One-dimensional time-independent conduction states and temperature distribution along a normal zone during a quench

Using time-independent states of the one-dimensional heat conduction equation, some analytical approximations have been used to study the temperature profile of the normal zone of a superconducting cable. For a one-dimensional time-independent conduction state, a constant with respect to the longitudinal coordinate is associated. This approach contains the cryogenic stabilization criterion as a particular case. Using the constant, the temperature profile along the conductor is studied considering the effect of thermal conductivity and heat transfer on helium. The analysis indicates that the heat transfer as well as the conductivity can make a nontrivial contribution to the temperature distribution during a quench.<>