Electromagnetic-thermal model of a millimeter-wave heat exchanger based on an AlN:Mo susceptor
Authors: Kumi Petra , Martin Stephanie A. , Yakovlev Vadim V. , Hilario Martin S. , Hoff Brad W. , Rittersdorf Ian M. 
Published: January 2020

Purpose
The paper introduces and illustrates the use of numerical models for the simulation of electromagnetic and thermal processes in an absorbing ceramic layer (susceptor) of a new millimeter-wave (MMW) heat exchanger. The purpose of this study is to better understand interaction between the MMW field and the susceptor, choose the composition of the ceramic material and help design the physical prototype of the device.

Design/methodology/approach
A simplified version of the heat exchanger comprises a rectangular block of an aluminum nitride (AlN) doped with molybdenum (Mo) that is backed by a thin metal plate and irradiated by a plane MMW. The coupled electromagnetic-thermal problem is solved by the finite-difference time-domain (FDTD) technique implemented in QuickWave. The FDTD model is verified by solving the related electromagnetic problem by the finite element simulator COMSOL Multiphysics. The computation of dissipated power and temperature is based on experimental data on temperature-dependent dielectric constant, loss factor, specific heat and thermal conductivity of the AlN:Mo composite. The non-uniformity of patterns of dissipated power and temperature is quantified via standard-deviation-based metrics.

Findings
It is shown that with the power density of the plane wave on the block’s front face of 1.0 W/mm2, at 95 GHz, 10 × 10 × 10-mm blocks with Mo = 0.25 – 4% can be heated up to 1,000 °C for 60-100 s depending on Mo content. The uniformity of the temperature field is exceptionally high – in the course of the heating, temperature is evenly distributed through the entire volume and, in particular, on the back surface of the block. The composite producing the highest level of total dissipated power is found to have Mo concentration of approximately 3%.

Research limitations/implications
In the electromagnetic model, the heating of the AlN:Mo samples is characterized by the volumetric patterns of density of dissipated power for the dielectric constant and the loss factor corresponding to different temperatures of the process. The coupled model is run as an iterative procedure in which electromagnetic and thermal material parameters are upgraded in every cell after each heating time step; the process is then represented by a series of thermal patterns showing time evolution of the temperature field.

Practical implications
Determination of practical dimensions of the MMW heat exchanger and identification of material composition of the susceptor that make operations of the device energy efficient in the required temperature regime require and expensive experimentation. Measurement of heat distribution on the ceramic-metal interface is a practically challenging task. The reported model is meant to be a tool assisting in development of the concept and supporting system design of the new MMW heat exchanger.

Originality/value
While exploitation of a finite element model (e.g. in COMSOL Multiphysics environment) of the scenario in question would require excessive computational resources, the reported FDTD model shows operational capabilities of solving the coupled problem in the temperature range from 20°C to 1,000°C within a few hours on a Windows 10 workstation. The model is open for further development to serve in the ongoing support of the system design aiming to ease the related experimental studies.