Heat transfer coefficient estimation for high-temperature superconducting coils under light over-current conditions

Understanding and modelling heat transfer coefficient is essential for optimising the performance of high-temperature superconducting (HTS) devices. The heat transfer coefficient exhibits highly non-linear behaviour with respect to temperature and is typically inferred from the properties of the cooling fluid. However, when the device is fully immersed in a liquid, the coefficient can deviate significantly from conventional estimations, especially if the operating conditions do not involve an extremely rapid temperature increase. This study presents a practical method for estimating the heat transfer coefficient of HTS coils immersed in liquid nitrogen, based on an experimental investigation of a prototype superconducting coil where precise temperature measurements are not guaranteed. By analysing transient temperature evolution and material properties, the coefficient is determined and validated through the comparison of measured and simulated device voltage and current. The proposed approach only relies on experimental voltage and current measurements, combined with known temperature-dependent material properties, to infer a global heat transfer coefficient. The methodology is tested on helical HTS coils under transient light over-current conditions and assumes an homogenised temperature rise along the winding. The estimated coefficient may lead to curves that slightly deviate from classical models while preserving their overall trend and physical significance. The proposed experimentally-based approach is conceived as a relatively straightforward and experimentally robust alternative to the computational burden of finite-element method simulations requiring reliable parameters, while overcoming the need for direct temperature measurements, within the limits of compact windings immersed in liquid nitrogen and subjected to mild transient conditions leading to distributed quench phenomena.