transfer properties of single fins and fins in arrays of extended surface. The use of these parameters has facilitated the solutions to several interesting fin problems, namely: a more careful characterization of one-dimensional flow configurations, a method for accommodating continuously distributed heat sources along the fin, a perturbation approach for the approximate computation of the parameters, and new insights into the precepts of the optimal fin shape. These developments are reported in this paper.