Optimizing the Design of Space Radiators

A procedure for optimizing the configuration of a heat pipe/fin radiating element in terms of heat rejected per radiating mass has been developed. The optimization was carried out analytically by expressing the heat radiated per radiating mass in terms of a function involving a dimensionless heat transfer coefficient and the dimensionless thermal gradient at the root of the fin where it joins the heat pipe. The dimensionless Stefan–Boltzmann radiation equation was solved numerically to determine the value that maximizes the function that determines the heat transfer per radiating mass. Once this value is obtained, the optimum width and thickness of the fins as well as the heat radiated per mass can be specified in terms of the operating temperature, emissivity, diameter, and mass/length of the heat pipe, and the density and thermal conductivity of the fin material. The resulting analytical expression can then be used to determine the maximum heat radiated per radiating mass over a wide range of operating conditions, to optimize the design of a specific heat pipe/fin combination, and to conduct analyses of the influence of design and materials properties on the performance of the system. The optimization procedure was carried out for the case of uniformly tapered fins as well as for flat fins.