In this work we proposed the governing equations for describing the microwave heating process where the complex interactions between the thermo-mechanical and electromagnetic fields are taken into account. Starting point are the general balance laws of mechanics and electrodynamics. Transient and spatial temperature profiles of liquids (water and corn solution) inside a cylindrical container during microwave heating at 2450 MHz were measured. Transient temperature rise at a given location was almost linear. The slowest heating region was at the container bottom due to small energy penetration through the bottom. Numerical simulations were carried out for microwave heating of 2D cylinders of pure water with internal convection in the liquid regions. The results are found to be consistent with those of the experiments. A generalized theoretical model was formulated for the process of microwave heating of materials. Finally stability analysis was done on a 1-D model of microwave heating and the equations for the perturbations were obtained.
