Effect of convection heat transfer on the design of vapor-cooled current leads

A general optimization method for vapor-cooled current leads is presented with taking into account the effect of convection heat transfer and extended surfaces. This analytical work is considered as a unified design method, since one formulation calculates the minimum heat load and the corresponding optimal design condition for arbitrary heat transfer condition, spanning two limiting cases—the zero convection (or conduction-cooled leads) and the perfect heat transfer. It is clearly shown that the augmentation of the convective cooling can reduce the heat load to a certain extent, but the optimum lead parameter required to minimize the heat load for the finite heat transfer may not exist between the two limiting values. A new dimensionless parameter called the Ch number is introduced to conveniently incorporate the convection effect into the optimization. The present method is demonstrated for two specific lead designs that have been recently developed for 10 kA level of applications.