High temperature superconductors (HTS) have been integrated in the high current leads for the Large Hadron Collider (LHC), under construction at CERN, in order to reduce the heat leak into the liquid helium bath due to the joule effect. The use of the HTS technology in the lower part of the current leads allowed to significantly reduce the heat charge on the cryogenic system. Hybrid current leads have been designed to fulfill the LHC requirements with respect to thermal load; several tests have been performed to study the lead behavior especially during a quench transient. Quench experiments have been performed at CERN on 13 kA prototypes to determine the adequate design and protection. In all the tests it is possible to know the temperature profile of the HTS only with the help of quench simulations that model the thermo-hydraulic processes during quench. The development of a theoretical model for the simulation allows reducing the number of test to perform and to scale the experimental result to other current lead sizes. In this work a theoretical quench model and a numerical code have been developed to compute the quench process and the thermal analysis in the HTS part of the current leads. The model approximates the heat balance equations with the finite difference method and considers the temperature dependence of material's properties. With this model it is possible to perform a thermal analysis of the HTS assembly in steady working condition as well as to study the resistive transition known as quench. The numerical approach is much more accurate than the analytical one, which involves a more approximated model with more physical approximations. In this work are given: the theoretical description of the model, its numerical implementation, the experimental validation and some simulation results
