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INDEX
II)Figure of merit and output
1)Figure of merit
A standard thermocouple will thus be composed of two semiconductor branches : one doped N, other P, connected by a metal ensuring thermal conduction.
The output of a thermocouple is:  where W is the electric output provided and Q the heat provided by the hot source to the cold cource.
Expressed with the parameters of the thermocouple:
The term top translates the electric output and the term of bottom the thermal transfer of to the thermal diffusion process (term in KdT) with the Joule effect (term in I^2*R/2) and with the Peltier effect. While having Rl chooses so that the output is maximum, the output can be put in the form :
The first factor represents the output of Carnot of a heat engine. The second term is a positive factor lower than 1 due to the irreversible effects of the process of conversion. K is related to a number Z (figure of merit or figure of merit). The more Z is raised, the more K tends towards 1. Thus Z makes it possible to classify the aptitude of materials to convert a heat flow into electricity.
It is noticed that < img src=images/formule7.png align=center > (total thermal conductivity is that due to the crystal lattice plus that ensured by the electrons).
The choice of the adequate thermoelement is a compromise between a strong coefficient of Seebeck, a strong electric conductivity and a low thermal conductivity.
The figure of merit also depends on the temperature:
One sees well in this graph that each thermoelement has a restricted field where its figure of merit is maximum, i.e. a maximum output. It is thus of primary importance to choose adequate material as for the temperatures of the future application.
The materials arriving at the best compromise of the parameters of the figure of merit are the semiconductor (for example Bi2Te3). The latter have in particular a coefficient of very high Seebeck compared to metals (of the order of the mV.K -1).
2) Serialization
Only one thermocouple, even if it has a very good figure of merit, will never produce enough an exploitable tension since it will be of the order of the millivolt. It is thus necessary to put several thermocouples in series electrically to add their tensions but in parallel thermically in order to have the same difference in temperature with the ends of the thermocouples:
If this process thus makes it possible in theory to obtain important tensions, it is however limited by the fact that with each serialization, the internal resistance of the generator increases what decreases its output.
2) Segmentation
We saw that each semiconductor has a restricted field where its effectiveness is maximum. However along the thermocouple a variation in temperature settles, the semiconductor used then does not have the same effectiveness on all along the thermocouple.
One has recourse to the "segmented" generators : each branch of the thermocouple is then made up of the semiconductor which has a maximum effectiveness on their sites.
One can see below an example of segmented generator:
The problem with this kind comes from the thermal incompatibilities between materials used. Indeed they have different dilation coefficients, the structure is thus fragile.
3)Cascaded generators
To avoid the problems of the segmentation, one can make cascaded couples. An intermediate stage distributes the heat flow more uniformly, and one can adjust the heat flow which crosses each branch by modifying its section:
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