Thermoelectric Leg

A thermocouple is made of two different conductors (legs) in contact with each other at one point (junction). When a temperature difference is established between the two legs, then a voltage is established across the junction. Therefore a thermocouple properly calibrated is a temperature sensor and can convert temperature gradients into electric currents. In this validation example, we verify the response of one leg when a current is passed through the device. A cooling effect, known as the Peltier effect, is expected.

Model Definition

The component is 1-by-1-by-6 mm, as shown in Figure 1. The core of the device, the thermoelectric part, is made of bismuth telluride (Bi2Te3). It is capped by two thin copper electrodes, 0.1 mm thick.

Figure 1: Thermoelectric leg geometry.

The material properties are available in COMSOL Multiphysics Material Library. However, since the properties for bismuth telluride slightly differ from these from the original benchmark, values from Ref. 1 are used in this application.

Table 1: Material properties for Bismuth Telluride.


Property	Value
Thermal conductivity	1.6 W/(m·K)
Density	7740 kg/m³
Heat capacity at constant pressure	154.4 J/(kg·K)
Electrical conductivity	1.1e5 S/m
Relative permittivity	1
Seebeck coefficient	2e-4 V/K

In addition Seebeck coefficient for copper, 6.5·10-6 V/K, is also taken from Ref. 1.

The bottom electrode surface is held at 0°C while the top electrode and the lateral surfaces are thermally insulated.

The bottom electrode is electrically grounded at 0 V. The total inward electric current through the top electrode is 0.7 A. The lateral surfaces are electrically insulated.

Results and Discussion

The current circulating in the thermoelectric device is responsible for the cooling effect shown in Figure 2. The temperature field is in complete agreement with the results from Ref. 1.

Figure 2: Temperature field on the thermoelectric leg surface.

Figure 3 shows the isothermal surfaces and the heat flux which is in the same direction as the electric current (from the top to the bottom).

Figure 3: Isothermal surfaces and heat flux in the thermoelectric leg.

The top level electrode reaches an electric potential of around 49.1 mV due to the inward current density set on this boundary. This corresponds to the value presented in Ref. 1.

Figure 4: Electric potential in the thermoelectric leg.

Reference

1. M. Jaegle, Multiphysics Simulation of Thermoelectric Systems, “Modeling of Peltier-Cooling and Thermoelectric Generation,” Proc. COMSOL Conf. 2008 Hanover, 2008.

Heat_Transfer_Module/Verification_Examples/thermoelectric_leg

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

Geometry 1

In the window, under click .

In the window for , locate the section.

From the list, choose .

Block 1 (blk1)

In the toolbar, click

In the window for , locate the section.

In the text field, type 6.

Click to expand the section. In the table, enter the following settings:


Layer name	Thickness (mm)
Layer 1	0.1

Find the subsection. Select the check box.

Click

Click the

button in the toolbar.

Now define the parameters that will be used for the model. The inward current density, J0, corresponds to a total current of 0.7 A through a 1x1 mm square.

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
T0	0[degC]	273.15 K	Temperature reference
J0	0.7[A]/(1[mm])^2	7E5 A/m²	Inward current density

Materials

Bismuth Telluride - Bi2Te3

In the toolbar, click

In the window for , type Bismuth Telluride - Bi2Te3 in the text field.

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


Property	Variable	Value	Unit	Property group
Thermal conductivity	k_iso ; kii = k_iso, kij = 0	1.6[W/(m*K)]	W/(m·K)	Basic
Density	rho	7740[kg/m^3]	kg/m³	Basic
Heat capacity at constant pressure	Cp	154.4[J/(kg*K)]	J/(kg·K)	Basic
Electrical conductivity	sigma_iso ; sigmaii = sigma_iso, sigmaij = 0	1.1e5[S/m]	S/m	Basic
Relative permittivity	epsilonr_iso ; epsilonrii = epsilonr_iso, epsilonrij = 0	1	1	Basic
Seebeck coefficient	S_iso ; Sii = S_iso, Sij = 0	2e-4[V/K]	V/K	Basic