This paper presents a theoretical-numerical analysis of longitudinal and annular fins and spines. We examine rectangular, triangular and parabolic profiles for the fins and cylindrical, conical and parabolic spines. In order to reach an understanding of the performance of these odd-shaped, but real world fins, the situation examined here is the case of fins subject to a temperature-dependent heat transfer coefficient. Figures as well as numerical correlations of performance and optimum dimensions of these fins are presented.