Temperature state of polymer dielectric layer, bounded by curvilinear surfaces, at constant voltage

Abstract The solution of one-dimensional nonlinear problem of stationary heat conduction in a dielectric layer with volumetric energy release at a constant difference in electric potentials on the curvilinear heat transfer surfaces, bounding the layer, is presented in a closed analytical form. The analytical form of the solution, being a set of integral relations, allows to conduct a quantitative analysis of the influence of governing parameters on temperature state of the layer, including the one preceding the occurrence of thermal dielectric breakdown. Such form of solution can be used to test the results of numerical solution of this problem. An example of quantitative analysis of the presented integral relations is given. Approximate formulas that make it possible to find estimates of the parameters of temperature state of dielectric layer and the maximum difference in electrical potentials, preceding the thermal breakdown of the layer, are obtained. Mathematics Subject Classification (2010). Primary 80A19; Secondary 97M50.