An Asymptotic Approach to Modeling Wave-geometry Interactions in an Electromagnetic Heat Exchanger

Gaone, Joseph Michael

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An Asymptotic Approach to Modeling Wave-geometry Interactions in an Electromagnetic Heat Exchanger

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Electromagnetic (EM) heat exchangers are devices that absorb EM radiation and convert its energy to thermal energy for a specific purpose such as to power a turbine. They have recently been of growing interest, yet the field is predominantly studied with thermal resistance network models and is in need of more rigorous continuum modeling. Homogenization has been used in low and high frequency electromagnetics to describe macroscopic behavior of traveling waves. While dielectric material parameters vary with temperature, coupling the energy equation with Maxwell’s equations, little effort has been made toward homogenization techniques that capture the effects of this dependence, which is necessary to accurately model porous medium heat exchangers. Firstly, we have examined the effect the wave-geometry interactions of high-frequency illumination has on a triple-layer laminate, which approximates the unit cell of a homogenization problem. Secondly, we develop an extension to a high-frequency homogenization (HFH) method developed for photonics. The extension is made by developing a three-dimensional vector-valued HFH of Maxwell’s curl-curl equation that includes dielectric loss. It is validated for a one-dimensional geometry where the exact solution to the scattering problem is known by implementing the Transfer Matrix Method. The HFH model produces perturbation approximations to the dispersion curves showing the nonexistence of band gaps and generates low attenuation outside the band gap regions.

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