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.
Issue Section:Technical Brief
Keywords:Joule, wire, nonuniform, conduction, convective boundary, thermophysical properties
Heat Transfer, Vol.
Heat Conduction and Mass Diffusion,
D. R., and
CRC Handbook of Chemistry and Physics, 99th ed.,
Boca Raton, FL,
H. S., and
Conduction of Heat in Solids, 2nd ed.,
Formulas for Calculating Temperature Distribution in Transformer Cores and Other Electric Apparatus of Rectangular Cross Section,”
Trans. Am. Inst. Elect. Eng.,
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