Evaluation of transient temperature distributions in a dielectric in an alternating field

Thermal catastrophe in dielectrics is a term which refers to a phenomenon in which the temperature in a dielectric subjected to an alternating electric field becomes infinite in a finite length of time. Mathematical aspects of this phenomenon are investigated in the paper. It is assumed that the rate of heat generation is proportional to the square of the field intensity and to an exponential function of temperature. A mathematical theory of existence and uniqueness for the initial-value/boundary-value problem for the phenomena is presented. It is shown analytically that there is a critical field intensity above which thermal catastrophe occurs. An estimate of the critical intensity is made analytically, and this is compared with critical intensities obtained numerically. Analytic lower boundaries to the solution to the equations for temperature in the dielectric are derived. A numerical solution is recomputed on a digital computer and compared with a solution obtained on a differential analyser.