Dual variational model of a thermal breakdown of a dielectric layer at an alternating voltage

Abstract

The article constructs the dual variational form of the model based on the presented differential form of a mathematical model describing the steady-state process of thermal conductivity in a plane or circular cylindrical layer of a solid dielectric at an alternating voltage. This form includes the main and alternative functionals, whose stationary points analysis makes it possible to establish a combination of the determining parameters corresponding to the occurrence of thermal breakdown of the dielectric layer. An example of the analysis of stationary points for two variants of test functions that are admissible for these functionals and approximating the steady temperature distribution in the dielectric layer is given. The estimation of the approximation error, which makes it possible to choose the function closest to the limiting temperature distribution in the layer preceding the thermal breakdown of the dielectric, is presented.