RF Heating

This is a model of an RF waveguide bend with a dielectric block inside. There are electromagnetic losses in the block as well as on the waveguide walls which cause the assembly to heat up over time. The material properties of the block are functions of temperature. The transient thermal behavior, as well as the steady-state solution, are computed.

Figure 1: A waveguide bend with a dielectric block inside. Top boundaries of the waveguide are removed only for visualization.

Model Definition

The waveguide bend shown in Figure 1 is connected to a 100 W power source, operating at 10 GHz, via a rectangular waveguide operating in the TE10 mode. The other end of the bend is also connected to a rectangular waveguide operating in the TE10 mode. The objective of such a bend is primarily to change the direction of propagation of the energy. Here, however, a block of dielectric is introduced as an example of a lossy material interacting with an electromagnetic field.

The waveguide is made of aluminum. To reduce surface losses, the inside walls are coated with copper, a high-conductivity metal. The dielectric block is modeled as having electrical conductivity of σ = 0, relative permeability of μr = 1, and a relative permittivity of εr = 2.1, with a loss tangent that is a function of temperature, δ = 0.001×(T/300 K). The thermal conductivity of this block is also a function of temperature, k = 0.3×(T/300 K) W/m/K. Furthermore, the density is 2200 kg/m3 and the specific heat is 1050 J/kg/K. These are generic properties representative of a dielectric material.

At the operating frequency, the skin depth of the copper coating is much smaller than the dimensions of the waveguide, that is, the electromagnetic fields penetrate a negligible distance into the walls. This means that the electromagnetic losses can be localized entirely on the surface, and that there is no need to solve Maxwell’s equations inside of the walls themselves. Thus, Maxwell’s equations only need to be solved in the air domain inside of the waveguide, as well as inside of the block. The heat transfer equation is solved in the block as well as the waveguide walls.

The objective of the analysis is to observe how the assembly of the dielectric block and waveguide heat up over time, as well as to find the steady-state temperature. The waveguide is initially assumed to be at a constant temperature throughout. After the power source is turned on, the electromagnetic fields interact with the highly conductive interior boundaries of the waveguide, as well as the lossy dielectric block. The losses in the block and on the walls are sources of heat that raises the temperature. The block is assumed to be in perfect thermal contact with the walls of the waveguide, that is, any heat generated in the block is conducted away into the walls. The outside boundaries of the walls are assumed to be facing ambient air, which leads to free convective cooling off of these faces. This example uses an averaged heat transfer coefficient to represent this free convection to ambient air.

The model solves two governing equations: Maxwell’s equations, which describe the electromagnetic fields, and the heat transfer equation, which describes the temperature. It is assumed that the operating frequency is much higher than any thermal transients, and thus it is possible to solve the problem either in a frequency-transient or a frequency-stationary sense.

A frequency-transient simulation solves Maxwell’s equations in the frequency domain. This implicitly assumes that all material properties used to solve Maxwell’s equations are constant over a single period of oscillation of the electromagnetic wave. The heat transfer equation is, on the other hand, is solved transiently. The electromagnetic fields are only recomputed when the material properties have changed significantly, as determined by a criterion involving the relative tolerance of the time-dependent solver. The objective of the analysis is to determine the change in temperature from given initial conditions and how long these changes take.

A frequency-stationary simulation solves Maxwell’s equations in the frequency domain, but it solves the stationary heat transfer equation under the assumption that all initial transient variations have died out. Although no transient information is obtainable, this computation is significantly faster than a frequency-transient analysis and gives the steady-state temperature distribution.

Results and Discussion

Figure 2 plots the peak temperature within the dielectric block over time, showing that it takes several minutes for the block to reach thermal equilibrium.

Figure 3 plots the fields inside of the waveguide, as well as the temperature of the assembly, for the steady-state temperature solution after all thermal transients have died out. The dielectric block shows a significant temperature variation, which affects the thermal conductivity and loss tangent, plotted in Figure 4.

Figure 2: The maximum temperature, evaluated over the volume of the block, is plotted as a function of temperature.

Figure 3: The electric fields (red arrows) magnetic fields (green arrows) and power flow (blue arrows) are shown inside of the waveguide. The steady-state temperature is plotted on the block and waveguide walls.

Figure 4: The loss tangent within the dielectric block for the steady-state solution shows that the variation in temperature affects the material properties.

RF_Module/Microwave_Heating/rf_heating

Modeling Instructions

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New

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Model Wizard

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Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
f0	10[GHz]	1E10 Hz	Current frequency
lda0	c_const/f0	0.029979 m	Wavelength, air
h_max	0.2*lda0	0.0059958 m	Maximum mesh element size, air

Here, c_const is a predefined COMSOL constant for the speed of light in vacuum.

Geometry 1

First, import the geometry of the waveguide including a dielectric block inside the waveguide.

Import 1 (imp1)

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In the window for , locate the section.

Click .

Browse to the model’s Application Libraries folder and double-click the file rf_heating.mphbin.

Click .

Use the wireframe rendering to see the inner parts of the waveguide.

Click the

button in the toolbar.

Definitions

Create a set of selections for use before setting up the physics. First, create a selection for the dielectric block.

Dielectric

In the toolbar, click

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

Select Domain 3 only.

Add a selection for the air-filled region inside the waveguide.

Air

In the toolbar, click

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

Select Domain 2 only.

Add a selection for the waveguide structure.

Waveguide

In the toolbar, click

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

Select Domain 1 only.

Add a selection for the inner surface of the waveguide.

Waveguide inside surfaces

In the toolbar, click

In the window for , type Waveguide inside surfaces in the text field.

Locate the section. From the list, choose .

Select Boundaries 16–18, 35, 53, 54, 72, 74, 75, 78, 96, and 97 only.

Add a selection for the outer surface of the waveguide.

Waveguide outside surfaces

In the toolbar, click

In the window for , type Waveguide outside surfaces in the text field.

Locate the section. From the list, choose .

Select Boundaries 48–52, 55, 69, and 98 only.

To get a better view, suppress some of the boundaries. Furthermore, by assigning the resulting settings to a View node, you can easily return to the same view later by clicking the button in the toolbar.

In the window, right-click and choose .

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Hide for Physics 1

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In the window for , locate the section.

From the list, choose .

Select Boundaries 18 and 50 only.

Electromagnetic Waves, Frequency Domain (emw)

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In the list, select .

Click

Select Domains 2 and 3 only.

Wave Equation, Electric 1

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In the window for , locate the section.

From the list, choose .

Heat Transfer in Solids (ht)

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In the window for , locate the section.

In the list, select .

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Select Domains 1 and 3 only.

Heat Flux 1

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and choose .

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From the list, choose .

Locate the section. Click the button.

In the h text field, type 5.

Electromagnetic Waves, Frequency Domain (emw)

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Wave Equation, Electric 2

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and choose .

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From the list, choose .

Impedance Boundary Condition 1

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Port 1

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Select Boundary 15 only.

In the window for , locate the section.

From the list, choose .

For the first port, wave excitation is by default.

In the Pin text field, type 100.

Port 2

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and choose .

Select Boundary 79 only.

In the window for , locate the section.

From the list, choose .

Materials

Next, assign material properties on the model. Begin by specifying Aluminum for the waveguide structure.

Add Material

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to open the window.

Go to the window.

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Materials

Aluminum (mat1)

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In the window for , locate the section.

From the list, choose .

Air (mat2)

In the window, click .

In the window for , locate the section.

From the list, choose .

Dielectric

In the window, right-click and choose .

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

Select Domain 3 only.

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


Property	Variable	Value	Unit	Property group
Relative permittivity (real part)	epsilonPrim_iso ; epsilonPrimii = epsilonPrim_iso, epsilonPrimij = 0	2.1	1	Loss tangent, loss angle
Loss tangent, loss angle	delta	0.001*(T/300[K])	rad	Loss tangent, loss angle
Relative permeability	mur_iso ; murii = mur_iso, murij = 0	1	1	Basic
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	0.3[W/m/K]*(T/300[K])	W/(m·K)	Basic
Density	rho	2200	kg/m³	Basic
Heat capacity at constant pressure	Cp	1050	J/(kg·K)	Basic