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Nuclear Thermal Propulsion systems are one of the technologies to unlock interplanetary travel in the solar system and there is currently an increasing demand for accurately simulating such systems. The present paper investigates the KIWI-B-4E reactor, the first prototype of the NERVA program that achieved a restart at full power in 1964. To simulate this reactor, we propose the use of the OpenMC Monte Carlo code and the GeN-Foam multi-physics code to model full-core neutronics and thermal-hydraulics. The results mostly show a good agreement with the available experimental data, although uncertainties on key design parameters do not allow for a detailed neutronics validation.