Quasi-linear electrical potentials in steady-state Joule heating

✍ Scribed by J. H. Young

• Publisher: Springer
• Year: 1987
• Tongue: English
• Weight: 336 KB
• Volume: 21
• Category: Article
• ISSN: 0022-0833
• DOI: 10.1007/bf00127691

✦ Synopsis

It is shown that, when account is taken of the temperature dependence of the electrical conductivity of a medium in steady-state conditions, the electrical potential obeys a quasi-linear, second-order partial differential equation. The equation is shown to be easily solved by means of a generalized Kirchhoff transformation, giving coordinate-free solutions in terms of functions which obey Laplace's equation. Steady-state temperatures resulting from the potential are shown to be significantly influenced by the quasi-linear potential when compared with the expected form which assumes the potential to satisfy Laplace's equation.