Variational Notation of a Thermal Breakdown Model for a Solid Dielectric with Temperature-Dependent Thermal Conductivity

We constructed a differential notation of a mathematical model describing a steady-state heat energy transfer process in a planar or circular cylindrical dielectric layer for the case of alternating voltage. Thermal conductivity of a dielectric material depends on temperature. Using a variational formulation of the non-linear steady-state thermal conductivity problem, we transform this model into variational notation containing a functional defined on a set of acceptable distributions of the thermal conductivity potential in the dielectric layer. Investigating stationary points on this functional makes it possible to find the combination of the parameters determining whether a thermal breakdown occurs in the dielectric. The paper presents an example of stationary point analysis and an estimation of the cumulative error allowing the approximation function to be selected so as to lie as close as possible to the limit thermal conductivity potential distribution prior to the thermal breakdown in the dielectric

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