In the present study the optimum dimensions of circular rectangular and triangular profile fins with fin to fin and fin to base radiant interaction are determined. The basic assumptions are one-dimensional heat conduction, and black surface radiation. The governing equations are formulated by means of dimensionless variables and solved numerically. The optimum fin dimensions, bore thickness and height, are presented in generalized dimensionless form. In order to assist the spacecraft thermal systems designers explicit correlations are provided for the dimensionless, bore thickness. The results are analyzed and reported in diagrams that give insight to the operational characteristics of the heat rejection mechanism. Moreover, special attention is given in the error analysis of the numerical methods used, since the accuracy and the reliability of the algorithms employed for the solution of the integro-differential equation is importand for the calculation of the heat dissipation at the fin base and its subsequent optimization.