Temperature State of a Hollow Cylinder Made of a Polymer Dielectric with Temperature-Dependent Characteristics
A mathematical model is constructed to describe a steady one-dimensional temperature distribution in a hollow circular cylinder made of a polymer dielectric with a constant difference in the electric field potentials on the cylinder surfaces. Based on systematized data on the dependence of the thermal conductivity and electrical conductivity of polymer materials used as dielectrics in engineering on temperature, a qualitative analysis of the model is performed for a prescribed density of the heat flux supplied to the inner surface of the cylinder and intensity of convective heat transfer on the outer surface. The results obtained in the study allow one to determine the area of applicability of polymer dielectrics used in various electrical engineering applications, including electrical insulation of DC high-voltage cables, and to formulate the conditions for the thermal breakdown of the cylindrical layer of the dielectric.