Thermal stability was examined theoretically for various commercial grades of alumina heated by microwave energy. The critical temperature for thermal runaway was evaluated as a function of Biot number and ambient temperature, employing various functional forms of the dependence of dielectric loss with temperature. Field‐temperature relationships were derived for the limit of small temperature gradients in the specimen. Finite difference methods were used under conditions where significant temperature gradients were sustained in the specimen. The critical temperature approached limiting asymptotes for the extremes in Biot number, with smooth variation in the intermediate regime. Stability diagrams were constructed which denote regions of stability and their dependence on important system parameters. The effects of ambient temperature on critical temperature were determined analytically and compared with experimental observations on heating alumina fiber bundles by a hybrid configuration utilizing an external suseptor. The results have implications for temperature control near the critical temperature and the design of hybrid heating systems.

A model of the local microstructure of a bundle of fibers is simulated and used as the basis for calculations of transport properties. This, in turn, can be used in a macroscopic model of the chemical vapor infiltration process. An expanding/overlapping circle representation of the microstructure simulates the deposition of matrix in a uniaxial bundle of fibers. An iterative heat conduction algorithm is used to calculate the transverse thermal conductivity based on the thermal conductivities of the solid and gas phases. The permeability of gas through the microstructure is calculated for flow both parallel and transverse to overlapping cylinders using a Stokes equation and assuming a Darcy's law behavior. Both the simulations of the microstructure and associated calculations of the transport properties compare favorably with experimental data. Darcy's law for the behavior of gas in a bundle of fibers is shown to be valid for gas pressures of 5-13 kPa.