Modelling and investigation of the heating process of a tungsten panel under the action of a quasi-steady-state electromagnetic field

Abstract

A nonferromagnetic electroconductive panel of rectangular cross-section is considered under the action of a quasi-steady electromagnetic field. Under such an action, unsteady volumetrically distributed Joule heat sources arise in it. To investigate the regularities of its thermal modes, a two-dimensional physico-mathematical model consisting of two stages is proposed. At the first stage, the tangent component of the magnetic field intensity vector to the panel bases is determined from Maxwell's relations. At the second stage, this component is used to calculate the Joule specific heat density. The solution to the electrodynamics problem is constructed by approximating the distribution of the determining function along the thickness coordinate with a cubic polynomial. The coefficients of the approximation polynomial are represented as a linear combination of the integral characteristics of the determining function along the thickness coordinate and its specified values at the panel bases. As a result, the original two-dimensional initial-boundary value problem for the defining function is reduced to a one-dimensional initial-boundary value problem for the integral characteristics of the defining function. The solutions of the one-dimensional problem are obtained by applying a finite integral transform along the transverse coordinate of the panel using the specified boundary conditions on the determining function at the end sections of the panel and the Laplace transform in time.
Numerical studies have been performed for a tungsten panel under the homogeneous action of a quasi-steady electromagnetic field. The thermal modes of the panel are analysed depending on the parameter characterising the relative depth of induction current penetration for two typical cases of near-surface and continuous heating.