In the present paper, the thermal analysis and optimization of straight taper fins has been addressed. With the help of the Frobenius expanding series the temperature profiles of longitudinal fin, spine and annular fin have been determined analytically through a unified approach. Simplifying assumptions like length of arc idealization and insulated fin tip condition have been relaxed and a linear variation of the convective heat transfer coefficient along the fin surface has been taken into account. The thermal performance of all the three types of fin has been studied over a wide range of thermo-geometric parameters. It has been observed that the variable heat transfer coefficient has a strong influence over the fin efficiency. Finally, a generalized methodology has been pointed out for the optimum design of straight taper fins. A graphical representation of optimal fin parameters as a function of heat duty has also been provided.