The Radiating Annular Fin Problem: A Solution Based on the Green's Function Method

Abstract

Radiating fins are essential elements in the thermal control systems of most spacecraft. The size and weight of the radiating surfaces dominate the design of the thermal control system, so the development of tools useful in the design and optimization of radiating fins is of interest. This paper presents a rigorous new approach for solving the non-linear diffusion problem which results from the analysis of an annular radiating fin. The steady-state, radial temperature profile in the fin is obtained using a Green's function method. The solution method described in this paper results in a single integral equation, whereas solution procedures described in the literature require simultaneous solution of coupled differential and integral equations. The analysis presented in this paper provides new insight into the solution of a classical problem in the thermal management of space vehicles. In addition, the approach outlined in this paper may be applied directly to other types of radiating fins or to other applications governed by non-linear problems.