Coupled Electromagnetic and Heat Transfer ODE Model for Microwave Heating With Temperature-Dependent Permittivity

In the traditional microwave heating partial differential equation (PDE) model, one of the main characteristics is the infinite-dimensional nature, which does not allow to readily design and implement a controller. Motivated by this obstruction, this paper proposes a microwave heating finite-dimensional ordinary differential equation (ODE) model, which can not only describe the thermodynamics field with nonhomogeneous boundary conditions but also be coupled with the variation of electromagnetic field in temperature-dependent dielectric media. Initially, the equivalent PDE model with a homogeneous boundary condition is derived by constructing an auxiliary function in order to directly derive the eigenspectrum of the spatial differential operator. With the help of model-reduction techniques, the dominant dynamics of temperature distribution are subsequently captured with a reasonable Galerkin truncation. The simulation results on microwave heating a water prototype show that the temporal and the spatial evolution of the temperature profile can be described by solving the temperature-dependent electromagnetic field and the finite-dimensional ODE model. Moreover, the effectiveness of the model is verified by comparing with the numerical results from the traditional COMSOL model. A further development of this ODE model may provide a useful numerical tool for the design and synthesis of microwave heaters to avoid thermal runaway phenomena.