Recent work has described microwave applicators which produce localized spot heating of a workpiece with a Gaussian spatial distribution of microwave power. Applicators of this type provide a nearly ideal heating pattern for joining of ceramics and other applications requiring localized heating, and offer several advantages over conventional methods utilizing surface heat flux.

A three-dimensional mathematical model of a circular volumetric heat source moving through a rectangular block was constructed to address some of the microwave heating concerns--electric field power requirements, uniform heating, and thermal runaway. The partial differential equation from the mathematical model was solved numerically with an implicit finite-difference method. Using experimentally measured dielectric loss properties for alumina, the required electric field strengths to raise the temperature of a localized spot in a rectangular block to 1500K are presented. With the block moving on an insulating support, the results also show that uniform temperature profiles through the depth of the alumina can be achieved, and thermal runaway can be prevented by choosing an appropriate block velocity and electric field strength. With the block on a highly conductive support, however, the high electric field power required to raise the temperature of the block makes thermal runaway and non-uniform temperature distributions likely. For the published dielectric loss coefficient data for glass, thermal runaway could not be avoided for a stationary block. Calculations suggest that maintaining a constant absorbed power in a moving workpiece could be a way of maintaining the desired maximum temperature within the blocks. From the preceding conclusions, a microwave spot heater appears to be an effective tool for the joining of ceramics.