Cryogenic liquids are increasingly being used on a big scale: in many applications, a predetermined quantity of such fluids must be stored for a long time within an insulated tank. A typical cryogenic liquid storage system consists of a horizontal or vertical tank containing a multi-phase liquid-vapor mixture: these tanks undergo pressure and mass changes because of heat transfer in the liquid, vapor and tank walls, and of mass transfer due to evaporation/condensation processes. In any of these storage systems, the flow of gas into the ullage space (pressurization) or external heat-fluxes leak during long term storage (self-pressurization) lead to a rise in ullage pressure and the creation of a thermal gradient at the gas-liquid interface.