Particle accelerators play a central role in the advancement of fundamental physics research. In circular accelerators such as the Large Hadron Collider (LHC) at CERN, the trajectory of the particle beams must be bent with magnetic fields. For this purpose, the LHC utilizes superconducting dipole magnets, which allow the electric current to flow without resistance. A cooling system of superfluid helium (He II) ensures the superconducting state by maintaining the magnets at temperatures below 2 K. However, the confined structures surrounding the dipole coils hinder the cooling process. The metal collars, which restrict the dipoles to counter the electromagnetic forces, are spaced 200 microns apart from each other. If the magnets lose the superconductive properties (i.e., during a magnet quench), the energy dissipated is such that helium undergoes drastic thermodynamic changes, causing the failure of the machine and severe damages to its components. The present work focuses on the thermal phenomena occurring at this level of geometrical confinement in He II when subject to high heat fluxes. Experiments were conducted in a cryostat with pressurized He II at various bath temperatures. The tests consisted of applying a clamped heat flux in rectangular cross-section channels with high aspect ratios, resembling the gap between the collars. Numerous tests were carried out with different channel orientations and thicknesses. A thermo-fluid dynamic numerical model was developed to simulate the heat and mass transfer in He II. Novel dimensionless numbers were derived to validate the assumption at the basis of the single-fluid governing equations implemented in the model. The numerical model, which is based on the finite volume method, is capable of simulating transient conjugate heat transfer events in multidimensional geometries. Moreover, a novel algorithm was conceptualized to deal with the second and first-order phase transitions that helium undergoes above the critical heat fluxes. At atmospheric pressure, the second-order one (i.e., lambda transition) is associated with the threshold of the superfluid state, whereas the first-order one relates liquid helium to helium vapour. The experiments in He II resulted in reliable temperature measurements with a precision uncertainty of around 0.12 %. The superfluid helium model was successfully validated against experimental data from both the literature and this work with a relative error around 1 %. The experiments that involved multiple helium phases revealed a significant dependence of the proportion between the different phases on the channel thickness and orientation, as well as the initial temperature of the fluid. The speed at which the liquid helium-He II interface travels appears to be highly affected by the presence of a helium vapour film. At high heat fluxes, the phase change fronts propagate at a similar rate, indicating a strong correlation between the two. The phase transitions algorithm was tested at moderate heat fluxes in both subcooled liquid helium and He II. The comparison with the channel experiments showed satisfactory agreement in the temperature profiles and propagation of the phase change fronts with a relative error around 10 %. The computational model may constitute the basis of further development of the code for the simulation of events at greater pressure and temperature variations.
