In the present study the optimum dimensions of longitudinal rectangular and triangular radiating fins with mutual irradiation are determined. The basic assumptions are one-dimensional heat conduction and gray diffuse surface radiation. The governing equations are formulated by means of dimensionless variables and solved numerically in order to carry out the required minimization procedure. The optimum fin dimensions, thickness and height, are presented in generalized dimensionless form and correlations are provided in order to assist the spacecraft thermal systems designer. The results are analyzed and expressed in explicit correlations. Several diagrams, are also included, that give insight to the operational characteristics of the heat rejection mechanism. Moreover, special attention is given to 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 important for the calculation of the heat dissipation at the fin base and its subsequent optimization.
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