Some exact solutions for electrothermal breakdown

Exact solutions for electrothermal breakdown have been given by H.J. Wintle (1981) for the case of a DC voltage between plane parallel thermally conducting electrodes. Wintle's solutions require specific functional dependence on temperature for both electrical and thermal conductivities, and he gives three pairs of suitable functions. In the present work, one of Wintle's models is chosen to extend the exact solutions to coaxial cylinders and concentric spheres. The boundary conditions used are either a thermally insulating inner electrode and a thermally conducting outer electrode, or both electrodes thermally conducting. For a thermally insulating center electrode, and an electrode radius ratio of 5, the field distorts to an almost constant value for a voltage that is 90% of critical; for a voltage that is 99% of critical, the field at the outer electrode is 10 times the value of the field at the inner electrode.<>