Modelling microwave heating

Although microwave radiation is best known far heating food in the kitchen, in recent years it has found new applications in many industrial processes, such as those involving melting, smelting, sintering, drying, and joining. Heating by microwave radiation constitutes a highly coupled nonlinear problem giving rise to new and unexpected physical behavior, the best known of which is the appearance of ''hot spots.'' That is, in many industrial applications of microwave heating it has been observed that heating does not take place uniformly but rather regions of very high temperature tend to form. In order to predict the occurrence of such phenomena it is necessary to develop simplified mathematical models from which insight might be gleaned into an inherently complex physical process. The purpose of this paper is to review some of the recent developments in the mathematical modelling of microwave heating, including models that consider in isolation the heat equation with a nonlinear source term, in which case the electric-field amplitude is assumed constant, models involving the coupling between the electric-field amplitude and temperature including both steady-state solutions and the initial heating, and also models that control the process of thermal runaway. Numerical modelling of the microwave heating process is also briefly reviewed.