This paper presents, the numerical analysis of heat and mass transfer during hydrogen generation in an array of fuel cylinder bars, each coated with a cladding and a steam current flowing outside the cylinders. The analysis considers the fuel element without mitigation effects. The system consists of a representative periodic unit cell where the initial and boundary-value problems for heat and mass transfer were solved. In this unit cell, we considered that a fuel element is coated by a cladding with steam surrounding it as a coolant. The numerical simulations allow describing the evolution of the temperature and concentration profiles inside the nuclear reactor and could be used as a basis for hybrid upscaling simulations.