×

Various methods to the thermistor problem with a bulk electrical conductivity. (English) Zbl 0941.78011

Summary: In this paper, Explicit Finite Difference (EFD), Galerkin Finite Element (GFE) and Heat-Balance Integral (HBI) methods are applied to the one-dimensional thermistor problem with a bulk electrical conductivity to obtain its steady-state solutions. It is shown that EFD, GFE and HBI solutions exhibit the correct physical characteristic of the problem, and they are in very good agreement with the exact solution. The only marked difference is time to attain steady states.

MSC:

78A55 Technical applications of optics and electromagnetic theory
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
78M20 Finite difference methods applied to problems in optics and electromagnetic theory
80A20 Heat and mass transfer, heat flow (MSC2010)
80M10 Finite element, Galerkin and related methods applied to problems in thermodynamics and heat transfer
80M20 Finite difference methods applied to problems in thermodynamics and heat transfer
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] and Integrated Electronics: Analog and Digital Circuits and Systems, McGraw-Hill (ISD), Tokyo, 1972.
[2] ABC’s of Thermistors, Foulsham-Sams, Slough, 1970.
[3] Thermistors, Butterworth (Iliffe Books), London, 1971.
[4] Thermistors, Electrochemical Publications, Scotland, 1979.
[5] Cimatti, Q. Appl. Maths. 40 pp 15– (1988)
[6] Cimatti, Q. Appl. Maths. 47 pp 117– (1989)
[7] Diesselhorst, Ann. Phys. 1 pp 312– (1900)
[8] and ?Temperature surges in thermistor?, in et al. (eds.), Proc. 3rd Eur. Conf. Maths. Industry, Kluwer Academic, Teubner, Stuttgart, 1990, pp. 197-204. · doi:10.1007/978-94-009-0629-7_18
[9] Fowler, SIAM J. Appl. Math. 52 pp 998– (1992)
[10] and ?Current problems in the glass industry?, in and (eds.), Moving Boundary Problems in Heat Flow and Diffusion, Clarendon Press, Oxford, 1975.
[11] ?Complex variables in industrial mathematics?, in (ed.), Proc. 2nd Eur. Symp. Maths. Industry, Oberwolfach, Kluwer Academic, Stuttgart, 1988, pp. 153-166. · doi:10.1007/978-94-009-2979-1_9
[12] Howison, Q. Appl. Maths. 47 pp 509– (1989)
[13] Westbrook, Numer. Meth. PDEs 5 pp 259– (1989) · Zbl 0676.65128 · doi:10.1002/num.1690050308
[14] ?Modelling the thermistor?, in (ed.), Proc. 5th Eur. Conf. Maths. Industry, Kluwer Academic, Stuttgart, 1991, pp. 397-400. · doi:10.1007/978-3-663-01312-9_71
[15] ?Thermistor cracking?, Tech. Univ. Eindhoven Report 89-02, 1989.
[16] Howison, J. Math. Anal. Appl. 174 pp 573– (1993)
[17] Biro, Int. J. Appl. Electromagn. Mater. 3 pp 151– (1992)
[18] Preis, IEEE Trans. Magn. 30 pp 3316– (1994)
[19] Wood, Int. J. Heat Mass Transfer 38 pp 1831– (1995)
[20] ?Applications of integral methods to transient nonlinear heat transfer?, in and (eds.), Advances in Heat transfer, Vol. 1, 1964, pp. 51-122.
[21] Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed, Clarendon Press, Oxford, 1987.
[22] The Finite Element Method, 3rd ed, McGraw-Hill, London, 1977.
[23] and Heat Conduction, Blackwell Scientific Publications, Oxford, 1987.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.