A numerical study of the thermal and fluid-dynamic behaviour of the two-phase flow inside ducts working under cryogenic conditions, coupled with the analysis of a phase change material PCM accumulator is presented. The numerical analysis is based on: i) a one-dimensional and transient integration of the conservative equations (mass, momentum and energy) in case of the fluid flow inside tubes, and ii) a twodimensional and transient integration of the conservative equations in case of the PCM accumulator. The discretization of the governing equations has been developed by means of the finite volume technique. The discretized governing equations are solved using a Semi-Implicit Method for Pressure-Linked Equations (SIMPLE). The two-fluid model has been used to simulate the two-phase flow phenomena inside tubes, which is an inter-penetrating model capable to define the behavior of the velocity, the pressure, the temperature and the distribution of each one of the phases (gas and liquid), separately. A group of parameters, used in the numerical model proposed, are evaluated by means of empirical correlations, which have been obtained from the technical literature in the cryogenic field. Numerical results of the whole system are shown, where the temperature distribution of the fluid flow, the wall pipe, and the PCM accumulator are presented