The number of heat pipes used was selected to ensure a 99.5% probability of the radiator surviving to the system end of life. The radiator system survival probability was calculated using the cumulative binomial distribution [15] as follows: wnere is tne required neat transport capability ot eacn neat pipe m kilowatts given the total waste heat, Q,, in kilowatts. Sodium heat pipes were used for the Rankine cycle system. The same design procedure and computer program (HPAD) was used as for the lithium heat pipes. During radiator design we optimized radiator temperature, heat pipe length and cone half angle. Minimization of Total System Mass. The total system mass was selected as the appropriate objective function to minimize. Optimization procedures were carried out which lowered it to below 29 tons-the maximum lift capacity of the space shuttle. The design variables used in each subsystem are as follows: • Reactor and core heat pipe number of core heat pipes, Nc core heat pipe operation temperature, Tc • Converter Rankine cycle superheat of potassium vapor, TWP where P is the individual heat pipe survival probability; Nt is the total number of heat pipes; Ns is the number of surviving heat pipes; and S is the probability that Ns heat pipes are not punctured during the 5-year mission. P was set to 0.99. Ns was determined such that s became larger than the required radiator reliability of 0.995. The required axial heat transport per heat pipe was determined using N, as follows:
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