How deep do microwaves heat?

The depth at which power falls to 1/e (penetration depth) at 2.45 GHz is about 17 mm in water and about 8 mm in beef (typical permittivities). Lowering frequency to 915 MHz makes it about 2.7 times deeper. Ice, with tiny dielectric loss, gives over 11 m — it barely absorbs, which is why thawing is uneven.

Why does a microwave oven heat unevenly?

Waves reflect inside the cavity to form standing waves, with strong and weak field regions repeating every half wavelength. At 2.45 GHz the half wavelength in air is about 6.1 cm; inside food the wavelength shortens, repeating every 0.7 cm or so in water. Turntables and mode stirrers move the pattern to average out the unevenness.

What is thermal runaway in microwave heating?

In materials whose dielectric loss rises with temperature, absorption grows as they heat until heat loss can't keep up and temperature shoots up. In the example, a field of 11.5 kV/m settles at 94 °C, but raising it 4% to 12 kV/m removes the steady state, and at 13 kV/m the sample passed 300 °C in about 66 minutes. Near the threshold, small differences change the outcome dramatically.

Microwave Heating Simulation

Category: Electromagnetic–Thermal Coupling | Revised 2026-10-01

Theory & Physics

Theory: heat from dielectric loss

Overview

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I'm designing an industrial microwave dryer. How do I link the electromagnetic and thermal analyses?

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Microwaves shake molecules in the material (especially water) with the electric field, producing heat through dielectric loss. The basic flow is to compute the field distribution electromagnetically, derive the heat-generation distribution, and pass it to the thermal analysis. But permittivity changes with temperature and moisture, so heating changes the generation pattern too. Whether you include this two-way coupling can change results greatly. First pin down three things: how deep it reaches, what pattern it heats in, and whether absorption rising with temperature causes runaway.

Heat generation and penetration depth

$$ P = 2\pi f\,\varepsilon_0\,\varepsilon''\,E_{rms}^2, \qquad D_p = \frac{\lambda_0}{2\pi\sqrt{2\varepsilon'}}\left[\sqrt{1 + \left(\frac{\varepsilon''}{\varepsilon'}\right)^2} - 1\right]^{-1/2} $$

$\varepsilon'$ is relative permittivity, $\varepsilon''$ the loss factor, $E_{rms}$ the RMS field and $\lambda_0$ the free-space wavelength. $D_p$ is the depth at which power falls to 1/e; in thicker material the centre heats poorly.

A simple runaway model

$$ \rho c_p V\,\frac{dT}{dt} = V P_0\,e^{\,b\,(T - T_0)} - hA\,(T - T_0), \qquad P_{0,crit} = \frac{hA}{V\,b\,e} $$

If dielectric loss rises exponentially with temperature, the threshold is where the heat-generation curve touches the heat-loss line. Beyond it there is no steady temperature and the temperature keeps climbing.

Coffee Break Trivia

A cooker born of a melted chocolate bar

The oft-told origin of the microwave oven is that around 1945, Raytheon engineer Percy Spencer, working near a radar magnetron, noticed the chocolate bar in his pocket had melted. He tried popcorn and eggs and confirmed that microwaves could heat food. The first product was the size of a refrigerator, but household units shrank in the 1960s–70s and spread worldwide. Today microwaves also serve industry: drying timber and pharmaceuticals, vulcanising rubber and sintering ceramics.

Worked examples

Example 1: penetration depth

Material (ε′, ε″)	2.45 GHz	915 MHz
Water (78, 10)	17.2 mm	46.1 mm
Beef (52, 17)	8.4 mm	22.4 mm
Ice (3.2, 0.003)	11.6 m	31.1 m

Permittivities are typical values, assumed the same at 915 MHz (they actually vary with frequency). At 1 kV/m water absorbs 1.36×10⁶ W/m³, heating at 0.33 K/s. The half wavelength is 6.1 cm in air, 0.69 cm in water and 0.85 cm in beef — the spacing of standing-wave highs and lows.

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Microwaves reach 11 m into ice, yet it barely heats?

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It reaches deep precisely because it's barely absorbed — ice's loss factor is about 1/3,000 of water's. So when heating frozen food, parts that melt first become water, absorption jumps and those spots overheat. The melted regions heat further and melt their surroundings — runaway thawing — sometimes cooking the outside while the inside stays frozen. Defrost modes pulse power on and off to let heat conduct and even out.

Example 2: thermal runaway

A 10 cm³ sample with 26 cm² surface and 20 W/m²K heat transfer, loss factor 0.01 at 25 °C rising e-fold per 100 K (2.45 GHz). The threshold field is 11.8 kV/m:

Field	Result
10 kV/m	Steady at 64 °C
11.5 kV/m	Steady at 94 °C
12 kV/m	No steady state (142 °C at 3 h, still rising)
13 kV/m	Passes 300 °C in about 66 min

A 4% increase in field decides whether a steady temperature exists. In materials whose loss rises with temperature, such as ceramics being sintered, slight field non-uniformity can trigger local runaway, causing cracking or melting.

Analysis workflow

Measure (or gather) permittivity and loss factor as functions of temperature, moisture and frequency.
Solve the field including cavity and waveguide to obtain heat generation.
Pass generation to the thermal model, update permittivity with temperature and re-solve the field (two-way coupling).
Include turntables, mode stirrers or conveyor motion to evaluate averaging.
Validate with fibre-optic thermometers or IR cameras (metal thermocouples disturb the field).

Coffee Break Trivia

“Only the prototype's corners scorch”

In industrial microwave heating of food, products in square trays scorched only at the corners. Field analysis showed the electric field concentrated at corners and edges, where waves entering from two or three directions overlapped and generation rose. As moisture left and temperature rose, the loss factor changed and the imbalance grew. Rounding the tray corners and adjusting layout and power fixed it. Corners are common starting points for local overheating in microwave heating.

Common mistakes

Mistakes and fixes

Mistake	Effect	Fix
Constant permittivity	Runaway and unevenness missed	Make it a function of temperature and moisture
Solving the field once	Generation pattern drifts	Re-solve with updated properties
Grid coarse relative to wavelength	Standing waves lost	Below 1/10 of in-material wavelength
Measuring with metal thermocouples	Field disturbed	Fibre-optic thermometers
Setting temperature by power alone	Runaway past the threshold	Control power by temperature

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I'd like to learn related topics.

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Check electromagnetic basics with the skin depth calculator and microwave transmission simulator. For related heating analyses see microwave heating basics, dielectric heating, RF heating and induction heating.

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