Microwave Oven

This is a model of the heating process in a microwave oven. The distributed heat source is computed in a stationary, frequency-domain electromagnetic analysis followed by a transient heat transfer simulation showing how the heat redistributes in the food.

Model Definition

The microwave oven is a metallic box connected to a 2.45 GHz microwave source via a rectangular waveguide operating in the TE10 mode. Near the bottom of the oven there is a cylindrical glass plate with a spherical potato placed on top of it. The microwave operates at 1 kW, but when we use symmetry to reduce the model size by one half, we only input 500 W in simulation. The symmetry cut is applied vertically through the oven, waveguide, potato, and plate. Figure 1 below shows both the full and reduced size geometry.

Figure 1: Geometry of the microwave oven, potato, and waveguide feed. Full size (left) and half size (right).

The model uses copper for the walls of the oven and the waveguide. Although resistive metals losses are expected to be small, the impedance boundary condition on these walls ensures that they get accounted for. For more information on this boundary condition, see the section Impedance Boundary Condition in the RF Module User’s Guide. The symmetry cut has mirror symmetry for the electric field and is represented by the boundary condition n × H = 0.

The rectangular port is excited by a transverse electric (TE) wave, which is a wave that has no electric field component in the direction of propagation. At an excitation frequency of 2.45 GHz, the TE10 mode is the only propagating mode through the rectangular waveguide. The cutoff frequencies for the different modes are given analytically from the relation

where m and n are the mode numbers and c denotes the speed of light. For the TE10 mode, m = 1 and n = 0. With the dimensions of the rectangular cross section (a = 7.8 cm and b = 1.8 cm), the TE10 mode is the only propagating mode for frequencies between 1.92 GHz and 3.84 GHz.

The port condition requires a propagation constant β, which at the frequency ν is given by the expression

With the stipulated excitation at the rectangular port, the following equation is solved for the electric field vector E inside the waveguide and oven:

where μr denotes the relative permeability, j the imaginary unit, σ the conductivity, ω the angular frequency, εr the relative permittivity, and ε0 the permittivity of free space. The model uses material parameters for air: σ = 0 and μr = εr = 1. In the potato the same parameters are used except for the permittivity which is set to εr = 65 − 20j where the imaginary part accounts for dielectric losses. The glass plate has σ = 0, μr = 1 and εr = 2.55.

Results and Discussion

Figure 2 below shows the distributed microwave heat source as a slice plot through the center of the potato. The rather complicated oscillating pattern, which has a strong peak in the center, shows that the potato acts as a resonant cavity for the microwave field. The power absorbed in the potato is evaluated and amounts to about 60% of the input microwave power. Most of the remaining power is reflected back through the port.

Figure 3 shows the temperature in the center of the potato as a function of time for the first 5 seconds. Due to the low thermal conductivity of the potato, the heat distributes rather slowly, and the temperature profile after 5 seconds has a strong peak in the center (see Figure 4). When heating the potato further, the temperature in the center eventually reaches 100°C and the water contents start boiling, drying out the center and transporting heat as steam to outer layers. This also affects the electromagnetic properties of the potato. The simple microwave absorption and heat conduction model used here does not capture these nonlinear effects. However, the model can serve as a starting point for a more advanced analysis.

Figure 2: Dissipated microwave power distribution (W/m3). Full size (top) and half size (bottom).

Figure 3: Temperature in the center of the potato during the first 5 seconds of heating. Full size (top) and half size (bottom).

Figure 4: Deformed electric field and Temperature distribution after 5 seconds of heating. Full size (top) and half size (bottom).

Notes About the COMSOL Implementation

In this example model, the material properties of the potato are assumed to be constant as temperature rises, for a simpler and faster numerical modeling. It uses manually configured multiple study steps to perform one-way physics coupling from electromagnetics in the frequency domain to heat transfer in the time domain. Two-way bidirectional physics coupling between electromagnetics and heat transfer, using a predefined multiphysics study step, is addressed in another Application Libraries example, RF Heating.

RF_Module/Microwave_Heating/microwave_oven

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

In the tree, select .

Click

Add a study sequence that add a study type for the interface followed by a study type for the interface.

In the tree, select .

Click

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type 2.45[GHz].

In the window, click .

In the window for , locate the section.

Select the check box.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file microwave_oven_parameters.txt.

Geometry 1

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type wo.

In the text field, type do.

In the text field, type ho.

Locate the section. In the text field, type -do/2.

Block 2 (blk2)

In the toolbar, click

In the window for , locate the section.

In the text field, type wg.

In the text field, type dg.

In the text field, type hg.

Locate the section. In the text field, type -wg.

In the text field, type -dg/2.

In the text field, type ho-hg.

Cylinder 1 (cyl1)

In the toolbar, click

In the window for , locate the section.

In the text field, type rp.

In the text field, type hp.

Locate the section. In the text field, type wo/2.

In the text field, type bp.

Sphere 1 (sph1)

In the toolbar, click

In the window for , locate the section.

In the text field, type rpot.

Locate the section. In the text field, type wo/2.

In the text field, type rpot+bp+hp.

Click

Now, it is possible exploit the mirror symmetry of the model by chopping the geometry and only simulating one half of the model. For this purpose, form a union of all geometric and build an intersection with a block that includes only half of the model.

Union 1 (uni1)

In the toolbar, click

and choose .

Click the

button in the toolbar.

Block 3 (blk3)

In the toolbar, click

In the window for , locate the section.

In the text field, type 0.4.

Locate the section. In the text field, type -0.1.

Click

Intersection 1 (int1)

In the toolbar, click

and choose .

Click the

button in the toolbar.

In the window for , click

If Full Geometry

In the toolbar, click

and choose .

In the window for , type If Full Geometry in the text field.

Locate the section. In the text field, type full_geometry.

Mirror 1 (mir1)

In the toolbar, click

and choose .

Select the object only.

In the window for , locate the section.

Select the check box.

Locate the section. In the text field, type 1.

In the text field, type 0.

Click

Click the

button in the toolbar.

Create the following selections definitions in order to make Domain and Boundary selections easier as you walk through these model instructions. Note that if you have problems finding certain numbers, you can always choose View > Selection List.

Definitions

Potato

In the toolbar, click

In the window for , type Potato in the text field.

Select Domains 7 and 8 only.

Plate

In the toolbar, click

In the window for , type Plate in the text field.

Select Domains 5 and 6 only.

Air

In the toolbar, click

In the window for , type Air in the text field.

Select Domains 1–4 only.

Port Boundary

In the toolbar, click

In the window for , type Port Boundary in the text field.

Locate the section. From the list, choose .

Select Boundaries 1 and 5 only.

Metal Boundaries

In the toolbar, click

In the window for , type Metal Boundaries in the text field.

Locate the section. From the list, choose .

Select Boundaries 2–4, 7–13, 15, 17, 19, 20, 39, and 40 only.

Symmetry

In the toolbar, click

In the window for , type Symmetry in the text field.

Locate the section. From the list, choose .

Select Boundaries 6, 16, 23, and 30 only.

Half Model

In the toolbar, click

In the window for , type Half Model in the text field.

Select Domains 2, 4, 6, and 8 only.

Next, define the materials. Air and Copper are already in the Material Library.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select .

Click in the window toolbar.

Materials

Air (mat1)

In the window for , locate the section.

From the list, choose .

Potato

In the window, right-click and choose .

In the window for , type Potato in the text field.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	65-20*j	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.55	W/(m·K)	Basic
Density	rho	1050	kg/m³	Basic
Heat capacity at constant pressure	Cp	3.64e3	J/(kg·K)	Basic

Glass

Right-click and choose .

In the window for , type Glass in the text field.

Locate the section. From the list, choose .

Locate the section. In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	2.55	1	Basic
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	0	S/m	Basic
Thermal conductivity	k_iso ; kii = k_iso, kij = 0		W/(m·K)	Basic
Density	rho		kg/m³	Basic
Heat capacity at constant pressure	Cp		J/(kg·K)	Basic

You do not need to define the listed thermal properties, as the glass plate will not be in the thermal part of the model.

Add Material

Go to the window.

In the tree, select .

Click in the window toolbar.

In the toolbar, click

to close the window.

Materials

Copper (mat4)

In the window for , locate the section.

From the list, choose .

Electromagnetic Waves, Frequency Domain (emw)

For the electromagnetic part of the problem, begin by defining the input port. In the full model, you can exploit the predefined settings of the rectangular port.

Port 1, Full Model

In the window, under right-click and choose .

In the window for , type Port 1, Full Model in the text field.

Locate the section. From the list, choose .

For the first port, wave excitation is by default.

In the Pin text field, type 1[kW].

Next, set up the remaining boundary conditions.

Impedance Boundary Condition 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Heat Transfer in Solids (ht)

In the toolbar, click and choose .

Electromagnetic Waves, Frequency Domain (emw)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Port 2, Half Model

In the toolbar, click

and choose .

Keep in mind that the excited power is only half of Port 1.

In the window for , type Port 2, Half Model in the text field.

Locate the section. From the list, choose .

From the list, choose .

In the Pin text field, type 1[kW]/2.

If you want to configure the port manually, the type port can be replaced with where the z-component of electric field is cos(pi*y/dg)[V/m] and the propagation constant is 2*pi/c_const*sqrt(freq^2-c_const^2/(4*dg^2)).

Exploit the mirror symmetry of the model by adding a PMC type symmetry plane.

Symmetry Plane 1

In the toolbar, click