The work of previous investigators on heat flow through extended surface is briefly reviewed and literature citations are given. General equations are derived for the temperature gradient and fin efficiency in any form of extended surface to which the assumptions listed are applicable. The solution of these equations in terms of Bessel functions is shown to cover practically any form of extended surface whose thickness varies as some power of the distance measured along an axis normal to the basic surface. Curves are presented for the fin efficiency of several forms of straight fins, annular fins, and spines.