Microwave Heating Analysis
Overview
Professor! Today let us talk about microwave heating analysis. What is it about?
Theory: dielectric loss and penetration depth
Overview
When thawing in a microwave, edges can cook while the centre stays frozen. Why?
Whether something heats depends on how much microwave energy it absorbs, its dielectric loss factor. Water absorbs strongly, but in ice molecules are locked in the crystal and can't rotate, so it barely absorbs. In thawing, regions that melt first heat rapidly, and heating makes them absorb even more. Penetration depth is the other reason: in moist food microwaves weaken greatly within about a centimetre of the surface, so the centre must wait for conducted heat. Ovens also have strong and weak field spots (standing waves). Analysing these together is coupled electromagnetic–thermal analysis.
Absorbed power density and heating rate
E is rms field, ε'' the imaginary part of relative permittivity (loss factor), ρ density and c_p specific heat.
Penetration depth
λ₀ is free-space wavelength (122 mm at 2.45 GHz) and ε' the real part of relative permittivity; the depth at which power falls to 1/e of its surface value.
The chocolate bar in the pocket
Microwave cooking is said to have begun around 1945 when Spencer, working with radar magnetrons at Raytheon in the US, noticed a chocolate bar melting in his pocket. The first commercial microwave oven appeared in 1947, and home ovens spread in the 1970s. The 2.45 GHz frequency is not water's absorption peak but one of the internationally allocated industrial, scientific and medical bands, used because it gives reasonable penetration depth.
Worked examples
Example: absorption and penetration at 2.45 GHz, 1 kV/m rms
| Material | ε′ | ε″ | Penetration depth | Power density | Heating rate |
|---|---|---|---|---|---|
| Water (20 °C) | 78 | 10 | 17 mm | 1.36 MW/m³ | 0.33 K/s |
| Water (80 °C) | 61 | 3.0 | 51 mm | 0.41 MW/m³ | 0.10 K/s |
| Meat-like food | 50 | 15 | 9.3 mm | 2.04 MW/m³ | 0.56 K/s |
| Frozen food | 4 | 1.0 | 39 mm | 0.14 MW/m³ | 0.07 K/s |
| Ice | 3.2 | 0.003 | 11.6 m | 409 W/m³ | ≈ 0 |
Permittivities are representative. At 915 MHz, food (ε′ 52, ε″ 21) has a penetration depth of 18 mm.
As water warms, absorption drops and penetration depth triples.
Water's loss factor falls as temperature rises, so hotter water lets microwaves penetrate deeper and heats more slowly in the same field — a tendency toward uniform heating. Conversely, when ice melts the loss factor jumps over a thousandfold, promoting non-uniform heating and causing uneven thawing. Analysis must therefore give permittivity as a function of temperature and solve the electromagnetic and thermal fields alternately or simultaneously. Industrial thawing uses 915 MHz with deeper penetration, or lower RF frequencies (tens of MHz), and lowers power with pauses so heat has time to conduct inward.
Analysis workflow
- Measure or obtain permittivity (ε′, ε″) versus temperature and frequency.
- Solve the electromagnetic field in the frequency domain including cavity, waveguide and load.
- Use absorbed power as the heat source for conduction (and moisture transport if needed).
- Update permittivity with temperature and iterate electromagnetics and heat.
- Evaluate turntables or mode stirrers by time-averaging or multiple positions.
“Same power, double the thaw time”
In a frozen-food thawing line, making the product slightly thicker roughly doubled the time to thaw completely at the same power, and corners began to cook. Coupled electromagnetic–thermal analysis showed fields concentrating at corners and edges, which thawed first, absorbed more and drew even more field, while the frozen centre absorbed almost nothing and waited for conduction. Lowering power with intermittent operation and switching to 915 MHz reduced non-uniformity and shortened the time.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Constant permittivity | Uneven thawing missed | Use temperature dependence |
| Analysing the load alone | Standing waves missed | Model the whole cavity |
| Ignoring penetration depth | Centre heating overestimated | Compare Dp with thickness |
| Ignoring evaporation | Wrong surface temperature | Include mass transfer |
| Mixing peak and rms fields | Power off by 2× | Use rms |
I'd like to learn related topics.
Related pages include dielectric heating, RF heating, induction heating, Joule heating and eddy-current heating.