Transverse electric-thermal-fluid instabilities in an electromagnetic heat exchanger

Abstract

Electromagnetic (EM) heat exchangers (HX) are critical components in power beaming applications where EM waves are radiated towards an EM HX, which then converts incident energy into heat or mechanical work. An EM HX consists of a lossy ceramic and a fluid flow that maintains thermal contact with and transfers heat from the ceramic. These materials have loss factors which increase with temperature, so that beyond a critical temperature thermal runaway can take place. Stable characteristic temperatures, which depend on the rate of energy removal from the system, during high-power EM heating of ceramic materials suggest that coolants would be in the gaseous phase. As a first step, we consider a model EM HX system consisting of a horizontal channel containing a viscous, dielectric fluid with a constant coefficient of thermal expansion, bounded from below by a grounded ceramic receiver of finite thickness. The system is subject to plane EM waves, propagating normally to the channel from above, and polarized in the same direction as a plane Poiseuille flow of the coolant. With the Boussinesq approximation, we calculate the base state solution of the system and then investigate the linear stability of this base-state. We find three modes of instability: thermal runaway, Rayleigh-Bénard convection, and a novel instability which we call the fringe-field instability, that takes place in the plane normal to base-state flow direction.