On gaseous coolants in porous ceramic electromagnetic absorbers: thermal runaway vs Joule-Thompson cooling at the microscale

An electromagnetic (EM) heat exchanger (HX) absorbs EM waves in high-power beaming applications and converts the internal energy to mechanical work. One design of an EM HX consists of a porous ceramic which is heated by EM waves, and a gaseous coolant flowing through the pores transfers the dissipated thermal power to the outlet. A nonlinear phenomenon associated with EM heating of ceramics with a temperature-dependent loss factor is thermal runaway—slight increase in the applied power causes significant rise of temperature (up to 2000K). Designing such an EM HX requires understanding of the coupling between compressible gas dynamics and thermal runaway at the pore-scale. To study the microscale phenomena, we consider a 2D thin and long EM HX, consisting of a single channel with an ideal compressible gas coolant in perfect thermal contact with a thin solid ceramic layer. We apply lubrication theory to derive the averaged conservations laws and solve the system numerically in MATLAB. We find that Joule-Thompson cooling occurs locally when work of expansion done by the gas dominates over the net heat added to the system. Finally, parametric studies on Péclet and bearing numbers are carried out to determine critical conditions for the onset of Joule-Thompson cooling within the gas.