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1. Background

James Clerk Maxwell is the most important English scientist after Newton. Einstein acknowledged Maxwell's importance in the development of tensor arithmetic he used in the general theory of relativity. Here E is the vector electric field, B is the magnetic field,
J is the total electric current density, rho is the total electric charge density, D is the displacement field and H is the magnetising field.

The palladium project is to cast molten palladium into jewelery without using fossil fuels. This requires the palladium to be heated to well past its melting point of 1555degC using induction heating. The theory of induction heating requires an understanding of Maxwell's equations (grads, curls, dot and cross products) and calculations using finite element analysis.

2. Induction Heater

In order to get the 1000 Amps at 95kHz required it was decided to use a planar transformer. These were first suggested by Lloyd Dixon of Texas Instruments in December 2013.

https://www.ti.com/download/trng/docs/seminar/Topic4LD.pdf

This is the design of the planar transformer. The ferrite chosen is FDK6H40 which has a Curie

a) Secondary                                                       b. Primary with bottom core                                                                       c.) Primary

temp of >200degC. This is a Ni-Zn ferrite developed in 2003 for use in wireless charging of electric cars. Ceramic replacements for ferrites based on Gadolinium, the only ferromagnetic lanthanide, are now in development.
Nevertheless with approx 15kW (max power from single phase of UK grid) passing through the transformer it was necessary to predict the temperature rise within the core and keep the temperature below say 60degC. The Ferroxcube type ER64 is 54mm x 50.8mm x 12.7mm and the green substrate for the primary and secondary is Aluminium Nitride one of the few materials that is electrically insulating but thermally conducting in order to remove the heat from the centre of the transformer. The secondary copper is also made thick (2mm) to aid heat removal.

3. Temperature Predictions

This is the design of the induction coil coupled by water cooled copper tube to the planar transformer. The details of the temperature predictions are shown on this page.