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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
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