Dielectric Heating Analysis
Theory: when heating outruns cooling
Overview
Why, in dielectric heating, does material sometimes scorch or crack one day under the same conditions?
Most likely the process runs close to the thermal-runaway threshold. In dielectric heating, molecules try to follow the changing field direction and absorb energy as heat. How readily they absorb is the loss factor, which in many materials grows with temperature. Warmer regions then absorb more and get warmer still. If cooling keeps up, temperature settles; if not, it keeps climbing. The threshold is sharp: a small change in field, moisture or placement can tip the process from settling to runaway. Dielectric-heating analysis therefore couples electromagnetic field and temperature, includes temperature-dependent loss, and checks how far the process is from the threshold.
Heating formula
f is frequency (2.45 GHz), ε₀ vacuum permittivity, ε''₀ loss factor at the reference temperature (0.05), β its temperature coefficient (0.02/K, illustrative) and E the RMS field inside the material.
Heat balance and critical condition
H is volumetric cooling coefficient: for a 10 mm plate cooled on both faces at 20 W/m²K, H = 2h/L = 4,000 W/m³K. ρc is volumetric heat capacity (2×10⁶ J/m³K). The threshold is where the heating curve touches the cooling line; with more heating there is no intersection.
PVC welds, polyethylene doesn't
High-frequency welding, which bonds plastic sheets with an RF field, is used for raincoats, inflatable rings and stationery folders. It works on high-loss plastics such as PVC; polyethylene and polypropylene have so little loss that they barely warm in the field. Even within dielectric heating, a material's loss factor decides whether it can be heated at all.
Worked examples
Example 1: field strength and settled temperature
| Field | Heating (reference) | Rise with constant loss | Rise with temperature dependence |
|---|---|---|---|
| 1,000 V/m | 6,815 W/m³ | 1.7 K | 1.8 K |
| 2,000 V/m | 27,259 W/m³ | 6.8 K | 8.0 K |
| 3,000 V/m | 61,334 W/m³ | 15.3 K | 25.6 K |
| 3,200 V/m | 69,784 W/m³ | 17.4 K | 35.4 K |
| 3,280 V/m | 73,317 W/m³ | 18.3 K | 45.9 K |
| 3,286 V/m | 73,576 W/m³ | 18.4 K | 50 K (critical) |
At low field the temperature dependence barely matters, but it grows abruptly near the critical 3,286 V/m.
Example 2: temperature history either side of the threshold
| Field | Result |
|---|---|
| 3,000 V/m | Stable at 25.6 K after 2 hours |
| 3,500 V/m | Rises 300 K in about 4,614 s (about 77 min) |
Between 3,000 and 3,500 V/m the field differs by only 17%, yet one is stable and the other runs away.
And runaway isn't immediate. Even at 3,500 V/m the first tens of minutes show only slow warming; temperature surges after passing a certain point. That is why it is easy to miss while watching. In real applicators field varies with position, with standing waves creating strong and weak spots. Even if average field is below critical, strong spots alone can run away and scorch or crack. Permittivity itself also changes with temperature, reshaping the field, which may concentrate in hot regions. Electromagnetic and thermal analyses are therefore solved alternately, updating local temperature and field as they evolve. In operation, surface temperature is measured to throttle power, and material is moved so it doesn't dwell in strong-field spots.
Modelling workflow
- Measure permittivity and loss factor at the operating frequency over temperature.
- Estimate the critical field from a simple heat balance.
- Solve the electromagnetic field in the applicator to get heating distribution.
- Solve temperature, update permittivity and loss, and re-solve the field.
- Check the hottest spot stays well below critical and set power and placement.
“Ceramics cracked only at the corners”
Heating ceramic parts by microwave occasionally cracked only their corners, though the furnace set point was unchanged. Coupled electromagnetic–thermal analysis showed field intensifying at corners, and since the material's loss rises sharply with temperature, the corners alone crossed the threshold into local runaway. Slowing the power ramp and surrounding parts with low-loss insulation to reduce temperature differences eliminated the cracking.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Constant room-temperature loss | Runaway missed | Temperature-dependent loss |
| Judging by average field | Local runaway missed | Solve field distribution |
| Solving the field once | Field change with temperature ignored | Re-solve alternately |
| Simulating too short | Delayed runaway missed | Simulate long enough |
| Overestimating cooling | Critical field overestimated | Fit heat transfer to measurements |
I'd like to learn related topics.
Related pages include microwave heating, RF heating, induction heating, Joule heating and eddy-current heating.