Joule Heating of a Microactuator

This simple tutorial model simulates the resistive heating — also known as Joule heating — of a two-hot-arm thermal actuator. The model couples the physics phenomena involved in one way only. However, as explained below, you can easily modify it to simulate a two-way coupling between the electric current and the heating of the actuator.

Model Definition

Figure 1 shows the actuator’s parts and dimensions as well as its position on top of a substrate surface.

Figure 1: The thermal microactuator.

MAterial Data

This model uses the material properties listed in Table 1 for the Joule Heating Model equations. The assumption of constant material properties means that the coupling between physics phenomena is one way only: the electric current through the actuator heats up the material, but the current itself is not affected by the temperature rise. By using a material where the electrical conductivity is temperature dependent, you can turn this into a two-way coupling.

Table 1: Material Data.
Property	Name	Value
Electrical conductivity	σ	5·104 S/m
Relative permeability	εr	4.5
Thermal conductivity	k	40 W/(m·K)
Density	ρ	2300 kg/m3
Heat capacity at constant pressure	Cp	600 J/(kg·K)

Boundary Conditions

An electric potential is applied between the bases of the hot arms’ anchors. The cold arm anchor and all other surfaces are electrically insulated.

Figure 2: Electrical boundary conditions.

The temperature of the base of the three anchors and the three dimples is fixed to that of the substrate’s constant temperature. Because the structure is sandwiched, all other boundaries interact thermally with the surroundings by conduction through thin layers of air.

The heat transfer coefficient is given by the thermal conductivity of air divided by the distance to the surrounding surfaces for the system. This exercise uses different heat transfer coefficients for the actuator’s upper and other surfaces.

Figure 3: Heat-transfer boundary conditions.

Results

Figure 4 shows the temperature distribution on the actuator’s surface. The line graph in Figure 5 provides more detailed information about the temperature along a single edge facing the substrate plane.

Figure 4: The temperature distribution on the actuator surface.

Figure 5: Temperature along the actuators longest edge facing the substrate.

COMSOL_Multiphysics/Multiphysics/thermal_actuator_jh

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select .

Click .

Click

In the tree, select .

Click

Thermal Actuator

In the window, right-click and choose .

In the dialog box, type Thermal Actuator in the text field.

Click .

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
htc_s	0.04[W/(m*K)]/2[um]	20000 W/(m²·K)	Heat transfer coefficient
htc_us	0.04[W/(m*K)]/100[um]	400 W/(m²·K)	Heat transfer coefficient, upper surface
DV	5[V]	5 V	Applied voltage

Geometry 1

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click .

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

Click

Click the

button in the toolbar.

Definitions

Substrate Contact

In the toolbar, click

Right-click and choose .

In the dialog box, type Substrate Contact in the text field.

Click .

In the window for , locate the section.

From the list, choose .

Select Boundaries 10, 30, 50, 70, 76, and 82 only.

Materials

Material 1 (mat1)

In the window, under right-click and choose .

By default, the first material you define applies to all domains.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	5e4	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	4.5	1	Basic
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	40	W/(m·K)	Basic
Density	rho	2.3e3	kg/m³	Basic
Heat capacity at constant pressure	Cp	600	J/(kg·K)	Basic

Electric Currents (ec)

Ground 1

In the window, under right-click and choose .

Select Boundary 10 only.

Electric Potential 1

In the toolbar, click

and choose .

Select Boundary 30 only.

In the window for , locate the section.

In the V0 text field, type DV.

Heat Transfer in Solids (ht)

In the window, under click .

Heat Flux 1

In the toolbar, click

and choose .

This boundary condition applies to all boundaries except the top-surface boundary and those in contact with the substrate. A condition on the substrate_contact boundaries will override this condition so you do not explicitly need to exclude those boundaries. In contrast, because the boundary condition is additive, you must explicitly exclude the top-surface boundary from the selection. Implement this selection as follows: