Thermal analysis of composite superconductors subjected to time-dependent disturbances

A one-dimensional heat conduction equation with time- and temperature-dependent heat sources was employed to study the steady-state and transient response of a composite superconductor subjected to a thermal disturbance. An integral formulation was used to solve the steady-state problem of current redistribution and heat generation. The results of the integral formulation are compared with those of an analytical solution. The two solutions agree with each other except when the analytical solution fails as the temperature in the superconductor begins to exceed the critical temperature. Transient solutions were obtained by the finite-difference technique and the results are compared with a known analytical solution. Results of numerical calculations of the transient response of a composite superconductor subjected to an initial pulsed disturbance are presented. It is demonstrated that the superconductor can switch between the superconducting and the current-sharing state. The transient response and the stability of the composite conductor depend on the magnitude and duration of the disturbance, the dimensionless temperature θ*, and the dimensionless parameter φ.