Electrode influence on transient thermal gradients in BaTiO3 PTC thermistors

The transient temperature distribution of a BaTiO3 PTC thermistor is sensitive to the electrical and thermal boundary conditions during the initial heating period after application of a voltage. A 2-dimensional model using finite difference analysis has been developed for the cylindrical geometry of small disc thermistors (radius = 5 mm, thickness = 2 mm). The predictions include current concentration at the edge of an electrode whose coverage is slightly smaller than the disc face. At 100 V, 150 V, or 200 V this leads to a ring of faster heating and transient thermal gradients upto 50 °C/mm can occur before relaxation to the steady state.