Вариационная форма модели теплового пробоя твердого диэлектрика с зависящей от температуры теплопроводностью

Вариационная форма модели теплового пробоя твердого диэлектрика…

ISSN 1812-3368. Вестник МГТУ им. Н.Э. Баумана. Сер. Естественные науки. 2017. № 5

VARIATIONAL NOTATION OF A THERMAL BREAKDOWN MODEL

FOR A SOLID DIELECTRIC WITH TEMPERATURE-DEPENDENT

THERMAL CONDUCTIVITY

V.S. Zarubin

fn2@bmstu.ru

Bauman Moscow State Technical University, Moscow, Russian Federation

Abstract

Keywords

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

Dielectric, thermal breakdown,

mathematical model, functional,

thermal conductivity potential

Received 28.11.2016

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