The effect of spatial inhomogeneity in thermal conductivity on the formation of hot-spots

The steady-state microwave heating of a unit slab consisting of three layer s of materials with different thermal conductivities is examined. The gover ning equations are a damped wave equation derived from Maxwell's equations and a heat-force equation for the temperature. As the primary concern is to investigate the dependence of the steady-state on the thermal-conductivity parameter, a simplifying assumption is made, namely that the electrical co nductivity is temperature-independent. Under this assumption, the damped wa ve equation governing the electric field may be solved separately. An eigen function expansion for the problem based on the Galerkin method is describe d and a fundamental-mode approximation is presented. If this approximation is applied to a unit slab composed of three layers with different thermal c onductivities, the hot-spot formation can be addressed and a global steady- state solution is found for the whole domain. Numerical results for some di fferent cases of the three-layer combinations are interpreted to gain some insight in parameter dependence and the position of the low-thermal-conduct ivity inner layer related to hot-spot formation.