Dynamic Nonlinear Temperature Field in a Ferromagnetic Plate Induced by High Frequency Electromagnetic Waves

Abstract

The subject of this paper is the thermal-behavior of an elastic metallic plate influenced by several harmonic electromagnetic plane waves at the upper and lower surfaces. The direction of wave propagation is normal to the surfaces of the plate. As a result of a time-varying electromagnetic field conducting currents appear in the plate. Distributions of eddy-currents and hysterisis power losses across the plate thickness are obtained using complex analysis. It is of the exponential type and depends on the plate thickness, wave frequency, electric conductivity, magnetic permeability and magnetic intensity. By treating this power as a volume heat source, differential equations governing distribution of the temperature field are formulated. The temperature field across the plate thickness is assumed to be in nonlinear form and a system of three coupled differential equations governing the temperature field is formed. Equations are solved in analytical form using the integral-transformation technique (Double Fourier finite-sine transformation and Laplace transformation). The influence of the skin depth, plate thickness, wave frequency and characteristic times of an impulse on the dynamic temperature field are considered. Nonlinear distribution of the temperature across the plate thickness is obtained. Strain and stress fields are obtained using the finite element method (FEM). Depending on the plate thickness thin shell finite elements (for a thin plate) or volume finite elements (for a thick plate) were applied.