Steady State Temperature Profile in a Cylinder Heated by Microwaves

We have developed a new theory to calculate the steady state temperature profile in a cylindrical sample positioned along the entire axis of a cylindrical microwave cavity. Temperature profiles were computed for alumina rods of various radii contained in a cavity excited in one of the TM0n0 modes with n = 1, 2, or 3. Sample surface and center temperatures will be presented as a function of total sample absorbed power or electric field strength at the sample surface. An approach for attaining more uniform heating within the sample by reducing the magnitude of the inverted temperature profile using a concentric outer cylindrical tube will be discussed. Also, parametric studies will be reported for model calculations in which the total hemispherical emissivity was varied at boundaries of the sample and surrounding tube and at the cavity wall. The results will be discussed in the context of controlling both the average sample temperature and the temperature distribution in the sample during microwave processing.