Analytical solution of a one-dimensional thermistor problem with Robin boundary condition

Hrynkiv, Volodymyr; Turchaninova, Alice

doi:10.2140/involve.2019.12.79

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Analytical solution of a one-dimensional thermistor problem with Robin boundary condition

Volodymyr Hrynkiv and Alice Turchaninova

Vol. 12 (2019), No. 1, 79–88

DOI: 10.2140/involve.2019.12.79

Abstract

A one-dimensional nonlinear heat conduction equation of steady-state Joule heating in the presence of an electric field in a metal with temperature-dependent conductivities is considered. A technique developed by Young (1986) is adapted and used to derive an analytical solution for the problem with a Robin boundary condition.

Keywords

thermistor problem, Robin boundary condition, Joule heating, analytical solution

Mathematical Subject Classification 2010

Primary: 35J60

Milestones

Received: 26 April 2017

Revised: 5 October 2017

Accepted: 14 February 2018

Published: 31 May 2018

Communicated by Suzanne Lenhart

Authors

Volodymyr Hrynkiv
Department of Mathematics and Statistics University of Houston - Downtown Houston, TX United States

Alice Turchaninova
University of Houston - Downtown Houston, TX United States

Vol. 12, No. 1, 2019