(1.53)
The current through the circuit can be obtained as
Thus, the equation for the power is given by
By introducing a parameter
When R in = R ex, the external load has the maximum power (P max),
(1.57)
Figure 1.23 shows the variations of the output power with the external load resistance at different temperature differences [34]. The output power increases when the temperature difference increases. However, at the optimal output power, the corresponding load resistance is independent of the temperature difference.
The equation for the efficiency (η) can be obtained as it is the ratio of the output power to the incident heat (Q in) into the system,
(1.58)
Heat energy transport through this system with the two thermoelectric legs, p‐ and n‐type legs. The incident heat at the hot side is balanced by the Peltier effect at the contacts between the legs and the metal electrodes, and the heat transfers due to the temperature gradient. The heat transferring from the hot to the cold side is equivalent to the Peltier effect at the contacts and the heat out from the cold side. Thus, the equations at the two boundaries (hot and cold side) are given by
Figure 1.23 Variations of the power output of a TEG with the load resistance at ΔT = 10 and 20 K.
Source: Madan et al. [34]. © American Chemical Society.
(1.60)
By ignoring the Thomson effect, the equation (1.50) for one leg becomes
(1.61)
Using the boundary conditions of T(0) = T H and T(L) = T C, the following equations can be obtained,
(1.62)
(1.63)
At x = 0,
(1.64)
Using Eq. (1.54) in Eq. (1.59), the expression for Q in can be obtained as below,
