1. Background about energy harvesting

Energy harvesting represents the energy derived from ambient sources that is extracted and directly converted into electrical energy. This way to provide energy is further used when another energy source is not available (off-grid use) to supply small- and medium-sized electronic devices, as well as electrical systems, with power from nW to hundreds of mW [1, 2]. Generally, energy harvesting refers to an environment with regular and well-assessed ambient energy sources. Energy harvesting is applied when there is a match between the available energy and the energy required.

Another term, energy scavenging, refers to an environment with strong nonuniform and unknown ambient energy sources [3]. Some examples of differences between the two terms are presented in Table 1.

The ambient energy sources used for energy harvesting are temperature gradient, electromagnetic radiation, light, motion and chemical energy (Figure 1).


Table 1.

The difference between the terms "scavenging" and "harvesting" [3].

harvesting with a multitude of advantages: maintenance-free, because of the use of highly reliable and compact solid-state device; silent and quiet; highly efficient in environmental terms because the heat is harvested from waste heat sources and converted into electricity; operation with high maximum temperatures (up to 250°C); useful scalable applications configured to harvest wide amounts of energy when necessary; possibility to harvest power from both hot surface or cold surface; green energy behaviour, being eco-friendly [5]. A TEG device produces energy without

Unlike thermodynamic PV systems or conventional heat engines (Rankine, Stirling), the energy conversion efficiency of the TEG is limited to about 5–15% [6]. The temperature difference across the TEG system and the dimensionless thermoelectric figure-of-merit (ZT) have a major impact on the energy conversion efficiency [7]. It is desirable to obtain the maximum electric output power and

efficiency when a TEG system operates. In case of waste heat recovery applications [8], only electric output power is significant and the heat not recovered is lost [9]. Considering that thermal energy harvesting has a reduced efficiency (5–6%), this could represent a major barrier for its extensive utilisation. An improvement in the TEG efficiency bigger than 10% has been lately obtained due to the progress of new

The recovery of the electrical energy from waste heat using diverse sources is

The thermoelectric effects are reversible phenomena leading to direct conversion between thermal and electrical energy [9]. Direct energy conversion relies on the physical transport properties of the thermoelectric materials (thermal conductivity, electric conductivity and Seebeck coefficient) and their energy conversion efficiency in terms of the figure-of-merit. These materials are suitable to convert thermal energy into electrical energy and vice-versa. The main phenomena that occur in a thermoelectric device are the thermoelectric effects (Seebeck, Peltier,

• When the electrical energy is converted into thermal energy, the phenomenon is known as the Peltier effect, with applications in cooling and heating. The device used in such applications is called thermoelectric cooler (TEC) [11–13]. In this case, thermoelectric modules are efficient temperature controllers [14].

using fossil fuel, leading to a reduction of greenhouse gas emissions.

Thermoelectric Energy Harvesting: Basic Principles and Applications

DOI: http://dx.doi.org/10.5772/intechopen.83495

2. Basic principles of thermoelectric energy generation

thermoelectric materials [10].

Electrical energy recovered from waste heat.

2.1 Thermoelectric effects

Thomson), and the Joule effect.

3

depicted in Figure 2.

Figure 2.

Figure 1. Energy harvesting sources.

An energy harvester consists of:


The most used energy harvesters are: thermal harvester based on the thermoelectric effect; light harvester based on the photoelectric effect; electromagnetic harvester based on induction; chemical harvester based on different reactions on the electrodes surfaces; piezoelectric harvester based on mechanical vibrations or human motion (which converts pressure or stress into electricity); radio-frequency (RF) harvester (that captures the ambient radio-frequency radiation).

Thermoelectric energy harvesting mainly depends on the operation of the thermoelectric generator (TEG). A TEG converts heat directly into electrical energy according to the Seebeck effect. In this case, the motion of charge carriers (electrons and holes) leads to a temperature difference across this device. Its operation is described in Section 2.3. Furthermore, the thermoelectric energy harvesting system can generate power from hundreds of μW to mW for different sensors and transmitters.

In the last decades, the specialists' attention has been focused on the development of green energy technology to decrease fossil fuel utilisation and greenhouse gas emissions. A thermoelectric harvester produces green energy for energy

Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

#### Figure 2.

An energy harvester consists of:

the harvested energy);

• process control electronics [4].

energy;

Energy harvesting sources.

Table 1.

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Figure 1.

transmitters.

2

• an energy source (which is natural or artificial);

The difference between the terms "scavenging" and "harvesting" [3].

• one or more transducers that convert environmental energy into electrical

• an energy storage device (e.g., a rechargeable battery or a capacitor that stores

Scavenging Harvesting

Thermal Forest fires Furnace covers Photonic Interior lighting Diurnal solar cycles Mechanical Foot traffic Motors, ductwork

The most used energy harvesters are: thermal harvester based on the thermoelectric effect; light harvester based on the photoelectric effect; electromagnetic harvester based on induction; chemical harvester based on different reactions on the electrodes surfaces; piezoelectric harvester based on mechanical vibrations or human motion (which converts pressure or stress into electricity); radio-frequency

Thermoelectric energy harvesting mainly depends on the operation of the thermoelectric generator (TEG). A TEG converts heat directly into electrical energy according to the Seebeck effect. In this case, the motion of charge carriers (electrons and holes) leads to a temperature difference across this device. Its operation is described in Section 2.3. Furthermore, the thermoelectric energy harvesting system

In the last decades, the specialists' attention has been focused on the development of green energy technology to decrease fossil fuel utilisation and greenhouse gas emissions. A thermoelectric harvester produces green energy for energy

(RF) harvester (that captures the ambient radio-frequency radiation).

can generate power from hundreds of μW to mW for different sensors and

Electrical energy recovered from waste heat.

harvesting with a multitude of advantages: maintenance-free, because of the use of highly reliable and compact solid-state device; silent and quiet; highly efficient in environmental terms because the heat is harvested from waste heat sources and converted into electricity; operation with high maximum temperatures (up to 250°C); useful scalable applications configured to harvest wide amounts of energy when necessary; possibility to harvest power from both hot surface or cold surface; green energy behaviour, being eco-friendly [5]. A TEG device produces energy without using fossil fuel, leading to a reduction of greenhouse gas emissions.

Unlike thermodynamic PV systems or conventional heat engines (Rankine, Stirling), the energy conversion efficiency of the TEG is limited to about 5–15% [6]. The temperature difference across the TEG system and the dimensionless thermoelectric figure-of-merit (ZT) have a major impact on the energy conversion efficiency [7]. It is desirable to obtain the maximum electric output power and efficiency when a TEG system operates. In case of waste heat recovery applications [8], only electric output power is significant and the heat not recovered is lost [9]. Considering that thermal energy harvesting has a reduced efficiency (5–6%), this could represent a major barrier for its extensive utilisation. An improvement in the TEG efficiency bigger than 10% has been lately obtained due to the progress of new thermoelectric materials [10].

The recovery of the electrical energy from waste heat using diverse sources is depicted in Figure 2.

#### 2. Basic principles of thermoelectric energy generation

#### 2.1 Thermoelectric effects

The thermoelectric effects are reversible phenomena leading to direct conversion between thermal and electrical energy [9]. Direct energy conversion relies on the physical transport properties of the thermoelectric materials (thermal conductivity, electric conductivity and Seebeck coefficient) and their energy conversion efficiency in terms of the figure-of-merit. These materials are suitable to convert thermal energy into electrical energy and vice-versa. The main phenomena that occur in a thermoelectric device are the thermoelectric effects (Seebeck, Peltier, Thomson), and the Joule effect.

• When the electrical energy is converted into thermal energy, the phenomenon is known as the Peltier effect, with applications in cooling and heating. The device used in such applications is called thermoelectric cooler (TEC) [11–13]. In this case, thermoelectric modules are efficient temperature controllers [14].

<sup>α</sup>AB <sup>¼</sup> <sup>E</sup>

<sup>Q</sup>\_ <sup>¼</sup> <sup>ρ</sup> � <sup>J</sup>

Thermoelectric Energy Harvesting: Basic Principles and Applications

DOI: http://dx.doi.org/10.5772/intechopen.83495

heating (the second term) changes its sign, following J.

the heat is neither generated nor absorbed.

2.2 Thermoelectric effects and thermodynamic processes

These are called Thomson relations [14]:

where <sup>ρ</sup> <sup>¼</sup> <sup>1</sup>

versible processes.

5

], and <sup>∇</sup><sup>T</sup> is <sup>∇</sup><sup>T</sup> <sup>¼</sup> <sup>d</sup><sup>T</sup>

[V�K�<sup>1</sup>

2 |ffl{zffl} Joule heating

in S � <sup>m</sup>�<sup>1</sup> ½ �, <sup>J</sup> is the current density in A � <sup>m</sup>�<sup>2</sup> ½ �, <sup>μ</sup>AB is the Thomson coefficient in

Joule heating occurs when an electric current that flows through a conductor produces heat. Joule heating does not change its sign in Eq. (3), while Thomson

• positive when the current flows from the low-temperature side to the hightemperature side of the conductor and the heat is absorbed through it;

• negative when the current flows inversely and the heat is rejected from it;

μAB ¼ T �

• null when the current flows from the high to the low side and vice-versa and

The following relationships hold between the Seebeck coefficient and the Peltier coefficient, as well as between the Seebeck coefficient and the Thomson coefficient.

Thermoelectric effects that take place in TEG devices are subject to the thermodynamic laws. According to thermodynamics, the heat transfer across a finite temperature difference is an irreversible process and the entropy change of such process is positive. The heat conduction and Joule heating are considered as irre-

The heat is irreversibly produced according to the Joule effect when an electrical current flows through a conductor or semiconductor. The Joule effect takes place at the TEG interconnects due to their electrical contact resistance or in a thermocouple. Other irreversibilities are found in the heat transfer between the TEG and the local environment [9]. If the irreversible processes are removed, the entropy becomes null. In this case, the ideal conditions given by the Carnot efficiency or COP (coefficient of performance) are achieved [19]. A deep overview of steadystate irreversible processes as heat conduction in semiconductor materials, metals and other solid-state devices is presented in [19, 20]. The Seebeck, Thomson and Peltier effects are reversible thermodynamic processes [21]. When the current flows through a conductor, both the Joule effect and the Thomson effect take place

dαAB

Therefore, the sign convention of the Thomson coefficient is considered as [17]:

The Thomson effect affirms that in any conductive material in which the electrical current flows in the presence of a temperature difference between two ends, heat is also released or absorbed. The Thomson heat released or absorbed is given as:

> � μAB � J � ∇T |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} Thomson heating

<sup>σ</sup> is the electrical resistivity in ½ � Ω � m , σ is the electrical conductivity

<sup>d</sup><sup>x</sup> is the temperature gradient along the conductor in K½ �:

πAB ¼ αAB � T (4)

<sup>d</sup><sup>T</sup> (5)

<sup>∇</sup><sup>T</sup> (2)

(3)

Figure 3. Schematic of the Seebeck effect in an open circuit.

• When the thermal energy is converted into electrical energy, the phenomenon is known as the Seebeck effect, with applications for power generation. The device used in such applications is called thermoelectric generator (TEG) [15, 16].

The Seebeck effect occurs when a temperature difference across a conductor provides a voltage at the conductor ends. Two distinct conductors A and B are linked together to compose the junctions of a circuit (Figure 3). These conductors are connected electrically in series and thermally in parallel. One junction has the hot temperature T<sup>h</sup> and another one has the cold temperature Tc, with T<sup>h</sup> bigger than Tc. The Seebeck effect appears due to the thermal diffusion which provokes the motion of the charge carriers (electrons or holes) across (or against) temperature difference in the conductors.

The Seebeck voltage at the circuit junctions can be written as:

$$V = \left(\underbrace{a\_{\text{A}} - a\_{\text{B}}}\_{a\_{\text{AB}}}\right) \cdot \left(\underbrace{T\_{\text{h}} - T\_{\text{c}}}\_{\Delta T}\right) \tag{1}$$

where α<sup>A</sup> and α<sup>B</sup> are the Seebeck coefficients for the conductors A and B, in V�K�<sup>1</sup> .

The Seebeck coefficient of a thermoelectric material or thermopower αAB is the connection parameter between the input temperature difference and the output voltage difference. The Seebeck coefficient of a thermoelectric material depends on temperature, as well as on other two physical transport properties (thermal conductivity, electric conductivity). It determines the thermoelectric material performance. Its magnitude ranges from <sup>μ</sup>V�K�<sup>1</sup> to mV�K�<sup>1</sup> and depends on the junction temperature, and its sign is influenced by the semiconductor material [17]. Furthermore, the sign of the Seebeck coefficient depends on the type of carriers (electrons e� and holes h<sup>+</sup> ) conducting the electric current. If the electric current is conducted by e�, the sign of the Seebeck coefficient is negative. If the electric current is conducted by h<sup>+</sup> , the sign of the Seebeck coefficient is positive [18].

The Seebeck coefficient αAB, the temperature gradient ∇T, and the electric field E are written under the following relationship:

Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

$$a\_{\rm AB} = \frac{E}{\nabla T} \tag{2}$$

The Thomson effect affirms that in any conductive material in which the electrical current flows in the presence of a temperature difference between two ends, heat is also released or absorbed. The Thomson heat released or absorbed is given as:

$$\dot{Q} = \underbrace{\rho \cdot J^2}\_{\text{Joule heating}} - \underbrace{\mu\_{\text{AB}} \cdot J \cdot \nabla T}\_{\text{Thomas heating}} \tag{3}$$

where <sup>ρ</sup> <sup>¼</sup> <sup>1</sup> <sup>σ</sup> is the electrical resistivity in ½ � Ω � m , σ is the electrical conductivity in S � <sup>m</sup>�<sup>1</sup> ½ �, <sup>J</sup> is the current density in A � <sup>m</sup>�<sup>2</sup> ½ �, <sup>μ</sup>AB is the Thomson coefficient in [V�K�<sup>1</sup> ], and <sup>∇</sup><sup>T</sup> is <sup>∇</sup><sup>T</sup> <sup>¼</sup> <sup>d</sup><sup>T</sup> <sup>d</sup><sup>x</sup> is the temperature gradient along the conductor in K½ �:

Joule heating occurs when an electric current that flows through a conductor produces heat. Joule heating does not change its sign in Eq. (3), while Thomson heating (the second term) changes its sign, following J.

Therefore, the sign convention of the Thomson coefficient is considered as [17]:


The following relationships hold between the Seebeck coefficient and the Peltier coefficient, as well as between the Seebeck coefficient and the Thomson coefficient. These are called Thomson relations [14]:

$$
\pi\_{\rm AB} = a\_{\rm AB} \cdot T \tag{4}
$$

$$
\mu\_{\rm AB} = T \cdot \frac{\rm da\_{\rm AB}}{\rm dT} \tag{5}
$$

#### 2.2 Thermoelectric effects and thermodynamic processes

Thermoelectric effects that take place in TEG devices are subject to the thermodynamic laws. According to thermodynamics, the heat transfer across a finite temperature difference is an irreversible process and the entropy change of such process is positive. The heat conduction and Joule heating are considered as irreversible processes.

The heat is irreversibly produced according to the Joule effect when an electrical current flows through a conductor or semiconductor. The Joule effect takes place at the TEG interconnects due to their electrical contact resistance or in a thermocouple. Other irreversibilities are found in the heat transfer between the TEG and the local environment [9]. If the irreversible processes are removed, the entropy becomes null. In this case, the ideal conditions given by the Carnot efficiency or COP (coefficient of performance) are achieved [19]. A deep overview of steadystate irreversible processes as heat conduction in semiconductor materials, metals and other solid-state devices is presented in [19, 20]. The Seebeck, Thomson and Peltier effects are reversible thermodynamic processes [21]. When the current flows through a conductor, both the Joule effect and the Thomson effect take place

• When the thermal energy is converted into electrical energy, the phenomenon is known as the Seebeck effect, with applications for power generation. The device used in such applications is called thermoelectric generator (TEG)

The Seebeck effect occurs when a temperature difference across a conductor provides a voltage at the conductor ends. Two distinct conductors A and B are linked together to compose the junctions of a circuit (Figure 3). These conductors are connected electrically in series and thermally in parallel. One junction has the hot temperature T<sup>h</sup> and another one has the cold temperature Tc, with T<sup>h</sup> bigger than Tc. The Seebeck effect appears due to the thermal diffusion which provokes the motion of the charge carriers (electrons or holes) across (or against) temperature

1

The Seebeck coefficient of a thermoelectric material or thermopower αAB is the connection parameter between the input temperature difference and the output voltage difference. The Seebeck coefficient of a thermoelectric material depends on temperature, as well as on other two physical transport properties (thermal conductivity, electric conductivity). It determines the thermoelectric material performance. Its magnitude ranges from <sup>μ</sup>V�K�<sup>1</sup> to mV�K�<sup>1</sup> and depends on the junction temperature, and its sign is influenced by the semiconductor material [17]. Furthermore, the sign of the Seebeck coefficient depends on the type of carriers (elec-

where α<sup>A</sup> and α<sup>B</sup> are the Seebeck coefficients for the conductors A and B,

conducted by e�, the sign of the Seebeck coefficient is negative. If the electric

The Seebeck coefficient αAB, the temperature gradient ∇T, and the electric field

<sup>A</sup> � <sup>T</sup><sup>h</sup> � <sup>T</sup><sup>c</sup> |fflfflfflffl{zfflfflfflffl} ΔT

) conducting the electric current. If the electric current is

, the sign of the Seebeck coefficient is positive [18].

1

A (1)

0 @

The Seebeck voltage at the circuit junctions can be written as:

V ¼ α<sup>A</sup> � α<sup>B</sup> |fflfflfflffl{zfflfflfflffl} <sup>α</sup>AB

0 @

[15, 16].

Green Energy Advances

Figure 3.

in V�K�<sup>1</sup> .

4

trons e� and holes h<sup>+</sup>

current is conducted by h<sup>+</sup>

E are written under the following relationship:

difference in the conductors.

Schematic of the Seebeck effect in an open circuit.

<sup>K</sup> <sup>¼</sup> <sup>n</sup> � <sup>k</sup><sup>P</sup> � <sup>S</sup><sup>P</sup> � ð Þ <sup>L</sup><sup>P</sup> �<sup>1</sup> <sup>þ</sup> <sup>k</sup><sup>N</sup> � <sup>S</sup><sup>N</sup> � ð Þ <sup>L</sup><sup>N</sup> �<sup>1</sup> h i (7)

<sup>L</sup> is the electrical resistivity of each leg, S is the cross-sectional area

<sup>R</sup> <sup>¼</sup> <sup>n</sup> � <sup>2</sup><sup>ρ</sup> � <sup>L</sup> � ð Þ<sup>S</sup> �<sup>1</sup> (8)

<sup>K</sup> <sup>¼</sup> <sup>n</sup> � <sup>2</sup> <sup>k</sup> � <sup>S</sup> � ð Þ <sup>L</sup> �<sup>1</sup> (9)

<sup>R</sup> <sup>¼</sup> <sup>n</sup> � <sup>2</sup><sup>ρ</sup> � <sup>L</sup> � ð Þ<sup>S</sup> �<sup>1</sup> <sup>þ</sup> <sup>R</sup><sup>a</sup> (10)

<sup>2</sup> is the Seebeck coefficient of the thermoelectric couple.

<sup>L</sup> in

(12)

of the each leg in m<sup>2</sup> ½ �, <sup>L</sup> is the leg length in m½ �, <sup>k</sup> is the thermal conductivity of each leg in W � ð Þ <sup>m</sup> � <sup>K</sup> �<sup>1</sup> h i, and the thermal conductance of each leg is <sup>K</sup> <sup>¼</sup> <sup>k</sup> <sup>S</sup>

are the same as form (L ¼ L<sup>P</sup> ¼ L<sup>N</sup> and S ¼ S<sup>P</sup> ¼ SN) and material properties (ρ ¼ ρ<sup>P</sup> ¼ ρN, and k ¼ k<sup>P</sup> ¼ kN). The equivalent internal resistance becomes:

and the equivalent thermal conductance is:

The voltage at the TEG terminals is:

The input electrical current in the circuit is:

linear, therefore αPN depends on temperature.

Schematic of a TEG device with n thermoelectric couples.

<sup>I</sup> <sup>¼</sup> VSeebeck n � R þ R<sup>L</sup>

where αPN ¼ ð Þ α<sup>P</sup> � α<sup>N</sup>

Figure 5.

7

resistance of the thermoelectric couples in series becomes:

Thermoelectric Energy Harvesting: Basic Principles and Applications

DOI: http://dx.doi.org/10.5772/intechopen.83495

These relations are further simplified considering that N-type and P-type legs

If the electrical contact resistance R<sup>a</sup> is not negligible, the equivalent internal

VTEG ¼ V<sup>2</sup> � V<sup>1</sup> ¼ n � ðI � R � αPN � ΔTÞ ¼ n � I � R � VSeebeck (11)

where the load resistance R<sup>L</sup> is connected to the output of the circuit where the

electric output power generated by TEG is consumed; the Seebeck voltage is VSeebeck = V<sup>P</sup> � V<sup>N</sup> = αPN � ΔT. The relationship between VSeebeck and ΔT is non-

<sup>¼</sup> <sup>n</sup> � <sup>α</sup>PN � <sup>Δ</sup><sup>T</sup> n � R þ R<sup>L</sup>

where <sup>ρ</sup> <sup>¼</sup> <sup>R</sup> � <sup>S</sup>

<sup>W</sup> � <sup>K</sup>�<sup>1</sup> � �

Figure 4. Schematic of a TEG device with a single thermoelectric couple and two legs.

simultaneously, and the magnitude of the Thomson effect is about two times less than the magnitude of the Joule effect [17].

#### 2.3 TEG structure and model

The TEG device is composed of one or more thermoelectric couples. The simplest TEG consists of a thermocouple, comprising a pair of P-type and N-type thermoelements or legs connected electrically in series and thermally in parallel. The differentiation between N- and P-doped materials is important. The P-type leg has a positive Seebeck coefficient and an excess of holes h<sup>+</sup> . The N-type leg has a negative Seebeck coefficient and an excess of free electrons e� [22]. The two legs are linked together on one side by an electrical conductor forming a junction or interconnect, usually being a copper strip. Let us denote the voltage at the outside terminal connected to the N-type leg on the cold side of TEG as V2, while the voltage at the external terminal connected to the P-type leg on the cold side of TEG is V<sup>1</sup> (Figure 4). An electrical load having resistance R<sup>L</sup> is connected in series with the output terminals of TEG creating an electric circuit. When the electric current flows in this electrical load, an electrical voltage is generated at its terminals. The TEG device will generate DC electricity as long as there is a temperature gradient between its sides. When the temperature difference ΔT = T<sup>h</sup> � T<sup>c</sup> across the TEG device increases, more electric output power will be generated.

A number of thermoelectric couples n form a TEG system wired electrically in series and sandwiched between two ceramic plates to maximise the output voltage from the TEG (Figure 5).

In this case, the equivalent internal resistance of the thermoelectric couples in series is:

$$R = n \cdot \left[ \rho\_{\rm p} \cdot L\_{\rm P} \cdot (\rm S\_{\rm P})^{-1} + \rho\_{\rm N} \cdot L\_{\rm N} \cdot (\rm S\_{\rm N})^{-1} \right] \tag{6}$$

and the equivalent thermal conductance of the thermoelectric couples in parallel is:

Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

$$K = n \cdot \left[ k\_{\rm P} \cdot \text{S}\_{\rm P} \cdot \left( L\_{\rm P} \right)^{-1} + k\_{\rm N} \cdot \text{S}\_{\rm N} \cdot \left( L\_{\rm N} \right)^{-1} \right] \tag{7}$$

where <sup>ρ</sup> <sup>¼</sup> <sup>R</sup> � <sup>S</sup> <sup>L</sup> is the electrical resistivity of each leg, S is the cross-sectional area of the each leg in m<sup>2</sup> ½ �, <sup>L</sup> is the leg length in m½ �, <sup>k</sup> is the thermal conductivity of each leg in W � ð Þ <sup>m</sup> � <sup>K</sup> �<sup>1</sup> h i, and the thermal conductance of each leg is <sup>K</sup> <sup>¼</sup> <sup>k</sup> <sup>S</sup> <sup>L</sup> in <sup>W</sup> � <sup>K</sup>�<sup>1</sup> � �

These relations are further simplified considering that N-type and P-type legs are the same as form (L ¼ L<sup>P</sup> ¼ L<sup>N</sup> and S ¼ S<sup>P</sup> ¼ SN) and material properties (ρ ¼ ρ<sup>P</sup> ¼ ρN, and k ¼ k<sup>P</sup> ¼ kN). The equivalent internal resistance becomes:

$$R = n \cdot 2\rho \cdot L \cdot \left(\mathbb{S}\right)^{-1} \tag{8}$$

and the equivalent thermal conductance is:

$$K = n \cdot \text{2 }k \cdot \text{S} \cdot \text{(}L\text{)}^{-1} \tag{9}$$

If the electrical contact resistance R<sup>a</sup> is not negligible, the equivalent internal resistance of the thermoelectric couples in series becomes:

$$R = n \cdot 2\rho \cdot L \cdot \left(\mathbb{S}\right)^{-1} + R\_{\text{a}} \tag{10}$$

The voltage at the TEG terminals is:

$$V\_{\rm TEG} = V\_2 - V\_1 = n \cdot (I \cdot R - a\_{\rm PN} \cdot \Delta T) = n \cdot I \cdot R - V\_{\rm Sebeck} \tag{11}$$

where αPN ¼ ð Þ α<sup>P</sup> � α<sup>N</sup> <sup>2</sup> is the Seebeck coefficient of the thermoelectric couple. The input electrical current in the circuit is:

$$I = \frac{V\_{Seebck}}{n \cdot R + R\_{\rm L}} = \frac{n \cdot a\_{\rm PN} \cdot \Delta T}{n \cdot R + R\_{\rm L}} \tag{12}$$

where the load resistance R<sup>L</sup> is connected to the output of the circuit where the electric output power generated by TEG is consumed; the Seebeck voltage is VSeebeck = V<sup>P</sup> � V<sup>N</sup> = αPN � ΔT. The relationship between VSeebeck and ΔT is nonlinear, therefore αPN depends on temperature.

Figure 5. Schematic of a TEG device with n thermoelectric couples.

simultaneously, and the magnitude of the Thomson effect is about two times less

The TEG device is composed of one or more thermoelectric couples. The simplest TEG consists of a thermocouple, comprising a pair of P-type and N-type thermoelements or legs connected electrically in series and thermally in parallel. The differentiation between N- and P-doped materials is important. The P-type leg

negative Seebeck coefficient and an excess of free electrons e� [22]. The two legs are linked together on one side by an electrical conductor forming a junction or interconnect, usually being a copper strip. Let us denote the voltage at the outside terminal connected to the N-type leg on the cold side of TEG as V2, while the voltage at the external terminal connected to the P-type leg on the cold side of TEG is V<sup>1</sup> (Figure 4). An electrical load having resistance R<sup>L</sup> is connected in series with the output terminals of TEG creating an electric circuit. When the electric current flows in this electrical load, an electrical voltage is generated at its terminals. The TEG device will generate DC electricity as long as there is a temperature gradient between its sides. When the temperature difference ΔT = T<sup>h</sup> � T<sup>c</sup> across the TEG

A number of thermoelectric couples n form a TEG system wired electrically in series and sandwiched between two ceramic plates to maximise the output voltage

In this case, the equivalent internal resistance of the thermoelectric couples in

<sup>R</sup> <sup>¼</sup> <sup>n</sup> � <sup>ρ</sup><sup>P</sup> � <sup>L</sup><sup>P</sup> � ð Þ <sup>S</sup><sup>P</sup> �<sup>1</sup> <sup>þ</sup> <sup>ρ</sup><sup>N</sup> � <sup>L</sup><sup>N</sup> � ð Þ <sup>S</sup><sup>N</sup> �<sup>1</sup> h i

and the equivalent thermal conductance of the thermoelectric couples in

. The N-type leg has a

(6)

than the magnitude of the Joule effect [17].

has a positive Seebeck coefficient and an excess of holes h<sup>+</sup>

Schematic of a TEG device with a single thermoelectric couple and two legs.

device increases, more electric output power will be generated.

2.3 TEG structure and model

Figure 4.

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from the TEG (Figure 5).

series is:

parallel is:

6

The electric output power delivered by TEG to the load is:

$$P = \mathfrak{n} \cdot \left( a\_{\text{PN}} \cdot I \cdot \Delta T - R \cdot I^2 \right) \tag{13}$$

On the other side, the electric output power absorbed by the load (considering the conventional sign, with the current flowing as indicated in Figure 5) is:

$$P = -\mathbf{V\_{TEG}} \cdot I = n \cdot \left(\mathbf{R} \cdot I^2 - a\_{\rm PN} \cdot I \cdot \Delta T\right) \tag{14}$$

The electric output power absorbed by the load resistance R<sup>L</sup> is:

$$P\_{\rm R} = I^2 \cdot R\_{\rm L} = \left(\frac{n \cdot a\_{\rm PN} \cdot \Delta T}{n \cdot R + R\_{\rm L}}\right)^2 \cdot R\_{\rm L} \tag{15}$$

The maximum electric output power of a TEG is obtained when the electrical output power is maximised with respect to the electric current:

$$P\_{\text{max}} = n \cdot \frac{(a\_{\text{PN}} \cdot \Delta T)^2}{4R} \tag{16}$$

$$I\_{\text{max}} = \frac{a\_{\text{PN}} \cdot \Delta T}{2R} \tag{17}$$

temperature of about 300°C; for higher operating temperature ranges other working fluids are used (e.g., naphthalene or liquid metals like potassium and sodium) [24]; heat pipes are used for temperature regulation of the TEGs; in some applications (e.g., industrial glass processes) a heat exchanger can be attached on the hot side; its role is to absorb the thermal energy (e.g., from the glass process exhaust stream) and to transfer it to the TEG, which converts it partially into electrical energy; the remaining unconverted thermal energy is transferred from the TEG cold side to the cold source, and is dissipated to the

• Cold source is the heat transfer system containing heat exchangers (heat sinks, coils, cooling blocks and radiators) to enhance the heat dissipation across the TEG; this process is useful to obtain a bigger temperature difference across the TEG [7, 25]; the heat sink is a device that has the role to transfer heat from a hot surface to a fluid (gas, ambient air or liquid); the assessment and design of different heat sink types for TEG system is presented in [26]. The metal heat sink contains many fins. To increase its dissipation rate, the fins area, the heat

The heat sink is required at the TEG when a high heat flow rate is applied on the TEG hot side, and the cold side is kept at low temperature, leading to high conversion efficiency; in this case, the TEG efficiency is strongly influenced by the

• DC-DC converter (Boost, Buck-Boost, Buck, Sepic, or Cuk converter), which is a power electronic circuit designed for voltage conversion (to convert a DC source from one voltage level to another voltage level) [27]; since the output

transfer coefficient, and the fin thermal conductivity are raised.

environment at ambient temperature Tamb.

Block diagram of a thermoelectric energy harvesting system.

Thermoelectric Energy Harvesting: Basic Principles and Applications

DOI: http://dx.doi.org/10.5772/intechopen.83495

TEG design.

9

Figure 6.

Figure 7.

Equivalent circuit of a TEG device.

The maximum electrical output power delivered by TEG is obtained if the load resistance is equal to the equivalent internal resistance of the thermoelectric couples in series ð Þ R<sup>L</sup> ¼ R [23].

The heat flow rate absorbed at the hot junction of the TEG depends on the Peltier heat, the heat conduction and the Joule heat. The heat flow rate absorbed at the hot junction depends on the thermoelectric material properties and leg geometries:

$$\dot{Q}\_h = n \cdot \left[ \mathbf{a}\_{\rm PN} \cdot T\_h \cdot I - \frac{R \cdot I^2}{2} + K \cdot \Delta T \right] \tag{18}$$

A TEG could be considered as a thermal battery, a physical structure used to store and release thermal energy. The electromotive force of this thermal battery is the Seebeck voltage (Figure 6).

#### 2.4 Components of a thermoelectric energy harvesting system

A thermoelectric energy harvesting system consists of the following parts (Figure 7):


Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

#### Figure 6.

The electric output power delivered by TEG to the load is:

P ¼ n � αPN � I � ΔT � R � I

the conventional sign, with the current flowing as indicated in Figure 5) is:

P ¼ �VTEG � I ¼ n � R � I

P<sup>R</sup> ¼ I

in series ð Þ R<sup>L</sup> ¼ R [23].

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the Seebeck voltage (Figure 6).

(Figure 7):

8

output power is maximised with respect to the electric current:

The electric output power absorbed by the load resistance R<sup>L</sup> is:

Pmax ¼ n �

<sup>Q</sup>\_ <sup>h</sup> <sup>¼</sup> <sup>n</sup> � <sup>α</sup>PN � Th � <sup>I</sup> � <sup>R</sup> � <sup>I</sup>

2.4 Components of a thermoelectric energy harvesting system

On the other side, the electric output power absorbed by the load (considering

<sup>2</sup> � <sup>R</sup><sup>L</sup> <sup>¼</sup> <sup>n</sup> � <sup>α</sup>PN � <sup>Δ</sup><sup>T</sup>

The maximum electric output power of a TEG is obtained when the electrical

<sup>I</sup>max <sup>¼</sup> <sup>α</sup>PN � <sup>Δ</sup><sup>T</sup>

The maximum electrical output power delivered by TEG is obtained if the load resistance is equal to the equivalent internal resistance of the thermoelectric couples

The heat flow rate absorbed at the hot junction of the TEG depends on the Peltier heat, the heat conduction and the Joule heat. The heat flow rate absorbed at the hot junction depends on the thermoelectric material properties and leg geometries:

A TEG could be considered as a thermal battery, a physical structure used to store and release thermal energy. The electromotive force of this thermal battery is

A thermoelectric energy harvesting system consists of the following parts

• Thermoelectric generator (TEG): if ΔT is kept between the hot and cold sides of the device, an external circuit can be supplied by the voltage resulting at the TEG output terminals, providing power to the external electrical load. A single TEG generates power from 1 to 125 W. The use of more TEGs in a modular connection may increase the power up to 5 kW and ΔTmax could be bigger than 70°C.

• Heat source, for example, a heat pipe system (the TEG devices and the heat pipe system can be used together in waste heat recovery systems). The heat pipe is a passive (no moving parts or fan) metallic device which has a high heat transfer capacity (very high thermal conductivity), with minimal thermal resistance and almost no heat loss; it operates in a medium temperature to high-temperature range; the common working fluid is water operating at a

2

<sup>2</sup> <sup>þ</sup> <sup>K</sup> � <sup>Δ</sup><sup>T</sup>

n � R þ R<sup>L</sup> <sup>2</sup>

ð Þ <sup>α</sup>PN � <sup>Δ</sup><sup>T</sup> <sup>2</sup>

<sup>2</sup> (13)

<sup>2</sup> � <sup>α</sup>PN � <sup>I</sup> � <sup>Δ</sup><sup>T</sup> (14)

<sup>4</sup><sup>R</sup> (16)

<sup>2</sup><sup>R</sup> (17)

� R<sup>L</sup> (15)

(18)

Equivalent circuit of a TEG device.

Figure 7.

Block diagram of a thermoelectric energy harvesting system.

temperature of about 300°C; for higher operating temperature ranges other working fluids are used (e.g., naphthalene or liquid metals like potassium and sodium) [24]; heat pipes are used for temperature regulation of the TEGs; in some applications (e.g., industrial glass processes) a heat exchanger can be attached on the hot side; its role is to absorb the thermal energy (e.g., from the glass process exhaust stream) and to transfer it to the TEG, which converts it partially into electrical energy; the remaining unconverted thermal energy is transferred from the TEG cold side to the cold source, and is dissipated to the environment at ambient temperature Tamb.

• Cold source is the heat transfer system containing heat exchangers (heat sinks, coils, cooling blocks and radiators) to enhance the heat dissipation across the TEG; this process is useful to obtain a bigger temperature difference across the TEG [7, 25]; the heat sink is a device that has the role to transfer heat from a hot surface to a fluid (gas, ambient air or liquid); the assessment and design of different heat sink types for TEG system is presented in [26]. The metal heat sink contains many fins. To increase its dissipation rate, the fins area, the heat transfer coefficient, and the fin thermal conductivity are raised.

The heat sink is required at the TEG when a high heat flow rate is applied on the TEG hot side, and the cold side is kept at low temperature, leading to high conversion efficiency; in this case, the TEG efficiency is strongly influenced by the TEG design.

• DC-DC converter (Boost, Buck-Boost, Buck, Sepic, or Cuk converter), which is a power electronic circuit designed for voltage conversion (to convert a DC source from one voltage level to another voltage level) [27]; since the output

voltage of the TEG is low or is not constant, it is necessary to provide a DC-DC converter; its role is to increase the output voltage obtained in the TEG (which depends on the number of TEGs in series and on the TEG features) corresponding the requirements of the external load. For these DC-DC converters, accurate control is necessary. In this case, the implementation of the Maximum Power Point Tracking (MPPT) algorithm within the DC-DC converter controller is essential. To enhance the real system feasibility, it is necessary to harvest from TEGs as much electric output power as possible; the effectiveness of TEG operation could be checked by assessing the DC-DC converter operation and the MPPT control.

where T is the absolute temperature representing the mean temperature between the cold side and hot side of the TEG and is written as <sup>T</sup> <sup>¼</sup> <sup>T</sup>hþT<sup>c</sup>

<sup>η</sup> TEG <sup>¼</sup> <sup>Δ</sup><sup>T</sup>

<sup>K</sup>�<sup>R</sup> is the figure-of-merit for a thermocouple. The thermoelectric conversion efficiency is maximised with respect to R<sup>L</sup>

<sup>m</sup> <sup>¼</sup> <sup>R</sup><sup>L</sup>

efficiency and is written, by introducing the reduced efficiency η r, as:

Th

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> ZT <sup>p</sup> � <sup>1</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> ZT <sup>p</sup> <sup>þ</sup> Tc


<sup>P</sup> <sup>η</sup> TEGmax ð Þ¼ <sup>n</sup> � ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

For a cold side temperature of T<sup>c</sup> = 300 K and ΔT in the range of 20 K,

As observed in Eq. (24), the TEG efficiency strongly depends on the operating temperatures of TEG (ΔT between the junctions), the dimensionless thermoelectric figure-of-merit ZT, and additionally the TEG design (cross-sectional area, length and

The TEG efficiency <sup>η</sup> TEG rises almost linearly with <sup>Δ</sup>T, and the ratio <sup>η</sup> <sup>r</sup>

thermoelectric conversion efficiency η TEG, and to a lesser extent by the heat exchanger design. The ratio between thermal efficiency η <sup>t</sup> and thermoelectric conversion efficiency represents the fraction of waste heat passed through the

constant [5]. The bigger the temperature difference, the more efficient the TEG device will be. A TEG can work at about 20% of the Carnot efficiency over a large temperature range [24]. The TEG efficiency is about 5% and its electric output power is delivered at any ΔT. If materials with ZT = 10 would exist, there could be

The thermoelectric waste heat recovery is influenced to a bigger extent by the

<sup>ε</sup> <sup>¼</sup> <sup>η</sup> <sup>t</sup> η TEG

and the corresponding electric output power is:

<sup>R</sup> <sup>¼</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>T</sup><sup>h</sup> <sup>¼</sup> <sup>Δ</sup><sup>T</sup>

<sup>T</sup><sup>h</sup> , 1 [31]:

<sup>¼</sup> <sup>m</sup> � <sup>1</sup> <sup>m</sup> <sup>þ</sup> Tc Th � ΔT Th

<sup>R</sup> � <sup>α</sup>PN � <sup>Δ</sup><sup>T</sup> ffiffiffiffiffiffiffiffiffiffiffiffiffiffi

<sup>1</sup> <sup>þ</sup> ZT <sup>p</sup>

The TEG device operates as all thermal engines with efficiency less than the

In this case, the thermoelectric conversion efficiency is limited by the Carnot

� <sup>Δ</sup><sup>T</sup> Th |{z} η C

<sup>1</sup> <sup>þ</sup> ZT <sup>p</sup>

The efficiency corresponding to Pmax is:

DOI: http://dx.doi.org/10.5772/intechopen.83495

Thermoelectric Energy Harvesting: Basic Principles and Applications

efficiency of ideal Carnot cycle <sup>η</sup> <sup>C</sup> <sup>¼</sup> <sup>T</sup>h�T<sup>c</sup>

η TEGmax ¼

η TEGmax ffi 1% is obtained [32].

TEGs with η TEG ¼ 25% at ΔT = 300 K [25].

thermoelectric couples, given as [34]:

shape) [33].

11

where <sup>Z</sup> <sup>¼</sup> <sup>α</sup><sup>2</sup>

[23] when

PN

<sup>2</sup> .

<sup>4</sup> � <sup>Z</sup>�<sup>1</sup> <sup>þ</sup> <sup>T</sup><sup>h</sup> <sup>þ</sup> <sup>T</sup> (21)

<sup>1</sup> <sup>þ</sup> ZT <sup>p</sup> (22)

<sup>¼</sup> <sup>η</sup> <sup>r</sup> Th

� � (25)

� ΔT (24)

Th is almost

(26)

η TEGmax , η <sup>C</sup> (23)

• DC load, used to be connected to a supercapacitor or to recharge a battery to store energy; the battery stores DC voltages at a charging mode and powers DC electrical energy in a discharging mode; typical DC loads for TEG like batteries operate at 12 V; the output voltage of the TEG device at the MPP (Maximum Power Point) must be higher than 12 V for example in buck converter applications [27]; to avoid the battery overcharging a battery regulator is sometimes used; the electric power output from the DC-DC converter can be stored over time in a supercapacitor, to be released to the load when needed [28].

The efficiency of the thermoelectric energy harvesting system is defined as the ratio of the electrical energy output (used or stored) to the total energy input. This efficiency also contains the electrical efficiency of TEGs, the heat exchangers efficiency, as well as the efficiency of the DC-DC converter. The total energy input especially depends on the energy obtained from the hot source. Also, the total energy input depends to a lesser extent on the mechanical energy needed to operate the thermoelectric energy harvesting system (e.g., pressure losses in the heat exchangers or cooling of the cold heat sink) [29].

Researchers are focused on the improvement of the thermoelectric conversion efficiency of TEGs. For this reason, two objectives must be fulfilled. The first objective is to improve the dimensionless figure-of-merit ZT by the optimisation of thermoelectric materials. The second objective is to decrease the thermal resistance between the heat source and the hot side of the TEG, as well as between the cold side of the TEG and the environment [30].

#### 2.5 Efficiency assessment of a TEG device

The electrical efficiency of a TEG (or thermoelectric conversion efficiency) is the ratio between the electric output power P delivered to the load and the rate of heat input Q\_ <sup>h</sup> absorbed at the hot junction of the TEG and transferred through the TEG. This means that a TEG converts the rate of heat input Q\_ <sup>h</sup> into electric output power P with electrical efficiency η TEG [5].

$$
\eta\_{\rm TEG} = \frac{P}{\dot{Q}\_h} \tag{19}
$$

Eq. (19) is written in more details as

$$\eta\_{\rm TEG} = \frac{n \cdot R\_{\rm L} \cdot \Delta T \cdot a\_{\rm PN}^2}{K \cdot \left(n \cdot R + R\_{\rm L}\right)^2 + n \cdot \left(R\_{\rm L} \cdot T\_{\rm h} + n \cdot R \cdot T\right) \cdot a\_{\rm PN}^2} \tag{20}$$

where T is the absolute temperature representing the mean temperature between the cold side and hot side of the TEG and is written as <sup>T</sup> <sup>¼</sup> <sup>T</sup>hþT<sup>c</sup> <sup>2</sup> .

The efficiency corresponding to Pmax is:

voltage of the TEG is low or is not constant, it is necessary to provide a DC-DC converter; its role is to increase the output voltage obtained in the TEG (which

• DC load, used to be connected to a supercapacitor or to recharge a battery to store energy; the battery stores DC voltages at a charging mode and powers DC electrical energy in a discharging mode; typical DC loads for TEG like batteries operate at 12 V; the output voltage of the TEG device at the MPP (Maximum Power Point) must be higher than 12 V for example in buck converter applications [27]; to avoid the battery overcharging a battery regulator is sometimes used; the electric power output from the DC-DC converter can be stored over time in a supercapacitor, to be released to the

The efficiency of the thermoelectric energy harvesting system is defined as the ratio of the electrical energy output (used or stored) to the total energy input. This efficiency also contains the electrical efficiency of TEGs, the heat exchangers efficiency, as well as the efficiency of the DC-DC converter. The total energy input especially depends on the energy obtained from the hot source. Also, the total energy input depends to a lesser extent on the mechanical energy needed to operate the thermoelectric energy harvesting system (e.g., pressure losses in the heat

Researchers are focused on the improvement of the thermoelectric conversion

The electrical efficiency of a TEG (or thermoelectric conversion efficiency) is the ratio between the electric output power P delivered to the load and the rate of heat input Q\_ <sup>h</sup> absorbed at the hot junction of the TEG and transferred through the TEG. This means that a TEG converts the rate of heat input Q\_ <sup>h</sup> into electric output

<sup>η</sup> TEG <sup>¼</sup> <sup>P</sup>

<sup>η</sup> TEG <sup>¼</sup> <sup>n</sup> � <sup>R</sup><sup>L</sup> � <sup>Δ</sup><sup>T</sup> � <sup>α</sup><sup>2</sup>

K � ð Þ n � R þ R<sup>L</sup>

Q\_ h

PN

<sup>2</sup> <sup>þ</sup> <sup>n</sup> � <sup>ð</sup>R<sup>L</sup> � <sup>T</sup><sup>h</sup> <sup>þ</sup> <sup>n</sup> � <sup>R</sup> � <sup>T</sup>Þ � <sup>α</sup><sup>2</sup>

(19)

(20)

PN

efficiency of TEGs. For this reason, two objectives must be fulfilled. The first objective is to improve the dimensionless figure-of-merit ZT by the optimisation of thermoelectric materials. The second objective is to decrease the thermal resistance between the heat source and the hot side of the TEG, as well as between the cold

depends on the number of TEGs in series and on the TEG features) corresponding the requirements of the external load. For these DC-DC converters, accurate control is necessary. In this case, the implementation of the Maximum Power Point Tracking (MPPT) algorithm within the DC-DC converter controller is essential. To enhance the real system feasibility, it is necessary to harvest from TEGs as much electric output power as possible; the effectiveness of TEG operation could be checked by assessing the DC-DC

converter operation and the MPPT control.

exchangers or cooling of the cold heat sink) [29].

side of the TEG and the environment [30].

2.5 Efficiency assessment of a TEG device

power P with electrical efficiency η TEG [5].

Eq. (19) is written in more details as

10

load when needed [28].

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$$\eta\_{\rm TEG} = \frac{\Delta T}{4 \cdot Z^{-1} + T\_{\rm h} + T} \tag{21}$$

where <sup>Z</sup> <sup>¼</sup> <sup>α</sup><sup>2</sup> PN <sup>K</sup>�<sup>R</sup> is the figure-of-merit for a thermocouple.

The thermoelectric conversion efficiency is maximised with respect to R<sup>L</sup> [23] when

$$m = \frac{R\_{\rm L}}{R} = \sqrt{\mathbf{1} + ZT} \tag{22}$$

The TEG device operates as all thermal engines with efficiency less than the efficiency of ideal Carnot cycle <sup>η</sup> <sup>C</sup> <sup>¼</sup> <sup>T</sup>h�T<sup>c</sup> <sup>T</sup><sup>h</sup> <sup>¼</sup> <sup>Δ</sup><sup>T</sup> <sup>T</sup><sup>h</sup> , 1 [31]:

$$
\eta\_{\text{TEGmax}} < \eta\_{\text{C}} \tag{23}
$$

In this case, the thermoelectric conversion efficiency is limited by the Carnot efficiency and is written, by introducing the reduced efficiency η r, as:

$$\eta\_{\text{TEGmax}} = \underbrace{\frac{\sqrt{1+ZT}-1}{\sqrt{1+ZT}+\frac{T\_c}{T\_h}}}\_{\eta\_r} \cdot \underbrace{\frac{\Delta T}{T\_h}}\_{\eta\_c} = \frac{m-1}{m+\frac{T\_c}{T\_h}} \cdot \frac{\Delta T}{T\_h} = \frac{\eta\_r}{T\_h} \cdot \Delta T \tag{24}$$

and the corresponding electric output power is:

$$P(\eta\_{\text{TEGmax}}) = \frac{n \cdot \sqrt{1 + ZT}}{R} \cdot \left(\frac{\alpha\_{\text{PN}} \cdot \Delta T}{\sqrt{1 + ZT}}\right) \tag{25}$$

For a cold side temperature of T<sup>c</sup> = 300 K and ΔT in the range of 20 K, η TEGmax ffi 1% is obtained [32].

As observed in Eq. (24), the TEG efficiency strongly depends on the operating temperatures of TEG (ΔT between the junctions), the dimensionless thermoelectric figure-of-merit ZT, and additionally the TEG design (cross-sectional area, length and shape) [33].

The TEG efficiency <sup>η</sup> TEG rises almost linearly with <sup>Δ</sup>T, and the ratio <sup>η</sup> <sup>r</sup> Th is almost constant [5]. The bigger the temperature difference, the more efficient the TEG device will be. A TEG can work at about 20% of the Carnot efficiency over a large temperature range [24]. The TEG efficiency is about 5% and its electric output power is delivered at any ΔT. If materials with ZT = 10 would exist, there could be TEGs with η TEG ¼ 25% at ΔT = 300 K [25].

The thermoelectric waste heat recovery is influenced to a bigger extent by the thermoelectric conversion efficiency η TEG, and to a lesser extent by the heat exchanger design. The ratio between thermal efficiency η <sup>t</sup> and thermoelectric conversion efficiency represents the fraction of waste heat passed through the thermoelectric couples, given as [34]:

$$
\varepsilon = \frac{\eta\_{\text{t}}}{\eta\_{\text{TEG}}} \tag{26}
$$

The maximum efficiency η TEGmax depends on the temperature difference ΔTTEG at which the TEG works [31]. The maximum conversion efficiency occurs when:

$$\frac{R\_L}{R} = \sqrt{\mathbf{1} + Z \frac{T\_c + T\_h}{2}} \tag{27}$$

• the operating range of thermoelectric materials to work with the ΔT as high

The most popular thermoelectric material is Bismuth Telluride (Bi2Te3). Its utilisation in TEGs is limited (only for industrial modules with an average value of ZT from 0.5 to 0.8) because the maximum temperature at the hot side of the devices is relatively reduced [29]. In the power generation applications, the best commercially available TEGs made of Bi2Te3 have a ZT of about 1 at the temperature 300 K, leading to a low thermal efficiency of the thermoelectric device (less than 4%) [24]. The thermoelectric materials must be both stable from the chemical point of view and strong from the mechanical point of view at high temperatures (e.g., for the automotive exhaust waste heat recovery, at specific working conditions, the range of the average exhausts temperature is from 500 to 600°C with values increasing up to 1000°C) [37]. To improve the thermoelectric properties of TEG, the researchers' attention is focused on the development of new thermoelectric materials. Calcium manganese and lead telluride are the thermoelectric materials used in the TEG legs, because they resist at higher temperatures. The hot side of TEG is made of materials having a high ZT at higher temperatures (e.g., lead telluride). The cold side of the TEG is made of materials having high ZT at reduced temperatures (e.g., Bi2Te3) [24]. At present, even though the research of the thermoelectric materials

development is focused on obtaining the high ZT of 2, unfortunately the efficiency

To obtain high efficiency, segmented TEGs use high-temperature differences to raise the Carnot efficiency η <sup>C</sup> [45]. When a TEG operates with a high-temperature difference, each thermoelement of the device can be divided into multiple segments of different thermoelectric materials. In this way, each material is working in a more limited temperature range where this has a good performance [46]. The segmented design of a TEG is an efficient mode to improve its performance. In this case, two or more thermoelectric materials along the direction of the leg height are used to match the optimal temperature range of the thermoelectric material. It means that a thermoelectric material with high efficiency at raised temperature is segmented with another thermoelectric material with high efficiency at reduced temperature [45]. The maximum efficiency is obtained when the relative current density J is equal to the compatibility factor u of the thermoelectric material [47]:

of TEG is limited to η TEG , 10% [38]. Significant progress has been made towards increasing the thermoelectric efficiency of different inorganic material classes (e.g., skutterudites [39], tellurides [40, 41], half-Heuslers [42] and silicides [43]). The researchers' attention is focused on the development of organic materials for thermoelectric energy harvesting due to their advantages (e.g., low-cost, reliability, low weight and so on). For this reason, some polymers with different doping levels (like polyaniline (PANI), polyamide (PA), and poly (3,4-ethylenediox-

ythiophene) or PEDOT) are assessed for future applications [44].

J k � ∇T |fflffl{zfflffl} J

13

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> ZT <sup>p</sup> � <sup>1</sup> α � T |fflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflffl} <sup>u</sup>

The compatibility factor is used for choosing the proper material [48]. El-Genk and Sabre [46] obtained a TEG energy conversion efficiency of about 12% by using a segmented thermoelectric couple. Snyder [47] observed that the segmentation of

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• the use of low-price materials to reduce the negative impact of low

Thermoelectric Energy Harvesting: Basic Principles and Applications

DOI: http://dx.doi.org/10.5772/intechopen.83495

as possible;

efficiency [29].

#### 2.5.1 The dimensionless thermoelectric figure-of-merit ZT

The dimensionless thermoelectric figure-of-merit ZT is used to characterise a thermoelectric material performance, as well as the efficiencies of various TEGs working at the same temperatures [24].

ZT depends on the physical transport properties: the thermal conductivity k, the electrical conductivity <sup>σ</sup> <sup>¼</sup> <sup>1</sup> <sup>ρ</sup>, and the Seebeck coefficient α:

$$ZT = \frac{a^2 \cdot T}{\rho \cdot k} = \frac{a^2 \cdot \sigma \cdot T}{k} \tag{28}$$

The upper side term <sup>α</sup><sup>2</sup> � <sup>σ</sup> is called the power factor, a parameter that assesses the performance of a thermoelectric material.

The higher is ZT, more performant is the thermoelectric material and the better is the TEG. In the practical applications, the maximum ZT is about 2 and corresponds to a maximum conversion efficiency of about 20% [35].

A good thermoelectric material must fulfil the following requirements:


The effective figure-of-merit of TEG, ZTTEG depends on the dimensionless thermoelectric figure-of-merit, and the specific contact electrical resistivity according to the expression:

$$ZT\_{\rm TEG} = \frac{L}{(L + 2\sigma \cdot \rho\_{\rm a})} \cdot ZT = \frac{L}{(L + 2\sigma \cdot \rho\_{\rm a})} \cdot \frac{a^2 \cdot \sigma \cdot T}{k} \tag{29}$$

where ρ<sup>a</sup> ¼ R<sup>a</sup> � S<sup>a</sup> is the specific contact electrical resistivity. Ideally, for an efficient TEG <sup>ρ</sup><sup>a</sup> , <sup>1</sup>μΩ � cm<sup>2</sup> and instead, for a typical TEG, <sup>ρ</sup><sup>a</sup> , <sup>2</sup> � <sup>10</sup>�<sup>4</sup><sup>Ω</sup> � cm2 [36].

Although the low efficiency is a drawback to the progress of TEGs, researchers' and manufacturers' attention is focused on the improvement of the following characteristics:

• the dimensionless thermoelectric figure-of-merit ZT;

Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

The maximum efficiency η TEGmax depends on the temperature difference ΔTTEG at which the TEG works [31]. The maximum conversion efficiency occurs when:

The dimensionless thermoelectric figure-of-merit ZT is used to characterise a thermoelectric material performance, as well as the efficiencies of various TEGs

ZT depends on the physical transport properties: the thermal conductivity k, the

<sup>ρ</sup>, and the Seebeck coefficient α:

<sup>ρ</sup> � <sup>k</sup> <sup>¼</sup> <sup>α</sup><sup>2</sup> � <sup>σ</sup> � <sup>T</sup>

The upper side term <sup>α</sup><sup>2</sup> � <sup>σ</sup> is called the power factor, a parameter that assesses the

The higher is ZT, more performant is the thermoelectric material and the better is the TEG. In the practical applications, the maximum ZT is about 2 and corre-

A good thermoelectric material must fulfil the following requirements:

• Seebeck coefficient as high as possible to maximise energy conversion; the generated open-circuit-voltage is proportional to the Seebeck coefficient and to the temperature difference across the TEG (VSeebeck = αPN � ΔT). In this case, a

high Seebeck coefficient leads to a high voltage. This condition is very

• Electrical conductivity σ as high as possible in order to reduce Joule heating due

• Thermal conductivity k as low as possible to maintain heat at the junctions, to allow a large ΔT maintained across the TEG, and to minimise thermal losses

The effective figure-of-merit of TEG, ZTTEG depends on the dimensionless thermoelectric figure-of-merit, and the specific contact electrical resistivity

<sup>L</sup> <sup>þ</sup> <sup>2</sup><sup>σ</sup> � <sup>ρ</sup><sup>a</sup> ð Þ � ZT <sup>¼</sup> <sup>L</sup>

where ρ<sup>a</sup> ¼ R<sup>a</sup> � S<sup>a</sup> is the specific contact electrical resistivity. Ideally, for an efficient TEG <sup>ρ</sup><sup>a</sup> , <sup>1</sup>μΩ � cm<sup>2</sup> and instead, for a typical TEG, <sup>ρ</sup><sup>a</sup> , <sup>2</sup> � <sup>10</sup>�<sup>4</sup><sup>Ω</sup> � cm2

Although the low efficiency is a drawback to the progress of TEGs, researchers' and manufacturers' attention is focused on the improvement of the following char-

<sup>L</sup> <sup>þ</sup> <sup>2</sup><sup>σ</sup> � <sup>ρ</sup><sup>a</sup> ð Þ �

<sup>α</sup><sup>2</sup> � <sup>σ</sup> � <sup>T</sup>

<sup>k</sup> (29)

<sup>k</sup> (28)

ZT <sup>¼</sup> <sup>α</sup><sup>2</sup> � <sup>T</sup>

sponds to a maximum conversion efficiency of about 20% [35].

important for increasing the energy conversion [22].

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi <sup>1</sup> <sup>þ</sup> <sup>Z</sup> Tc <sup>þ</sup> Th 2

(27)

RL R ¼

2.5.1 The dimensionless thermoelectric figure-of-merit ZT

working at the same temperatures [24].

performance of a thermoelectric material.

to the internal electrical losses [22].

according to the expression:

[36].

12

acteristics:

through the thermoelectric material [19].

ZTTEG <sup>¼</sup> <sup>L</sup>

• the dimensionless thermoelectric figure-of-merit ZT;

electrical conductivity <sup>σ</sup> <sup>¼</sup> <sup>1</sup>

Green Energy Advances

r


The most popular thermoelectric material is Bismuth Telluride (Bi2Te3). Its utilisation in TEGs is limited (only for industrial modules with an average value of ZT from 0.5 to 0.8) because the maximum temperature at the hot side of the devices is relatively reduced [29]. In the power generation applications, the best commercially available TEGs made of Bi2Te3 have a ZT of about 1 at the temperature 300 K, leading to a low thermal efficiency of the thermoelectric device (less than 4%) [24]. The thermoelectric materials must be both stable from the chemical point of view and strong from the mechanical point of view at high temperatures (e.g., for the automotive exhaust waste heat recovery, at specific working conditions, the range of the average exhausts temperature is from 500 to 600°C with values increasing up to 1000°C) [37]. To improve the thermoelectric properties of TEG, the researchers' attention is focused on the development of new thermoelectric materials. Calcium manganese and lead telluride are the thermoelectric materials used in the TEG legs, because they resist at higher temperatures. The hot side of TEG is made of materials having a high ZT at higher temperatures (e.g., lead telluride). The cold side of the TEG is made of materials having high ZT at reduced temperatures (e.g., Bi2Te3) [24]. At present, even though the research of the thermoelectric materials development is focused on obtaining the high ZT of 2, unfortunately the efficiency of TEG is limited to η TEG , 10% [38]. Significant progress has been made towards increasing the thermoelectric efficiency of different inorganic material classes (e.g., skutterudites [39], tellurides [40, 41], half-Heuslers [42] and silicides [43]). The researchers' attention is focused on the development of organic materials for thermoelectric energy harvesting due to their advantages (e.g., low-cost, reliability, low weight and so on). For this reason, some polymers with different doping levels (like polyaniline (PANI), polyamide (PA), and poly (3,4-ethylenedioxythiophene) or PEDOT) are assessed for future applications [44].

To obtain high efficiency, segmented TEGs use high-temperature differences to raise the Carnot efficiency η <sup>C</sup> [45]. When a TEG operates with a high-temperature difference, each thermoelement of the device can be divided into multiple segments of different thermoelectric materials. In this way, each material is working in a more limited temperature range where this has a good performance [46]. The segmented design of a TEG is an efficient mode to improve its performance. In this case, two or more thermoelectric materials along the direction of the leg height are used to match the optimal temperature range of the thermoelectric material. It means that a thermoelectric material with high efficiency at raised temperature is segmented with another thermoelectric material with high efficiency at reduced temperature [45]. The maximum efficiency is obtained when the relative current density J is equal to the compatibility factor u of the thermoelectric material [47]:

$$\underbrace{\frac{J}{k \cdot \nabla T}}\_{\overline{J}} = \underbrace{\frac{\sqrt{1 + ZT} - 1}{a \cdot T}}\_{u} \tag{30}$$

The compatibility factor is used for choosing the proper material [48]. El-Genk and Sabre [46] obtained a TEG energy conversion efficiency of about 12% by using a segmented thermoelectric couple. Snyder [47] observed that the segmentation of

the thermoelements with SnTe or PbTe produced low extra power, while the filled Skutterudite obtained an increment in efficiency from 10.5 to 13.6%. Further studies [47, 48] reported that the segmentation was efficient only for u ≤2: Ngan et al. [49] demonstrate that segmentation reduces the total efficiency by neglecting the compatibility factor of thermoelectric materials. Hung et al. [50] showed that the performance and the power production of the segmented TEG are three times bigger than a normal TEG. The analytical assessment concerning the effect of the leg geometry on the performance of the segmented TEG was performed in [51, 52]. Their conclusion is that both power and efficiency are increased when the segmented TEG is used. Vikhor and Anatychuk [53] carried out a theoretical analysis. The results showed an efficiency of the segmented TEGs bigger than 15% compared to the non-segmented TEGs. Zhang et al. [54] proposed a design method of optimization with predictive performance to obtain maximum conversion efficiency. In this case, the segmented modules consisted of Bi2Te3-based alloys and CoSb3-based skutterudites, with an efficiency of 12% when working under a Δt = 541°C. The very low losses and the good design based on the numerical evaluation showed that the conversion efficiency was up to 96.9% of the theoretical efficiency.

internal electrical resistance will be low, the electric output power will not be

Lavric et al. [57] demonstrated that the electric output power is influenced by the effects above mentioned (a reduction of the leg length leads to a reduction of the electrical resistance; an increase of the leg length leads to the higher temperature difference across the TEG). If the geometric parameters of the TEG (leg length, semiconductor pair number and the base area ratio of semiconductor columns to TEG) are optimised, the electric output power and the thermoelectric conversion efficiency are considerably improved. Such an improvement is also reported in [58]. The first step was to consider the electric output power as the objective function and the inputs were the geometric parameters. The electrical output power values were about 269, 314, 338, and 893% higher than the values of the initial design. The second step was to consider the TEG conversion efficiency η TEG as the objective function. A η TEG rise is obtained for the optimal design at the same time with an important reduction of P. Finally, the third step was to use multi-objective optimi-

Two dimensionless parameters influence the maximisation of the electric output

<sup>x</sup> <sup>¼</sup> SP � ð Þ LP �<sup>1</sup>

<sup>y</sup> <sup>¼</sup> <sup>R</sup><sup>L</sup>

The thermal efficiency of the TEG can be improved while decreasing the slenderness ratio for large external load parameters. Yilbas and Sahin [35] obtained high conversion efficiency for the slenderness ratio 0 , x , 1 in the case of all the exter-

Zhang et al. [55] propose a design method of thermoelectric elements segmentation of TEG, considering their length as the first design parameter. The optimal length ratio, referring to the highest values of the maximum electric output power, and the thermoelectric conversion efficiency are influenced by thermoelectric materials, leg geometry and heat transfer characteristics. Zhang et al. [59] proposed two new parameters, namely, the power factor associated with the electric output power, and the efficiency factor associated with the thermoelectric conversion efficiency. These new parameters are useful for obtaining the optimum temperature

considering that the thermoelectric materials of the TEG legs have the same physical transport properties (α<sup>P</sup> = –αN; σ<sup>p</sup> = σN; k<sup>P</sup> = kN) and m is a variable factor that depends on the leg cross-sectional area, and on the heat transfer coefficients on

SN � ð Þ LN �<sup>1</sup> (31)

<sup>L</sup><sup>N</sup> � ð Þ <sup>σ</sup><sup>N</sup> � <sup>S</sup><sup>N</sup> �<sup>1</sup> (32)

ð Þ ZJ <sup>P</sup> <sup>¼</sup> <sup>α</sup><sup>2</sup> � <sup>σ</sup> � ð Þ <sup>1</sup> <sup>þ</sup> <sup>m</sup> � <sup>k</sup> �<sup>2</sup> (33) ð Þ ZJ <sup>η</sup> <sup>¼</sup> <sup>Z</sup> � ð Þ <sup>1</sup> <sup>þ</sup> <sup>m</sup> � <sup>k</sup> �<sup>1</sup> (34)

significant and the electric conversion efficiency will be low [9].

Thermoelectric Energy Harvesting: Basic Principles and Applications

DOI: http://dx.doi.org/10.5772/intechopen.83495

zation to improve both P and η TEG, simultaneously.

• slenderness ratio, which is a geometric parameter:

power and the conversion efficiency of TEG [35]:

• external load parameter:

nal load parameters.

range of each segment:

both TEG sides.

15

#### 2.5.2 TEG design for energy harvesting applications

In TEG systems, a crucial factor is the optimisation of the systems design, together with the heat source and heat sink attached to the TEG device. Industrial utilisation of TEGs needs other components (like heat exchangers and DC-DC converter) to form a powerful TEG [29].

The TEG performance is influenced not only by the low conversion efficiency, but also by the heat transfer conditions on the cold and hot sides of TEG and its geometry. The ΔT between two junctions depends on the good heat transfer between TEGs and heat sources or heat sinks. For this reason, the design and interactions between heat exchangers and TEGs are very important problems. There are two paths to solve these problems together. The first path is the optimisation of the TEGs system. The second path is the enhancement of the heat transfer at the TEG sides [55].

#### 2.5.2.1 Optimization of the TEG device

The TEG device optimisation is correlated with the impact of the geometry device [56]. It has been demonstrated that an important rise in the electric output power from TEG is obtained by changing the leg geometry. The leg geometry is optimised by determining the leg height and the number of thermocouples, leading to maximisation of electric output power or efficiency at given operating conditions. Therefore, there is interdependence between the optimal leg geometry and the electrical load resistance R<sup>L</sup> for a TEG. Hodes [23] presented a method to compute the leg geometry (number and height) that maximises the electric output power and η TEG with negligible or finite electrical contact resistance at TEG interconnects. If a TEG has a low number of legs, the energy conversion is low, because the R<sup>L</sup> is not sufficient to obtain an adequate high voltage. Inversely, if a TEG has too many legs, the total equivalent resistance of the TEG will increase and relatively high Joule losses will occur in the TEG when the load is supplied.

There is an optimal solution also for the leg length. If the leg is long, the electric output power is limited due to the increase in the internal resistance of the leg that limits the electric current. Conversely, a short leg will behave as a good thermal conductor that reduces the temperatures between its ends; hence, even though the

#### Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

internal electrical resistance will be low, the electric output power will not be significant and the electric conversion efficiency will be low [9].

Lavric et al. [57] demonstrated that the electric output power is influenced by the effects above mentioned (a reduction of the leg length leads to a reduction of the electrical resistance; an increase of the leg length leads to the higher temperature difference across the TEG). If the geometric parameters of the TEG (leg length, semiconductor pair number and the base area ratio of semiconductor columns to TEG) are optimised, the electric output power and the thermoelectric conversion efficiency are considerably improved. Such an improvement is also reported in [58]. The first step was to consider the electric output power as the objective function and the inputs were the geometric parameters. The electrical output power values were about 269, 314, 338, and 893% higher than the values of the initial design. The second step was to consider the TEG conversion efficiency η TEG as the objective function. A η TEG rise is obtained for the optimal design at the same time with an important reduction of P. Finally, the third step was to use multi-objective optimization to improve both P and η TEG, simultaneously.

Two dimensionless parameters influence the maximisation of the electric output power and the conversion efficiency of TEG [35]:

• slenderness ratio, which is a geometric parameter:

$$\boldsymbol{\omega} = \frac{\mathbf{S}\_{\mathbb{P}} \cdot (\mathbf{L}\_{\mathbb{P}})^{-1}}{\mathbf{S}\_{\mathbb{N}} \cdot (\mathbf{L}\_{\mathbb{N}})^{-1}} \tag{31}$$

• external load parameter:

the thermoelements with SnTe or PbTe produced low extra power, while the filled Skutterudite obtained an increment in efficiency from 10.5 to 13.6%. Further studies [47, 48] reported that the segmentation was efficient only for u ≤2: Ngan et al. [49] demonstrate that segmentation reduces the total efficiency by neglecting the compatibility factor of thermoelectric materials. Hung et al. [50] showed that the performance and the power production of the segmented TEG are three times bigger than a normal TEG. The analytical assessment concerning the effect of the leg geometry on the performance of the segmented TEG was performed in [51, 52]. Their conclusion is that both power and efficiency are increased when the segmented TEG is used. Vikhor and Anatychuk [53] carried out a theoretical analysis. The results showed an efficiency of the segmented TEGs bigger than 15% compared to the non-segmented TEGs. Zhang et al. [54] proposed a design method of optimization with predictive performance to obtain maximum conversion efficiency. In this case, the segmented modules consisted of Bi2Te3-based alloys and CoSb3-based skutterudites, with an efficiency of 12% when working under a Δt = 541°C. The very low losses and the good design based on the numerical evaluation showed that the

conversion efficiency was up to 96.9% of the theoretical efficiency.

In TEG systems, a crucial factor is the optimisation of the systems design, together with the heat source and heat sink attached to the TEG device. Industrial utilisation of TEGs needs other components (like heat exchangers and DC-DC

The TEG performance is influenced not only by the low conversion efficiency, but also by the heat transfer conditions on the cold and hot sides of TEG and its geometry. The ΔT between two junctions depends on the good heat transfer between TEGs and heat sources or heat sinks. For this reason, the design and interactions between heat exchangers and TEGs are very important problems. There are two paths to solve these problems together. The first path is the optimisation of the TEGs system. The second path is the enhancement of the heat transfer

The TEG device optimisation is correlated with the impact of the geometry device [56]. It has been demonstrated that an important rise in the electric output power from TEG is obtained by changing the leg geometry. The leg geometry is optimised by determining the leg height and the number of thermocouples, leading to maximisation of electric output power or efficiency at given operating conditions. Therefore, there is interdependence between the optimal leg geometry and the electrical load resistance R<sup>L</sup> for a TEG. Hodes [23] presented a method to compute the leg geometry (number and height) that maximises the electric output power and η TEG with negligible or finite electrical contact resistance at TEG interconnects. If a TEG has a low number of legs, the energy conversion is low, because the R<sup>L</sup> is not sufficient to obtain an adequate high voltage. Inversely, if a TEG has too many legs, the total equivalent resistance of the TEG will increase and relatively

There is an optimal solution also for the leg length. If the leg is long, the electric output power is limited due to the increase in the internal resistance of the leg that limits the electric current. Conversely, a short leg will behave as a good thermal conductor that reduces the temperatures between its ends; hence, even though the

high Joule losses will occur in the TEG when the load is supplied.

2.5.2 TEG design for energy harvesting applications

converter) to form a powerful TEG [29].

2.5.2.1 Optimization of the TEG device

at the TEG sides [55].

Green Energy Advances

14

$$\mathcal{Y} = \frac{R\_{\rm L}}{L\_{\rm N} \cdot \left(\sigma\_{\rm N} \cdot \mathcal{S}\_{\rm N}\right)^{-1}} \tag{32}$$

The thermal efficiency of the TEG can be improved while decreasing the slenderness ratio for large external load parameters. Yilbas and Sahin [35] obtained high conversion efficiency for the slenderness ratio 0 , x , 1 in the case of all the external load parameters.

Zhang et al. [55] propose a design method of thermoelectric elements segmentation of TEG, considering their length as the first design parameter. The optimal length ratio, referring to the highest values of the maximum electric output power, and the thermoelectric conversion efficiency are influenced by thermoelectric materials, leg geometry and heat transfer characteristics. Zhang et al. [59] proposed two new parameters, namely, the power factor associated with the electric output power, and the efficiency factor associated with the thermoelectric conversion efficiency. These new parameters are useful for obtaining the optimum temperature range of each segment:

$$(\text{Zf})\_P = \text{\textdegree \text{\textdegree } \sigma \cdot (1 + m \cdot k)^{-2}} \tag{33}$$

$$\left(\mathbf{Z}\right)\_{\eta} = \mathbf{Z} \cdot \left(\mathbf{1} + \boldsymbol{m} \cdot \boldsymbol{k}\right)^{-1} \tag{34}$$

considering that the thermoelectric materials of the TEG legs have the same physical transport properties (α<sup>P</sup> = –αN; σ<sup>p</sup> = σN; k<sup>P</sup> = kN) and m is a variable factor that depends on the leg cross-sectional area, and on the heat transfer coefficients on both TEG sides.

#### 2.5.2.2 Heat transfer enhancement at the hot and cold sides

The fins attached to the heat transfer surfaces are very important for enhancing the heat transfer at the hot and cold sides. One interface is between the heat sink and the TEG cold side, and the other interface is between the heat source and the TEG hot side.

An increment of the fin height and fin number results when the electric output power of the TEG rises [60]. An optimal connection between the height and the number of fins to provide the maximum net electric output power is obtained in Jang et al. [60]. The heat transfer increases when the fin number is higher and the fin height rises, due to the extension of the heat transfer area. However, when the height of the fin increases over a given value, the change in the output electrical power becomes less significant. Borcuch et al. [61] investigated the effect of hot side heat exchanger design on the operating parameters of a TEG. Furthermore, the heat sink connected to the TEG device must be thermally matched with the TEG to maximise the electric output power and voltage. In this case, the thermal interface losses are practically negligible, that means Theat sink ffi T<sup>c</sup> and Theat source ffi Th.

To maximise the output voltages of TEG, a big number of thermocouples are necessary, and their total thermal resistance must be equal to the thermal resistance of the heat sink. The reduced thermal resistance of the TEG decreases very much the temperature difference [62].

The thermal resistance of the heat sink is:

$$R\_{\rm hs} = \frac{T\_{\rm heat\ sink} - T\_{\rm amb}}{\dot{Q}\_{\rm h}} \tag{35}$$

• When <sup>R</sup>

in [26].

17

thermal resistance.

<sup>R</sup>hs ¼ 1, the electric output power has a peak. In this case, the lengths and

cross sections of thermoelectric legs are adapted, R ¼ Rhs and ΔT is equally

Also, when the heat sinks are attached to both sides of the TEG, the total thermal resistance (thermal interfaces resistances and thermal resistances of the heat sinks) is equal to the RTEG for maximum electric output power [62]. The contact resistance decreases the electric output power by decreasing ΔT across the TEG. Furthermore, the thermal contact resistance between the TEG and the heat sink or heat source is

Astrain et al. [64] demonstrated the significance of decreasing the thermal resistance between the heat source and the hot side of the TEG, as well as the cold side of TEG and the environment. The numerical model assesses the TEG performance, taking into account the heat exchangers attached on both sides of the TEG, the heat source, as well as the heat sink. The results obtained show a good accuracy of the model. The results demonstrated that increasing by 10% the thermal resistances of both heat exchangers, the electric output power is

improved by 8%. Martínez et al. [65] optimised the heat exchangers fixed on both sides of a TEG to maximise the electric output power. They have concluded that the thermal resistances of the heat exchangers are very important for TEG design. Zhou et al. [66] studied the heat transfer features of a TEG device. The heat transfer intensification on the cold side of the TEG leads to a significant

reduction of the temperature and thermal resistance on this side, and implicitly a rise of the electric output power of the TEG device. Furthermore, Zhou et al. [66] highlighted that the refrigerant which flows by heat exchangers produce higher net powers than conventional heat sink with fins. An in-depth review of the heat sink for TEG and parameters affecting TEG performance is presented

The refrigeration system of the TEG has been assessed by Aranguren et al. [30]. This system consists of a multi-channel heat exchanger attached to the cold side of the TEG, another heat exchanger used to decrease the refrigerant temperature, the pump to circulate the refrigerant, and the connecting pipes. A numerical model has been implemented to compute the total thermal resistance and the power consumption in the system components. In this model, all system elements have been included to obtain an accurate analysis. The combination of computational and experimental results shows that the system configuration leading to the maximum net power is different with respect to the configuration resulting in the lowest total

3. Applications using thermoelectrics in the power generation mode

The favourable characteristics of the thermoelectric devices promote the development of standalone TEGs for energy harvesting in a wide range of applications (Figure 8) as military, aerospace (e.g., powering spacecraft), biological systems (e.g., to power implanted pacemakers) and other applications (e.g., power for wristwatches or mobile communications) [67]. The key element to improve the energy conversion efficiency of TEG is the effect of waste heat recovery. Waste heat represents the heat produced by machines (e.g., exhaust pipes from automobiles), industrial processes (e.g., cooling towers, burnt solid waste and radioactive wastes), electrical equipment (e.g., kerosene lamps) and the human body. For various TEG applications (e.g., waste thermal power recovery using TEGs and powering of

divided between the heat sink and the TEG.

Thermoelectric Energy Harvesting: Basic Principles and Applications

decreased to reduce the contact effect [63].

DOI: http://dx.doi.org/10.5772/intechopen.83495

where Q\_ <sup>h</sup> the heat flow is given by Eq. (18) through the TEG, Theat sink is the heat sink temperature, and Tamb is the environmental temperature.

The thermal resistance and thermal conductance of TEG are linked with each other by an inverse ratio as:

$$R = \frac{1}{K} \tag{36}$$

The thermal energy through the TEG is written as:

$$
\dot{Q}\_h = \frac{T\_{\text{heat source}} - T\_{\text{amb}}}{R\_{\text{tot}}} \tag{37}
$$

considering that Rhs and R are connected in series with the total resistance Rtot ¼ R þ Rhs, and Theat source is the heat source temperature.

The following cases may be considered:


Thermoelectric Energy Harvesting: Basic Principles and Applications DOI: http://dx.doi.org/10.5772/intechopen.83495

2.5.2.2 Heat transfer enhancement at the hot and cold sides

TEG hot side.

Green Energy Advances

the temperature difference [62].

other by an inverse ratio as:

• If <sup>R</sup>

• If <sup>R</sup>

16

power.

The thermal resistance of the heat sink is:

sink temperature, and Tamb is the environmental temperature.

The thermal energy through the TEG is written as:

Rtot ¼ R þ Rhs, and Theat source is the heat source temperature.

The following cases may be considered:

to a limited electric output power.

The fins attached to the heat transfer surfaces are very important for enhancing the heat transfer at the hot and cold sides. One interface is between the heat sink and the TEG cold side, and the other interface is between the heat source and the

An increment of the fin height and fin number results when the electric output power of the TEG rises [60]. An optimal connection between the height and the number of fins to provide the maximum net electric output power is obtained in Jang et al. [60]. The heat transfer increases when the fin number is higher and the fin height rises, due to the extension of the heat transfer area. However, when the height of the fin increases over a given value, the change in the output electrical power becomes less significant. Borcuch et al. [61] investigated the effect of hot side heat exchanger design on the operating parameters of a TEG. Furthermore, the heat sink connected to the TEG device must be thermally matched with the TEG to maximise the electric output power and voltage. In this case, the thermal interface losses are practically negligible, that means Theat sink ffi T<sup>c</sup> and Theat source ffi Th. To maximise the output voltages of TEG, a big number of thermocouples are necessary, and their total thermal resistance must be equal to the thermal resistance of the heat sink. The reduced thermal resistance of the TEG decreases very much

> <sup>R</sup>hs <sup>¼</sup> <sup>T</sup>heat sink � <sup>T</sup>amb Q\_ h

where Q\_ <sup>h</sup> the heat flow is given by Eq. (18) through the TEG, Theat sink is the heat

The thermal resistance and thermal conductance of TEG are linked with each

<sup>R</sup> <sup>¼</sup> <sup>1</sup>

<sup>Q</sup>\_ <sup>h</sup> <sup>¼</sup> <sup>T</sup>heat source � <sup>T</sup>amb Rtot

considering that Rhs and R are connected in series with the total resistance

<sup>R</sup>hs , 1, a big heat source-to-environment ΔT occurs across the heat sink and ΔTTEG , ΔTheat sink. In this case, a reduction of the thermoelectric conversion efficiency η TEG is observed, leading to a reduction of the TEG electric output

<sup>R</sup>hs . 1, a big heat source-to-environment ΔT occurs across the TEG and ΔTTEG . ΔTheat sink. In this case, an increment of the η TEG is observed, leading

<sup>K</sup> (36)

(35)

(37)

• When <sup>R</sup> <sup>R</sup>hs ¼ 1, the electric output power has a peak. In this case, the lengths and cross sections of thermoelectric legs are adapted, R ¼ Rhs and ΔT is equally divided between the heat sink and the TEG.

Also, when the heat sinks are attached to both sides of the TEG, the total thermal resistance (thermal interfaces resistances and thermal resistances of the heat sinks) is equal to the RTEG for maximum electric output power [62]. The contact resistance decreases the electric output power by decreasing ΔT across the TEG. Furthermore, the thermal contact resistance between the TEG and the heat sink or heat source is decreased to reduce the contact effect [63].

Astrain et al. [64] demonstrated the significance of decreasing the thermal resistance between the heat source and the hot side of the TEG, as well as the cold side of TEG and the environment. The numerical model assesses the TEG performance, taking into account the heat exchangers attached on both sides of the TEG, the heat source, as well as the heat sink. The results obtained show a good accuracy of the model. The results demonstrated that increasing by 10% the thermal resistances of both heat exchangers, the electric output power is improved by 8%. Martínez et al. [65] optimised the heat exchangers fixed on both sides of a TEG to maximise the electric output power. They have concluded that the thermal resistances of the heat exchangers are very important for TEG design. Zhou et al. [66] studied the heat transfer features of a TEG device. The heat transfer intensification on the cold side of the TEG leads to a significant reduction of the temperature and thermal resistance on this side, and implicitly a rise of the electric output power of the TEG device. Furthermore, Zhou et al. [66] highlighted that the refrigerant which flows by heat exchangers produce higher net powers than conventional heat sink with fins. An in-depth review of the heat sink for TEG and parameters affecting TEG performance is presented in [26].

The refrigeration system of the TEG has been assessed by Aranguren et al. [30]. This system consists of a multi-channel heat exchanger attached to the cold side of the TEG, another heat exchanger used to decrease the refrigerant temperature, the pump to circulate the refrigerant, and the connecting pipes. A numerical model has been implemented to compute the total thermal resistance and the power consumption in the system components. In this model, all system elements have been included to obtain an accurate analysis. The combination of computational and experimental results shows that the system configuration leading to the maximum net power is different with respect to the configuration resulting in the lowest total thermal resistance.
