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Nonlinear effects of variable conductivities in thermistor-related problems: an explicit example

Published online by Cambridge University Press:  16 July 2009

J. H. Young  and
G. Tenti
J. H. Young
Affiliation:
Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294, USA
G. Tenti
Affiliation:
Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
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Abstract

The coupled nonlinear partial differential equations obeyed by the electrical potential and temperature distribution for a medium undergoing steady state electrical heating are applied to a one-dimensional rod having its surface temperature held constant as current is conducted along its length due to a potential difference maintained between its ends. Extension is given to the previously discussed class of solutions by the inclusion of a thermal conductivity which varies linearly with temperature. The resulting electrical current and resistance are found to be significantly influenced by the thermal conductivity of the medium. Molybdenum is identified as a material exemplifying such a thermal conductivity and the general effects are then numerically illustrated.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 1 , Issue 3 , September 1990 , pp. 245 - 257
Copyright
Copyright © Cambridge University Press 1990

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