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Numerical solutions of the thermistor problem with a ramp electrical conductivity. (English) Zbl 1072.78523

Summary: This paper presents approximate steady-state solutions of a positive temperature coefficient thermistor problem, having a ramp electrical conductivity that is a highly nonlinear 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.

MSC:

78M20 Finite difference methods applied to problems in optics and electromagnetic theory
80A20 Heat and mass transfer, heat flow (MSC2010)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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[1] Cimatti, G., Remark on existence and uniqueness for the thermistor problem under mixed boundary conditions, Q. Appl. Maths., 47, 117-121 (1989) · Zbl 0694.35137
[2] Cimatti, G.; Prodi, G., Existence results for a non-linear elliptic system modelling a temperature dependent electrical resistor, Ann. Mater. Pura Appl., 162, 33-42 (1992)
[3] Diesselhorst, H., ber das probleme eines elektrisch erwarmten leiters, Ann. Phys., 1, 312-325 (1900) · JFM 31.0808.01
[4] Fowler, A.; Frigaard, I.; Howison, S. D., Temperature surges in thermistors, SIAM J. Appl. Math., 52, 998-1011 (1992) · Zbl 0800.80001
[5] Howison, S. D.; Rodrigues, J. F.; Shillor, M., Stationary solutions to the thermistor problem, J. Math. Anal. Appl., 174, 573-588 (1993) · Zbl 0787.35033
[6] Wiedmann, J., The thermistor problem, Nonlinear Differen. Equat. Appl., 4, 133-148 (1997) · Zbl 0992.35102
[7] Preis, K.; Biro, O.; Dyczij-Edlinger, R.; Richter, K. R.; Badics, Zs.; Riedler, H.; Stönger, H., Application of FEM to coupled electric, thermal and mechanical problems, IEEE Trans. Magn., 30, 5, 3316-3319 (1994)
[8] Westbrook, D. R., The thermistor: a problem in heat and current flow, Numer. Meth. PDEs., 5, 259-273 (1989) · Zbl 0676.65128
[9] Wood, A. S.; Kutluay, S., A heat balance integral model of the thermistor, Int. J. Heat Mass Transfer, 38, 10, 1831-1840 (1995) · Zbl 0924.73029
[10] Kutluay, S.; Bahadir, A. R.; Ozdes, A., A variety of finite difference methods to the thermistor with a new modified electrical conductivity, Appl. Math. Comput., 106, 205-213 (1999) · Zbl 1049.80501
[11] Kutluay, S.; Bahadir, A. R.; Ozdes, A., Various methods to the thermistor problem with a bulk electrical conductivity, Int. J. Numer. Meth. Eng., 45, 1-12 (1999) · Zbl 0941.78011
[12] Wood, A. S., Modelling the thermistor, (Heiliö, M., Proceedings of 5th European Conference on Maths. Industry (1991), Kluwer Academic: Kluwer Academic Stuttgart), 397-400
[13] Howison, S., Complex variables in industrial mathematics, (Neunzert, H., Proceedings of 2nd European Symposium Maths. Industry, Oberwolfach (1988), Kluwer Academic: Kluwer Academic Stuttgart), 153-166 · Zbl 0709.00507
[14] Smith, G. D., Numerical Solution of Partial Differential Equations: Finite Difference Methods (1987), Clarendon: Clarendon Oxford
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