Rating of conductors for short-duration currents

The heat equation for the mean temperature of a conductor carrying a short-duration current is solved for adiabatic conditions at the surface and for all the relevant thermophysical properties varying quadratically with temperature. A simplified approximation to the solution is also given. Curves showing the variation of temperature with energy input and with the time integral of the square of the current density ¿ J2dt are presented for various conducting materials. These are in fair agreement with experimental data. Equations are given for calculating ¿ J2dt for various time-dependent current forms. It is shown from the measured prearcing energy and ¿ J2dt that, for current densities in the ranges 108¿1012 A/m2 and rupture times down to a few microseconds, the conductor rarely melts completely before rupture, owing to the radial temperature gradient, the loss of mechnical strength and the effect of electromagnetic forces. With rupture times faster than 1¿s, complete melting and even vaporisation can occur, because inertia and magnetic forces tend to cause the conductor to retain its physical shape. A method is given for calculating the loss of tensile strength of conductors subjected to repeated current transients.