Vol. 12, No. 1, 2019

Download this article
Download this article For screen
For printing
Recent Issues

Volume 12, 1 issue

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Addresses
Editors’ Interests
Scientific Advantages
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
Coming Soon
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Analytical solution of a one-dimensional thermistor problem with Robin boundary condition

Volodymyr Hrynkiv and Alice Turchaninova

Vol. 12 (2019), No. 1, 79–88

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.

thermistor problem, Robin boundary condition, Joule heating, analytical solution
Mathematical Subject Classification 2010
Primary: 35J60
Received: 26 April 2017
Revised: 5 October 2017
Accepted: 14 February 2018
Published: 31 May 2018

Communicated by Suzanne Lenhart
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