Electric fields at thermal maximum voltage (DC) in multi-layer dielectrics in plane-parallel geometry

Cable joints are one of the examples of multilayer dielectrics. Joints are subjected to high electric and thermal stress, the former depending on the cable itself, while the latter is a consequence of ohmic losses in a conductor due to load current and leakage current flowing through the layers of the insulation. This coactive effect might cause the cable joint to undergo thermal/electrical breakdown at some point. Hence the estimation of Electric fields at maximum thermal voltage of cable joint/multilayer dielectrics in general, is of quite significant importance. Current continuity equation, heat flux equation and Poisson's equation along with appropriate boundary conditions were simultaneously solved at various current densities by finite difference method and voltage versus current density is plotted. The peak value of voltage, after which the solution of temperature goes haywire is the Thermal Maximum Voltage and electric field distribution and temperature distribution at that voltage/current density are investigated.