The Thermistor Problem with Hyperbolic Electrical Conductivity
M. O. Durojaye *
Department of Mathematics, University of Abuja, Nigeria.
J. T. Agee
Discipline of Electrical, Electronic and Computer Engineering, University of Kwazulu-Natal, South Africa.
*Author to whom correspondence should be addressed.
Abstract
This paper presents the one-dimensional, positive temperature coefficient (PTC) thermistor equation, using the hyperbolic-tangent function as an approximation to the electrical conductivity of the device. The hyperbolic-tangent function describes the qualitative behaviour of the evolving solution of the thermistor in the entire domain. The steady state solution using the new approximation yielded a distribution of device temperature over the spatial dimension and all the phases of the temperature distribution of the device without having to look for a moving boundary. The analysis of the steady state solution and the numerical solution of the unsteady state is presented in the paper.
Keywords: Thermistor, electrical –conductivity, hyperbolic-tangent, method of lines.