Thermal Conductivity of a Matrix

In MPI and high power electronics in general, the limiting factor is often heat transfer as is the case for the shift coils limiting gradient strength and drive coil heating limiting imager stability. Further complicating the situation are the materials and environmental limitations inherent to MPI -- all accessory components, especially those targeted towards the transmit system, must be free of any non-linear magnetic behavior. Sadly most commercial potting compounds have some degree of non-linearity to them. To address this necessity for a thermally conductive, magnetically linear, and preferably cheap solution awe have utilized a custom-blended epoxy doped with aluminum oxide (or other doping materials).

Perhaps unsurprisingly there is a profound basis for this in the literature with analytical estimations for the composite's effective thermal conductivity. One thorough review from Hongyu Chen and colleagues (here) describes the topic and another paper here shows some experimental data with similar fillers and a comparable epoxy matrix. Regardless of which model is used to calculate the effective conductivity the implications are the same, and that is with increasing filler volume fraction, the conductivity monotonically increases suggesting you should use as much filler as practical. To the limit, you hit issues with the material being too thick to reasonably spread over surfaces.

We use a MATLAB script that uses two models to calculate the effective thermal conductivity and have included that model in this GitHub repository.