Resonance, Rayleigh Flows and Thermal Choking: Compressible Coolant States in Porous Electromagnetic Heat Exchangers*

Electromagnetic (EM) Heat Exchangers (HX) are systems which convert EM energy into heat or mechanical work. One potential design consists of a porous lossy ceramic material heated by EM waves with a compressible gas coolant. EM heating of ceramics is nonlinear, since the loss factor is temperature dependent.  Designing such EM HXs requires an understanding of the coupling between temperature, the electric field, and gas dynamics at the pore scale. To mimic this microscale phenomena, a single channel with a high-speed gas coolant in perfect thermal contact with a thin solid ceramic layer is considered, with an applied plane-wave electric field propagating normal to the channel walls. From a thin-domain asymptotic analysis, the conservation laws reduce to a Rayleigh flow in the gas coupled with averaged thermal energy conservation equations at leading order. The kinetic energy of the gas increases about 12 times the inlet value when thermal runaway occurs in the ceramic region, and themal choking is possible when the coolant reaches the sonic state. Local maximum efficiencies occur on a discrete set of ceramic thicknesses which correspond to Fabry-Bragg resonances of the electric field.