The steady-state microwave heating of slabs with small Arrhenius absorptivity

Abstract

The steady-state microwave heating of a finite one-dimensional slab 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 magnetic permeability are assumed constant. The governing equations are the steady-state versions of the forced heat equation and Maxwell's Equations while the boundary conditions take into account both convective and radiative heat loss. Approximate analytical solutions, valid for small thermal absorptivity, arc found for the steady-state temperature and the electric-field amplitude using the Galerkin method. As the Arrhenius law is not..