Numerical solutions of the thermistor problem with a ramp electrical conductivity S. Kutluay a, * , A.S. Wood b a Department of Mathematics, Faculty of Arts and Science, In€on€u University, 44069 Malatya, Turkey b Department of Mechanical and Medical Engineering, University of Bradford, BD7 1DP West Yorkshire, UK Abstract This paper presents approximate steady-state solutions of a positive temperature coefficient thermistor problem, having a ramp electrical conductivity that is a highly non-linear function of the temperature, using a standard explicit finite difference method. It is shown that numerical solutions exhibit the correct physical characteristics of the problem and, they are in good agreement with the exact solution. Ó 2003 Elsevier Inc. All rights reserved. Keywords: Thermistor; Ramp electrical conductivity; Finite difference 1. Introduction We consider the one-dimensional heat and current flow through a therm- istor, a thermo-electric device whose electrical conductivity is a highly non-linear function of temperature. Mathematical problems related to the combined heat and current flow have been proposed in the literature under the title of ‘‘the thermistor problem’’. The steady-state thermistor problem has been considered by several authors [1–6] where aspects of modelling, existence, uniqueness, and behaviour of solutions were presented. Preis et al. [7] treated a two-dimensional thermistor problem by finite elements and computed tem- perature gradients that were thought to be implicated in causing mechanical * Corresponding author. E-mail address: skutluay@inonu.edu.tr (S. Kutluay). 0096-3003/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/S0096-3003(02)00834-2 Applied Mathematics and Computation 148 (2004) 145–162 www.elsevier.com/locate/amc