Thermoelectric devices are solid state devices based on the principle of the Seebeck-Peltier effect that convert thermal energy to electrical energy and vice versa. A thermoelectric device creates a voltage when temperature difference is applied on each side. In the other way, temperature difference is created when a voltage is applied to it. This duality allows thermoelectric devices to act both as a power generator, given a heat source, and a heater or refrigerator when supplied with electrical power.
Thermoelectric modules are used across a variety of industries for both power generation and heating / cooling applications. For instance, they are used as small scale, precision temperature control devices for electronics. Thermoelectric devices are also playing a significant role in the renewable energy movement, used in such applications as solar thermal generators. Generally, they are used wherever there is a small temperature gradient that can be exploited for power generation.
ANSYS is an engineering simulation software to solve the most challenging product engineering problems. In this project, the finite element method (FEM) in the ANSYS software is used to simulate the model of thermoelectric device with the aim of getting the better efficiency.
2 Motivation
The potential of using thermoelectric devices to generate power usefully has increased significantly in recent years. Advancements in new higher temperature materials with figure of merit (ZT) substantially greater than unity are under development at places such as Michigan State University and Lincoln Laboratory at Massachusetts Institute of Technology (MIT). [2]
The finite element method (FEM) has become an essential solution technique in many areas of engineering and physics. The FEM versatility lies in its ability to model arbitrary shaped structures, work with complex materials, and apply various types of loading and boundary conditions. The ANSYS finite element program has a large library of elements that support structural, thermal, fluid, acoustic, and electromagnetic analyses, as well as coupled-field elements that simulate the interaction between the above fields. Examples of ANSYS coupled-physics capabilities include thermal-structural, fluid-structure, electromagnetic-thermal, thermal-electric, structural-thermal-electric, piezoelectric, piezoresistive, magneto-structural, and electrostatic-structural analyses [3]. In this project, only the thermal-electric capability has been used to seek the optimization of a thermoelectric device.
3 Literature Review
3.1 Basic Model
A thermoelectric device usually consists of two junctions which is n-type and p-type semiconductor incorporating different metals or alloys as shown in Figure 1. In a n-type material, hot electrons diffuse to the cold side and cold electrons diffuse to the hot side and eventually resulting in a constant temperature structure. If something changes the imbalance of hot/cold electron diffusion, a net charge can result on one side relative to the other. For example, if hot electrons are scattered more than cold electrons, the flux of electrons from hot to cold is less than from cold to hot creating a charge imbalance and thus a "thermovoltage". The same effect in a p-type material produces the opposite sign of thermovoltage. If the p-type and n-type semiconductor are placed in electrical series, the voltage is added.
Figure 1: Bulk semiconductor thermocouple in generating mode [4]
3.2 Thermoelectric effect
The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice-versa. This effect can be used to measure temperature, change the temperature of objects, or generate electricity. Since the direction of heating and cooling is determined by the polarity of the applied voltage, thermoelectric devices can be efficient temperature controllers. There are 3 established thermoelectric effects known as Seebeck, Peltier and Thomson effects.
(i) Seebeck Effect
The Seebeck effect is a phenomenon which produces a voltage difference between the two substances where a temperature difference is applied between two dissimilar electrical conductors or semiconductors. When the heat is applied to one of the junction, heated electrons flow toward the cooler electrons. Direct current flows through that circuit if the pair is connected through an electrical circuit.
Figure 2: Power generation when heat is applied [5]
The Seebeck effect is caused by charge-carrier diffusion and phonon drag.
(a) Charge-carrier diffusion
Charge carriers in the materials will diffuse when a temperature difference is applied to the one end of a conductor. Since there is a lower density of hot carriers at the cold end of the conductor, and vice versa, the hot carriers diffuse from the hot end to the cold end. If the thermodynamic equilibrium of the conductor is achieved, the heat will be distributed evenly throughout the conductor. The movement of heat from one end to the other is a heat current and an electric current as charge carriers are moving.
(b) Phonon drag
Phonon drag is an increase in the effective mass of conduction electrons or valence holes due to interactions with the crystal lattice in which the electron moves. As an electron moves past atoms in the lattice its charge distorts or polarizes the nearby lattice. This effect leads to a decrease in the electron (or hole) mobility, which results in increased the magnitude of the thermopower. Hovewer, the magnitude of this effect is applicable only at low temperature which is below 200K.
(ii) Peltier Effect
The Peltier effect occurs when a current is passed through a junction of two dissimilar electrical conductors or semiconductors and causes one junction to release heat, and the other to absorb heat as shown in Figure 3.
.
Figure 3: Peltier Effect [5]
When a current is applied across a junction, holes and electrons are created and flow to the other side where they recombine. The process of creating the holes and electrons removes energy from the junction, thus heat is absorbed. While the process of recombining the holes and electrons releases energy, hence heat is released.
(iii) Thomson Effect
The Thomson effect occurs when a temperature difference in a material will cause the mobile electrons to have different velocities. There will thus be a net flow of electrons from the higher temperature region to the lower temperature. This will result in the build up of a space charge and hence of an electromotive force (EMF), whose sign will depend on the charge of the carriers.
3.3 Thermoelectric Material
Thermoelectric materials are special types of semiconductors that as a function of heat pump when it is coupled. It shows the thermoelectric effect in a strong or convenient form. Three parameters are considered in the classification of thermoelectric materials: Seebeck coefficient, electrical conductivity and thermal conductivity.
(i) Seebeck Coefficient
Seebeck coefficient is also known as thermopower or thermoelectric power. It is a measure of the magnitude of an induced thermoelectric voltage in response to a temperature difference across that material. The Seebeck coefficient has units of volts per kelvin (V/K). The expression of the Seebeck coefficient is
S = where is the thermovoltage and is the temperature difference
(ii) Electrical conductivity
Electrical conductivity is the reciprocal of electrical resistivity and measures a material's ability to conduct an electric current. Its SI unit is siemens per metre (S⋅m−1). Electrical conductivity is given as the product of the concentration and the mobility of charge carriers. It is high with metals, very low with insulators, with an intermediate position taken by semiconductors.
Metals are typically good electrical conductors, but the higher the temperature, the lower the conductivity, given by the equation for electrical conductivity
σmetal = ne2τ/m
where n is carrier density, e is electron charge, τ is electron lifetime and m is mass. As temperature increases, τ decreases, thereby decreasing σmetal. By contrast, electrical conductivity in semiconductors correlates positively with temperature
σsemiconductor = neμ
where n is carrier density, e is electron charge and μ is carrier mobility. Carrier mobility decreases with increasing temperature, but carrier density increases faster with increasing temperature, resulting in increasing σsemiconductor.
(iii) Thermal conductivity
Thermal conductivity is the property of a material's ability to conduct heat. The materials of high thermal conductivity have the higher rate of heat transfer than across materials of low thermal conductivity. The SI unit of thermal conductivity is measured in watts per meter kelvin (W.m-1.k-1).
For metals and non-metals, the effect of temperature on thermal conductivity is different. In metals, conductivity is primarily due to free electrons. In pure metals the electrical resistivity often increases proportional to temperature and thus thermal conductivity stays approximately constant. In alloys the change in electrical conductivity is usually smaller and thus thermal conductivity increases with temperature. Meanwhile, the thermal conductivity in non-metals is mainly due to lattice vibrations (phonons). The phonon mean free path is not reduced significantly at higher temperatures hence the thermal conductivity of non-metals is almost constant at temperature which is not too low.
3.4 Figure of merit
Figure of merit, Z is a measure of the effectiveness of a material to function in a thermoelectric couple for heating or cooling applications. A knowledge of the temperature dependence of Z is important in optimizing couples for specific applications. Z for thermoelectric devices is defined as
Z =
where σ is the electrical conductivity, λ is the thermal conductivity, and S is the Seebeck coefficient. The dimensionless figure of merit ZT is formed by multiplying Z with the absolute temperature, T. A larger ZT indicates a higher thermodynamic efficiency. [6]
4 Objectives
The objective of the project is to:
create the basic thermoelectric model
simulate the thermal and electrical analysis to investigate the thermoelectric effect
optimize the efficiency of the thermoelectric model by changing the dimension, size or shape.
5 Project Methodology
In this project, the ANSYS software has been used to simulate the environment of the thermoelectric. ANSYS workbench provides a finite element modeling and simulation environment for thermal-electric. In the initial condition for the performance of thermoelectric devices it has been assumed that the Seebeck coefficient S, the electrical resistivity σ and the thermal conductivity λ of thermoelectric elements are dependent of temperature.
In ANSYS, the Seebeck coefficient of the thermoelectric device is not able to obtain from the thermal-electric analysis. In order to obtain the Seebeck coefficient, the equation below is used:
S =
where is the difference of maximum voltage and the minimum voltage at the certain temperature and is the temperature difference of the hot end junction and cold end junction.
With the information of Seebeck coefficient, electrical conductivity and the thermal conductivity, the figure of merit which represents the efficiency of the thermoelectric device is computed as the following equation:
Z =
6 Work Done So far
6.1 Specify the materials and properties
The metal using in the project is copper where the material properties is shown as below:
Seebeck coefficient, S (V/K)
6.5 x 10-6
Electrical conductivity, σ (S/m)
5.9 x 108
Thermal conductivity, λ (W/m/k)
350
Table 1: Numerical properties of copper [7]
The thermoelectric material of p-type doped in the thermoelectric model using is the (Bi0.5Sb0.5)2Te3 which is single crystals doped with Indium atoms. Its properties are temperature dependent as shown below:
Temperature, T (K)
S, (10-6 V/K)
σ (103 S/m)
λ (W/m/k)
100
75
185
2.5
150
125
142
2
200
170
100
1.55
250
200
72
1.35
300
218
60
1.28
350
225
55
1.35
400
218
70
1.75
Table 2: Temperature dependent material properties of (Bi0.5Sb0.5)2Te3 [7]
For the n-type doped material in the thermoelectric model using is same as p-type. Its electrical conductivity and thermal conductivity are same value as p-type but Seebeck coefficient values are in negative of the p-type values.
6.2 Set up the model
The model using for simulation is the basic two leg junction of thermoelectric device as shown in Figure 4. The unit of the length for the model is in millimeter (mm). The length and height of the model is shown in Figure 4 and the depth of the model is 10mm.
48mm
12mm
36mm
10mm
12mm
36mm
5mm
5mm
Figure 4: Length and height of the model
The material of the top, p-base and n-base are using copper. The material of the p-leg is the (Bi0.5Sb0.5)2Te3 in p-type whereas the material of the n-leg is the (Bi0.5Sb0.5)2Te3 in n-type as shown in Figure 5.
p-leg
n-leg
n-base
p-base
top
Figure 5: Assignment of the material in each junction
For the analysis setting, the end time of simulation is set as 7s and number of steps is 7. For the hot junction, temperature of 750K is applied to the top surface of the top body. Meanwhile, temperature of 50K is applied to the bottom surface of the n-base and p-base as the cold junction. For the low potential and high potential area, voltage of 0V is applied to the outer surface of the n-leg and other-side outer surface of the p-leg respectively. For the convection pane, the magnitude of 3.65 x10-9 W/(m2K) and temperature of 50K are applied to all the surfaces except the surfaces which have been assigned in the hot & cold junction and low and high potential.
Figure 6: Analysis setting of the model
6.3 Simulation Result
Temperature and voltage analysis are selected and tested for the thermoelectric model. Table 3 shows the simulation result of the temperature analysis and voltage analysis.
Times (s)
Tmin (K)
Tmax (K)
Vmin ( 10-3 V)
Vmax ( 10-3 V)
1
50
150
-4.37
4.39
2
50
250
-11.80
11.84
3
50
350
-20.03
20.11
4
50
450
-28.00
28.11
5
50
550
-36.07
36.21
6
50
650
-44.28
44.45
7
50
750
-52.05
52.24
Table 3: Tabular data of temperature and voltage analysis
From the tabular data above, the Seebeck coefficient can be calculated using the equation S =
The calculated results are shown in Table 4.
= Tmax - Tmin (K)
= Vmax - Vmin (10-3 V)
Seebeck Coefficient, S (10-5 V/K)
100
8.76
8.76
200
23.64
11.82
300
40.14
13.38
400
56.11
14.03
500
72.28
14.46
600
89.03
14.84
700
104.29
14.90
Table 4: Calculated values of , and S
By referring the data of the Seebeck coefficient calculated from Table 4, electrical conductivity and thermal conductivity from Martin Jaegle [7], the figure of merit, Z can be computed as shown in Figure 5.
Temperature, T (K)
S, (10-6 V/K) (from [7])
σ (103 S/m) (from [7])
λ (W/m/k) (from [7])
Figure of merit, Z (theoretical)
Figure of merit, Z (simulated)
100
75
185
2.5
4.163 x 10-4
5.677 x 10-4
150
125
142
2
1.109 x 10-3
9.921 x 10-4
200
170
100
1.55
1.865 x 10-3
1.155 x 10-3
250
200
72
1.35
2.133 x 10-3
1.050 x 10-3
300
218
60
1.28
2.228 x 10-3
9.795 x 10-4
350
225
55
1.35
2.063 x 10-3
8.908 x 10-4
400
218
70
1.75
1.901 x 10-3
8.878 x 10-4
Table 5: Figure of merit, Z (theoretical and simulated)
Figure 7: Graph of figure of merit, Z (simulated and theoretical) versus temperature
7 Future Work
At the current stage, the graph of the figure of merit from the simulated exists small difference compared with the theoretical. However, the behaviour of the simulated graph is quite similar with the theoretical. The next improvement could be generating a more similar graph by changing the dimension of the model.
In addition, the efficiency of the thermoelectric model should be optimized. It is possible to implement by changing the shape of the model suggested by Bell [8]. The advanced modeling and optimization techniques will help optimize the design concepts to really progress towards maximizing the performance of a TPG system.
