Natural air convection for cooling of particle accelerator electromagnets: case studies at CERN

Cooling by natural convection is investigated on two air-cooled corrector magnets at CERN. The heat transfer coefficient (HTC) for each magnet is estimated analytically using established empirical correlations for certain geometries. The HTC is also estimated numerically with three-dimensional steady-state finite element simulations. Air convection around the respective coils as well as heat conduction inside the coils are modelled. Different formulas for the HTC are tested in the post-processing of the simulation results. The HTC for each magnet is then determined experimentally by measuring surface temperatures on the coils through time at constant currents. A method to extract the HTC from these temperature curves is developed, in which the curves are fitted to a function that is derived from a thermodynamical analysis of the heating process. Some plausible ranges for the HTC for each magnet for different currents are obtained. The results of the different estimation methods are compared with the experimental results of the HTC.