2.2.5 Calculating the current I when a load resistor RL is connected across the thermoelectric couple output terminals

If a load resistance RL is now connected across the output terminals of the thermoelectric couple, as shown in Figure 3(b), the current I can be expressed as:

2.2.1 Calculating the thermoelectric couple open-circuit voltage Voc

Voc ¼ α<sup>p</sup> � α<sup>n</sup>

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found by:

Figure 3.

in Kelvin.

16

According to [8], if we consider the thermoelectric couple in Figure 3 (a), and assume that no other heat arrives at the cold side Tc other than through the two thermoelectric legs, the thermoelectric couple open-circuit voltage Voc can be

A single thermoelectric couple configured as a thermoelectric generator with a volt meter measuring the opencircuit voltage Voc (a) and in (b) with a load resistor RL connected across the couple's output terminals [7].

where α<sup>p</sup> and α<sup>n</sup> is the Seebeck coefficient of the p-type and n-type pellets of the

The electrical resistivity ρ of each pellet can be found and/or measured, with a typical resistivity for p-type Bi2Te3 thermoelectric pellets of around 1.75 � <sup>10</sup>�<sup>3</sup> Ohms-centimetre, and for n-type Bi2Te3 pellets of around 1.35 � <sup>10</sup>�<sup>3</sup> Ohmscentimetre [10]. The resistance Rp of the p-type pellet can then be found by:

thermoelectric couple respectively, and may be found quoted in manufacturer literature or obtained by practical measurement. Typical values for Bi2Te3 thermoelectric couples are <sup>α</sup><sup>p</sup> of around 230 � <sup>10</sup>�<sup>6</sup> V/K and <sup>α</sup><sup>n</sup> of around �<sup>195</sup> � <sup>10</sup>�<sup>6</sup> V/K [9]. Th is the surface temperature of the hot side of the thermoelectric couple, and Tc is the surface temperature of the cold side of the thermoelectric couple, measured

2.2.2 Calculating the resistance Rp and Rn of the thermoelectric couple pellets

Rp <sup>¼</sup> Lpρ<sup>p</sup> Ap

ð Þ Th � Tc measured in volts (1)

measured in Ohms (2)

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$$I = \frac{V}{R\_T} \text{ measured in amperes} \tag{9}$$

hot junction from the heat source Th is used to balance the Peltier cooling effect in the thermoelectric couple, and an opposing flow of heat occurs due to the thermal conduction of the thermoelectric legs, and by Joule heating within the device. The

The opposing heat by conduction in the thermoelectric legs (or pellets) can be

where Kp and Kn are the thermal conductance of the p-type and n-type thermoelectric legs, respectively. The cooling effect is opposed by Joule heating Qj within

According to [8], it can be shown that half of the Joule heating passes to the sink Tc and half to the source Th, with each half equal to (Eq. (19)). The expression for the heat energy absorbed at the hot junction, which is the same as the cooling power

� � � <sup>I</sup>

Hence, the efficiency of the thermoelectric couple η can now be found by

<sup>η</sup> <sup>¼</sup> PL Qh

Substituting Qh from (Eq. (20)) and PL from (Eq. (14)) into (Eq. (21)), we

ð Þ <sup>α</sup>p�α<sup>n</sup> ð Þ Th�Tc RpþRnþRL � �<sup>2</sup>

In thermoelectricity, efficiency is expressed as the dimensionless figure-of-merit Z, or more commonly, expressed as a function of the temperature over which the device is operated ZT. The thermoelectric figure-of-merit Z describes the thermoelectric efficiency of a thermoelectric couple for a given pair of p-type and n-type

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

where α is the Seebeck coefficient of the thermoelectric couple, λ is the thermal

conductivity, and ρ is the couple's electrical resistivity. In the context of this

� �ITh � ð Þ Tc � Th Kp <sup>þ</sup> Kn

<sup>2</sup> Rp <sup>þ</sup> Rn � �

RL

� � � <sup>I</sup>

2 ð Þ RpþRn 2

λρ (23)

� �ILTh measured in watts (17)

� � measured in watts (18)

measured in watts (19)

<sup>2</sup> measured in watts

(20)

(21)

(22)

cooling effect at the source Qsource can be found by:

Qj <sup>¼</sup> <sup>I</sup>

� �ITh � ð Þ Tc � Th Kp <sup>þ</sup> Kn

the thermoelectric legs, found by:

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DOI: http://dx.doi.org/10.5772/intechopen.85670

Qh ¼ α<sup>p</sup> � α<sup>n</sup>

(Eq. (16)), and written as:

η ¼

α<sup>p</sup> � α<sup>n</sup>

thermoelectric materials, and is normally shown as:

obtain:

19

found by:

Qsource ¼ α<sup>p</sup> � α<sup>n</sup>

Qlegs ¼ ð Þ Th � Tc Kp þ Kn

<sup>2</sup> Rp <sup>þ</sup> Rn � � 2 !

at the hot side of the thermoelectric couple Qh can now be found by:

where V is the closed-circuit voltage, and RT is the total resistance of the thermoelectric couple and the load. It is possible to find RT using:

$$R\_T = R\_p + R\_n + R\_L \text{ measured in Ohms} \tag{10}$$

Using (Eq. (1)) and (Eq. (10)), the current I can be found by:

$$I = \frac{(a\_p - a\_n)(T\_h - T\_c)}{R\_p + R\_n + R\_L} \text{ measured in amperes} \tag{11}$$
