Asymptotic analysis of magnetic induction with high frequency for solid conductors. (English) Zbl 0915.65125

Coulaud, Olivier

RAIRO, Modélisation Math. Anal. Numér. 32, No. 6, 651-669 (1998).

This paper describes the behaviour in time and in space of an induction field created by an imposed high frequency alternating current around a solid conductor. Two time scales have been used. The induction field is decomposed in a mean field and an oscillating field. With the help of singular perturbations theory and the multiple scales method, two uncoupled models are obtained. For a cross section of a solid column of metal, two first terms of the asymptotic expansion of the induction field are build. In the case of a cylinder column, the previous results are applied by computing numerically the induction for different values of the frequency.

Reviewer: Laura-Iulia Aniţa (Iaşi)

MSC:

65Z05	Applications to the sciences
35Q60	PDEs in connection with optics and electromagnetic theory
78A25	Electromagnetic theory (general)

Keywords:

multiple time scales; singular perturbation; Maxwell’s equations; high frequency; eddy current; boundary layer; time average

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