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4. Temperature Predictions

What is required is a two stage finite element analysis - firstly of the electric E and magnetic B fields at resonance and then of the thermal conduction of the heating from the electric current density J, all derived from Maxwell's equations in 1. Background.

a) Induction Coil                                                      b. Planar Transformer                                        c.) Planar Transformer detail

Secondly each of the components was meshed into 3D tetrahedra, charge on left, transformer middle and primary right. The number of tetrahedra was about 2,000,000.
Thirdly Maxwell's equations were solved to compute the B and J fields, shown below on three orthogonal planes. This involved an immense amount of computing, the matrices taking 60GBytes and four hours of processing using my 48 processor workstation. I gather that commercial companies such as car manufacturers use the cloud and AI programs to adjust the geometry of their designs for EV wireless charging. From the results it was possible to compute the inductance of the primary, secondary and crucible coils.

               a).B and J fields with coil                                        b.) B and J fields without coil

Fourthly two resonant circuits were constructed in a simulation program (SPICE) with capacitors in series with the primary and crucible coils, the values of the capacitors chosen to give a resonance at about 100kHz.

               a).circuit for resonance                                       b.) circuit for dissipation

The first circuit was to derive the resonant information and the second to confirm the dissipation of the driving H-bridge IGBT transistors. The results of this simulation are shown below

a) Power                                                               b. Magnitude of capacitor volts                            c.) Magnitude of capacitor current

Two factors arose from the simulation a) the driving transistors needed to cope with 3.5kVolts and 750Amps.. Luckily insulated gate bipolar transistors (IGBT) have been developed for electric motors in the rail industry that can cope with this requirement. I expect that Silicon Carbide MOSFETs will soon be developed with higher voltage and current capacities b) the capacitors have to have a very low internal resistance or they will overheat at resonance. To obtain the 1mOhm internal resistance (ESR) a polyproplene capacitor is required. Only two sources were found Celem in Jerusalem, Israel and Cornell Dublier in the USA. I suspect they are used in slapper fuses, and thus general sale is restricted. From the power vs frequency graph on the left it can be seen that at resonance 99.96 of the 15kW power is transferred across the planar transformer.

Fifthly the eddy current dissipations were transferred to a thermal simulation of the heat fluxes at resonance

               a).temerature charge and crucible                       b.) temperature core

The picture on the right shows that the core reaches a maximum temperature of 38degC well below the Curie temperature of FDK6H40; and on the left the charge 1860degC well above the palladium melting temperature of 1555degC.