Thermal Runaway in Ceramics Arising from the Temperature Dependence of the Thermal Conductivity

Thermal runaway during microwave heating in ceramic materials has been explained recently in terms of a microscopic model involving a nonlinear feedback between microwave absorption and heat dissipation. We study here an alternate model of thermal runaway which is based on the temperature dependence of the thermal conductivity of the material being heated. If the thermal conductivity decreases as the temperature increases, a decrease could occur in the removal of heat from the central regions of the sample which, unlike the surface, cannot cool off quickly through processes such as radiation. The result would be an enhanced heating of the central regions and a further decrease of the thermal conductivity thus providing a feedback loop. A quantitative analysis of these concepts is provided