Abstract

Analytic solution for nonuniform internal Joule heating in a wire of rectangular cross section is obtained. The eigenvalues for convective or weak radiative boundary conditions are accurately estimated by asymptotic expansions. The problem is governed by the aspect ratio, the convection parameter β, and a nonuniform parameter α which relates to the slope of the electric resistivity. There exists a maximum α above which the conductor would fail due to high temperature.

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