Effect of radiation losses on hotspot formation and propagation in microwave heating

Abstract

The use of microwaves for the rapid heating of materials has found widespread industrial use. However, a number of potential problems are inherent in this rapid heating, including the hotspot phenomenon. A hotspot is a type of thermal instability which arises because of the nonlinear dependence of the electromagnetic and thermal properties of the material on temperature. The evolution of a hotspot in a cylindrical material is studied. The propagation of the microwaves is treated in the Wentzel-Kramers-Brillouin (WKB) limit (geometric optics), and the thermal behaviour is studied in the limit of small thermal diffusivity. The resulting temperature distributions are in excellent agreement with full numerical solutions of the governing equations, even outside the strict range of the asymptotic validity of the WKB approximation.