4. Analysis of thermoelectric elements

transferred from the cooled space to the hot-side heat sink through n-type and p-type semiconductor thermoelements which rejects the heat to the environment. The heat flow direction through the semiconductor materials will be reversed if the electric current direction is

A typical TE module usually consists of a large number of n-type and p-type bulk semiconductor thermoelements that are connected electrically in series and thermally in parallel and

Commercially available TE coolers are used in applications where design criteria of the cooling system include factors such as high reliability, low weight, small size, intrinsic safety for hazardous electrical environments and accurate temperature control. TE coolers are more appropriate for unique applications such as space missions, medical and scientific equipment

TE cooling devices are used for cooling small volumes, such as portable and domestic refrigerator, portable icebox and beverage can cooler [12, 16–21], where the cooling requirements are not too high. In general, the COP for both domestic and portable thermoelectric refrigerators is usually less than 0.5, when operating at an inside/outside temperature difference between 20 and 25C. Electronic devices like PC processors produce very large amount of heat during their operation which add great challenge to the thermal management as reliable operation temperature for these electronic devices has to be maintained. TE cooling devices have also been applied to scientific and laboratory equipment cooling for laser diodes and integrated circuit chips [22] to reduce the thermal noise and the leakage current of the electronic components where conventional passive cooling technologies cannot fully meet the heat dissipation requirements. For example, cooling CdZnTe detectors for X-ray astronomy between 30 and 40C can reduce the leakage current of the detectors and allows the use of pulsed reset preamplifiers and long pulse shaping times, which significantly improves their energy resolution. Integrating thin film TE coolers with microelectronic circuits has been implemented using micromachining technology. TE cooler appears to be especially favorable for automotive applications [23]. Besides the automobile air-conditioning system and automobile mini refrigerators, researchers also utilized TE device to control car seat temperature to either cooling down or heating up [24].

Some researchers are trying to improve thermoelectric domestic air-conditioning systems [25–27] hoping that these systems can be competitive with the current widely used vapor compression systems. They investigated TE cooling devices for small-scale space's conditioning application in buildings [26]. A TE cooling unit was assembled and generated up to 220 W of cooling capacity with a maximum COP of 0.46 under the input electrical current of 4.8 A for each module.

Active thermal window (ATW) and transparent active thermoelectric wall (PTA) were also introduced for room cooling application in applications where conventional air-conditioning

sandwiched between two ceramic plates, as illustrated in Figure 2.

3. Applications using thermoelectric coolers

where low COP is not an apparent disadvantage.

reversed.

250 Bringing Thermoelectricity into Reality

The basic unit of the TE cooler is the n-type and p-type thermoelements. A bottom-up modeling approach is to construct the model at element level with the assumption that both types of thermoelements are exactly the same but opposite direction of the Peltier-Seebeck effect.

In the cooling mode, the cooling capacity Qc = (mcp)c (Tcout - Tcin), the heat dissipated in the hotside heat sink Qh = (mcp)h (Thout - Thin), the electric input power W=Qh - Qc, and the cooling COPc can be expressed by:

$$\text{COP}\_{\text{c}} = \frac{Q\_{\text{c}}}{W} = \frac{1}{\frac{T\_{\text{hut}} - T\_{\text{cin}}}{T\_{\text{out}} - T\_{\text{cin}}} \text{C}\_{r} - 1} \tag{1}$$

where Tcin is the temperature of the inlet fluid in the cold side of the TE system, Tcout is the temperature of the outlet fluid in the cold side of the TE system, Thin is the temperature of the inlet fluid in the hot side of the TE system, Thout is the temperature of the outlet fluid in the hot side of the TE system, (mcp)c is the thermal conductance of cold side of the TE system, (mcp)h is the thermal conductance of hot side of the TE system, m is the mass rate of the fluid, cp is the specific heat capacity of the fluid and C<sup>r</sup> = ð Þ mcp <sup>h</sup> ð Þ mcp <sup>c</sup> is the heat capacity ratio. In the heating mode, COPh<sup>¼</sup> Qh <sup>W</sup> ¼ 1 + COPc.

If some of the parameters for TE elements are available, the ideal COPc (COPC,id) and COPh (COPh,id) can be expressed as:

$$\text{COP}\_{\text{C,id}} = \frac{Q\_c}{W} = \frac{\alpha\_{pn} T\_c - \frac{\text{KRAT}}{V} - \frac{1}{2}V}{V + \alpha\_{pn} \Delta T} \tag{2}$$

$$\text{COP}\_{\text{h,id}} = \frac{Q\_h}{W} = \frac{\alpha\_{pn} T\_h - \frac{\text{KRAT}}{V\_R} + \frac{1}{2}V}{V + \alpha\_{pn} \Delta T} \tag{3}$$

where αpn is the Seebeck coefficient, R is the electrical resistivity, K is the thermal conductivity, V is electrical applied volt and ΔT = Th�T<sup>c</sup> is the temperature difference between the cold and the hot side of thermoelements at the ceramic plate locations.

For the optimum working voltage Vopt and optimum working current Iopt,

$$\mathbf{V\_{opt}} = \frac{\alpha\_{pn} \,\Delta T}{\sqrt{1 + Z T\_m} - 1} \tag{4}$$

coolers, the expression for the cooling rate qi per unit area for the ith stage, depending on the COP of the ith stage and on the cooling rate per unit area of the ith stage qI in connection with

In this context, each stage, that is considered from the heat source to the heat sink, must have a cooling capacity higher than the one in the previous stage. Truly, each stage will reject both the extracted heat from the previous stage and the electrical power supplied to the stage. Theoretical study for internally cascaded multistage TE couples showed that an enhancement of a 25.2% in the maximum COP can be achieved by using cascaded 3-stage TE modules [39]. A

As shown by the primary criterion of merit, a good thermoelectric material should possess high Seebeck coefficient, low thermal conductivity and high electrical conductivity. However, these three parameters are interrelated; hence they have to be optimized to get the maximized ZT [41, 42]. The changes in these parameters will unlikely lead to a net increase in ZT, since any favorable change in one parameter will be accompanied by an unfavorable change in the other parameters. For instance, if the electrical conductivity is too low, we might like to increase the carrier concentration. However, during increasing the carrier concentration which in turn will increase the electrical conductivity, the Seebeck coefficient will also decrease and the electronic contribution to the thermal conductivity will increase. This dilemma forced the maximum ZT of any thermoelectric material to be held at ZT = 1 for many years [43]. The devices made of

Conventional thermoelectric materials are bulk alloy materials such as Bi2Te3, PbTe, SiGe and CoSb3. Eventually it was determined that the most efficient bulk thermoelectric materials are high carrier concentration alloyed semiconductors. The high carrier concentration results in a good electrical conductivity while optimizing the electrical properties can be achieved by varying the carrier concentration. Transport of phonons (quantized lattice vibrations which carry heat) can be disrupted by alloying, which results in a reduced thermal conductivity. For this approach, it was discovered that good thermoelectric materials are phonon-glass electroncrystal material [44, 45], where high mobility electrons are free to transport charge and heat but the phonons are disrupted at the atomic scale from transporting heat. The recent trend to optimize the thermoelectric material's performance is achieved by reducing the material thermal conductivity, especially the lattice thermal conductivity [46]. Reducing the lattice thermal conductivity can be achieved by adding low sound velocity heavy elements, such as Bi, Te, and Pb. Examples of commercial thermoelectric alloys include BixSb2\_xTe3 at room temperature,

A new strategy for high efficiency "phonon-liquid electron-crystal" thermoelectric materials where a crystalline sublattice for electronic conduction is surrounded by liquid like ions was

1400 W TE air-conditioning system using multiple TE modules was investigated [40].

these materials were operated at a power conversion efficiency of only 4–5%.

PbTe–PbSe at moderate temperature, and Si80Ge20 at high temperature.

I�1 :… <sup>1</sup> <sup>þ</sup> COP�<sup>1</sup>

I�i

(11)

http://dx.doi.org/10.5772/intechopen.75791

Thermoelectric Cooling

253

the heat source, can be presented by [38]:

qi <sup>¼</sup> qi <sup>1</sup> <sup>þ</sup> COP�<sup>1</sup>

5. Development of thermoelectric materials

I <sup>1</sup> <sup>þ</sup> COP�<sup>1</sup>

$$\mathbf{I}\_{\rm opt} = \frac{V\_{\rm opt}}{R} = \frac{\alpha\_{\rm pu} \,\Delta T / R}{\sqrt{1 + Z T\_{\rm m}} - 1} \tag{5}$$

The corresponding maximum COPc,d, i.e., COPc,opt, will be;

$$\text{COP}\_{c, \text{opt}} = \frac{Tc}{T\_h - T\_c} \frac{\left(\sqrt{1 + ZT\_m} - \frac{T\_h}{T\_c}\right)}{\left(\sqrt{1 + ZT\_m} + 1\right)} \tag{6}$$

where T<sup>m</sup> is the average temperature of the thermocouple defined as:

$$\mathbf{T\_m} = \frac{1}{2} (T\_h + T\_c) \tag{7}$$

Similarly, the optimum coefficient of performance of heating COPh,opt can be expressed as:

$$\text{COP}\_{\text{h,opt}} = \frac{T\_h}{T\_h - T\_c} \left( 1 - 2 \frac{\sqrt{1 + ZT\_m} - 1}{ZT\_m} \right) \tag{8}$$

A comprehensive parameter that described the thermoelectric characteristics is the figure of merit of the thermocouple Z which can be defined as:

$$\mathbf{Z} = \frac{\left(\alpha\_p - \alpha\_n\right)^2}{\left(\mathbf{KR}\right)\_{\min}} = \frac{\alpha\_{pn}^2}{\left(\mathbf{KR}\right)\_{\min}}\tag{9}$$

This parameter can be made dimensionless by multiplying it by T (the average temperature of the hot side and the cold side of the TE module):

$$\text{ZT} = \frac{\alpha\_{pn}^2 T}{\left(\text{KR}\right)\_{\text{min}}} \tag{10}$$

The value of Z is related only to the physical properties of the thermocouple material. The higher the figure of merit Z for the material, the better the thermoelectric properties it has. The best commercial thermoelectric materials currently have ZT values around 1.0. The highest ZT value reported in research is about 3 at temperature of 550 K [36].

Maximizing Qc and COP can been obtained by optimizing some parameters like the number of thermoelement pairs for each stage and the applied electrical current [37]. For cascaded coolers, the expression for the cooling rate qi per unit area for the ith stage, depending on the COP of the ith stage and on the cooling rate per unit area of the ith stage qI in connection with the heat source, can be presented by [38]:

$$\eta\_i = \eta\_i \left( 1 + \mathbb{C}OP\_I^{-1} \right) \left( 1 + \mathbb{C}OP\_{I-1}^{-1} \right) \dots \left( 1 + \mathbb{C}OP\_{I-i}^{-1} \right) \tag{11}$$

In this context, each stage, that is considered from the heat source to the heat sink, must have a cooling capacity higher than the one in the previous stage. Truly, each stage will reject both the extracted heat from the previous stage and the electrical power supplied to the stage. Theoretical study for internally cascaded multistage TE couples showed that an enhancement of a 25.2% in the maximum COP can be achieved by using cascaded 3-stage TE modules [39]. A 1400 W TE air-conditioning system using multiple TE modules was investigated [40].
