Microwave heating of two-dimensional slabs with small Arrhenius absorptivity

Abstract

The microwave heating of two-dimensional slabs in a long rectangular waveguide propagating the TE10 mode is examined. The temperature dependency of the electrical conductivity and the thermal absorptivity is assumed to be governed by the Arrhenius law, while both the electrical permittivity and the magnetic permeability are assumed constant. The governing equations are the forced heat equation and the steady-state version of Maxwell's equations while the boundary conditions take into account both convective and radiative heat loss. Approximate analytical solutions, valid for small thermal absorptivity, are found for the temperature and the electric-field amplitude using the Galerkin method. ..