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Heat pipe reactors have been considered by the Space Nuclear Propulsion program for Nuclear Electric Propulsion (NEP) power conversion systems and will require the use of heat exchangers to transfer heat via heat pipes to the Brayton working fluid from the reactor. Sodium (Na) and lithium (Li) were considered as viable working fluids inside the heat pipes which were assumed to have the same geometry based on studies and information from the Los Alamos National Laboratory. The heat exchanger was assumed to be a rectangular duct with heat pipes serving as tubes from previous NEP work and recommendations. Based on this geometry, Zukauskas correlations were used to model the convective heat transfer and pressure losses. Parametric sizing of the reactor component involved operational limits-based heat pipe thermal hydraulic modeling in cohesion with required user input geometry for the in-core lattice and various subcomponents. This work considered various power conversion inlet temperatures (PCIT) of 1100 K, 1150 K, and 1200 K for Na heat pipes and 1100 K, 1150 K, 1200 K, and 1400 K for Li heat pipes based on recommendations from prior work. Using these different PCITs, the subsystem masses and pressure losses were determined and analyzed. Na showed a lower overall operating temperature and about a fifth of the maximum heat throughput capability than that of Li for the same geometry. Due to this, the entire Na-based subsystem ended up being three times more massive than the Li-based subsystem given five times the required number of heat pipes. At the low PCIT of 1100 K, the Na-based subsystem exhibited the lowest pressure losses given the large overall cross sectional flow area and relatively low frictional pressure losses. However, as the PCIT increased, the frictional pressure losses increased resulting in higher pressure losses at the 1200 K PCIT than Li-based subsystem. However, the Li-based subsystem exhibited the largest pressure losses of all analyzed cases at the 1400 K PCIT due to the low density of the Brayton working fluid at this temperature.