Joule Heating of a Plate Electrode in a Free Arc Discharge

摘要

To estimate the heating of an airplane wing from a lightning stroke, the Joule heating in an infinite plate was analyzed. From experiments with argon arcs, it has been observed that the surface current density from an arc in which the plate acts as anode is approximated closely by a Gaussian distribution. With this boundary condition on one surface, the quasi-steady current distribution inside the plate was found from a solution of Maxwell's equations. By the use of a simple approximation of the interior current density distribution for plates which are thin compared with the arc radius as the source term in the heat equation, the solution to the temperature enhancement in the plate was found by means of the Bessel and Laplace transforms. A solution for thick plates also was obtained by using an approximation to the current in the plate in the neighborhood of the arc axis where most of the heating occurs. (Author)