The main objective of the work is to apply the thermal efficiency method to analyze the heat exchange process in a heat exchanger used in a nuclear power plant to produce hydrogen. The fluids that exchange heat are superheated Helium and the liquid metal Sodium, the first used as the primary refrigerant and the second as the secondary heat exchanger refrigerant. The presented solution is restricted to the heat exchange and considers the two-phase heat exchange process as a nucleated boiling heat exchange for Sodium. The quantities determined for global heat transfer process analysis are thermal efficiencies, thermal effectiveness, heat transfer rates, and fluid exit temperatures in the three heat exchange regions by the liquid metal Sodium: subcooled fluid, saturated steam, and superheated steam. The theoretical analysis is a powerful tool that makes it possible to analyze situations under different operating conditions, which are not permissible through experimental means due to the high cost involved. The results are compared with the literature, and the absolute deviation for the quantities under analysis does not exceed 13%. The use of the equation developed by Rhosenow in 1963 for nucleated boiling heat exchange proved consistent in the simulation presented.