Minimum-Weight Analysis of Anisotropic Plane-Fin Heat-Pipe Space Radiators

Equations are formulated for the two-dimensional, anisotropic conduction of heat in space radiator fins. The transverse temperature field is obtained by the integral method, and the axial field by numerical integration. A shape factor, defined for the heat-pipe interface boundary condition, simplifies the analysis and renders the results applicable to general heat-pipe/conduction-fin designs. The thermal results are summarized in terms of the fin efficiency, a fin length parameter, and a radiation/axial-conductance number. These relations, together with those for mass distribution between fins, heat pipes, and headers are used in formulating a radiator mass/heat-rate criterion function. Minimization of the criterion function results in asymptotic solutions for the optimum radiator geometry and conditions. The effect of physical properties on the optimum design is determined; in particular, performance is found to vary with fin conductivity to the 1/3 power for large conductivity values.