Temperature loading of a thin metallic plate subjected transversal to law-frequency electromagnetic field

Abstract

Since many devices (such as magnetic circuits of motors, generators, inductors, transformers) work under the influence of the electromagnetic fields, obtaining Joule's heat as a thermal loading of the thin metallic plate subjected transversal in homogenous, time-varying electromagnetic field is presented in this paper. The direction of the field propagation is normal to the surfaces of the plate. Plate thickness is small compared to the depth of penetration of the magnetic field. Time-varying electromagnetic field is the reason of the conducting currents appearance in the material. The problem is solved in analytical form as the interior Dirichlet boundary problem. The intensity of thermal loading of the plate is obtained in dynamic form using the integral-transformation technique (Double Fourier finite-sine transformation and Laplace transformation). It depends on the plate thickness, electric conductivity, magnetic permeability, frequency and magnetic intensity of the external electromagnetic field, impulse's cycle... The influence of the plate thickness, field frequency and characteristic times of an impulse on the dynamic thermal loading are considered. Thermal loading is the entrance for the further calculation of the behavior of the plate, which is usually done by FEM.

Keywords

• depth of penetration
• thin metallic plate
• electromagnetic field
• magnetic induction
• heat power