This work is a compilation of the research steps that are conducted in a CFD study of a cross-flow heat exchanger (HX) to be used as a the recuperator of a regenerative Closed Brayton Cycle (CBC). This concept will be applied in "TERRA" (an acronym for the portuguese translation to "Technology of Advanced Fast Reactors"), a Brazilian Air Force strategic project which is ongoing in IEAv (Institute for Advanced Studies, in portuguese) with the objective of developing a nuclear microreactor to provide electrical power supply for space missions or difficult access regions. The CBC is thermally coupled to the reactor core and the radiator by heat pipes. Thermal energy from the reactor core is converted into shaft power in the CBC to be then turned into electricity by alternators. In a regenerative CBC cycle, the recuperator provides heat exchange between the cold and hot segments, pre-heating fluid in the heat source inlet and increasing the system thermal eficiency. The recuperator usually represents the major part of the overall system total volume and mass because its effectiveness depends on heat transfer area. A thermodynamic optimization on the recuperator can provide sereval improvements in space reactor design, as volume and mass are critical parameters to be minimized for space applications. In the Entropy Generation Minimization (EGM) method, the rate of irreversibility production, which is proportional to the Lost Available Work (LAW), is used as a Performance Evaluation Criteria (PEC) for system analysis and optimization. As fluid flows through both sides of the heat exchanger, entropy is produced mainly by heat transfer and pressure drop. This study aims to find a solution-of-compromise for the regenerator by a trade-of analysis between mass and efficiency. Geometry and mass flow rate are varied in the search for an optimal configuration. The flow is resolved in the heat exchanger's interior using the Finite Volume Method (FVM) in a 3D Computational Fluid Dynamics (CFD) commercial platform. Relevant data is used for thermodynamical and thermal-hydraulical optimizations.