A temperature difference ∆Tg in such a thermocouple generates an electric potential. Following the Seebeck effect, the resulting output voltage U for N pairs of thermocouples is
(2.7)
where αs denotes the Seebeck coefficient in [V/K] of the thermocouple.
The ohmic resistance causes thermal losses of an electric current I in a conductor of a resistance R, also known as Joule heating PJ
(2.8)
In a heterogeneous material consisting of materials A and B, an electric flow at the material junction yields a heat flow. This is described by the Peltier effect, where πAB is the Peltier coefficient of the material in [V], with
(2.9)
In a homogeneous material, the emission and absorption of heat due to temperature difference in a conductor is represented by the Thomson effect. The Thomson coefficient in [V/K] is
(2.10)
The influence of these effects on the TEG performance depends on the size, design and the application environment. Freunek et al. have investigated the detailed modeling of the performance of TEG [33].
Any temperature difference of an environment couples into the TEG with a thermal resistance Kg. Kg is optimized when it equals the sum of the coupling resistance of the hot and the cold Th and Tc side of the TEG, respectively, where
(2.11)
The maximum achievable temperature difference decreases with increasing miniaturization. The heat sink needs to be dimensioned in a sufficient size, to make a temperature difference usable for a thermoelectric conversion. The size of the heat sink therefore is mostly the limit to miniaturization in TEG systems.
The maximum power output of a TEG Pout can be approximated to [33]
(2.12)
The thermoelectric figure of merit Z is device specific. Figure 2.3 provides a schematic of a TEG.
The output voltage of TEG typically ranges around a few 100 mV. Therefore, DC/DC converters are required.
In indoor industrial applications, the heat from machines can be used with the room temperature as cold sink. In these applications, and especially if the system size is not limited, TEG systems can achieve output powers in the milliwatt range. The same is valid in cold areas or seasons if the temperature difference between outside and indoors can be made usable. However, in most consumer and office applications, the main source for a temperature potential is the difference between wall temperatures and the room temperature. In this case, a TEG will yield a few microwatts.
Figure 2.3 Schematic of a TEG with n- and p-type legs, and a hot and cold side.
2.4 Electrochemical Potential
The electrochemical potential from biological sources can be converted to electric energy. Biologic sources have the advantage that the host continuously and actively recharges these power sources by eating and drinking or photosynthesis. Such a host for a biochemical converter can be a plant, an animal or a human.
The first research on the use of biochemical energy, such as adenosine triphosphate (ATP) in the human body, was the ATP powered nanomotor by Cornell University [34]. Voltree Power’s bioenergy harvester uses the electrochemical potential resulting from the different pH concentration between soil and a plant [35]. The output voltage was reported to reach 50 to 200 mV for an estimated short circuit current between 0.1 to 1 mA [36]. The induced voltage U for an output voltage Uʹ results from the Nernst equation
(2.13)
where R = 8.31447 Jmol-1K-1 denotes the molecular gas constant, F = 96485,34 C mol-1 the Faraday constant, T the temperature, n the number of transmitted electrons and DpH the difference of both potentials.
Other than in some horticultural and agricultural applications, indoor bioelectrochemical potentials are almost solely found in animals and humans. Rasmussen and coworkers demonstrated a biofuel cell with a power of 55 μW, that was implanted in a cockroach [37]. The output voltage was 0.2 V. Such implantable fuel cells can work as an alternative to batteries or cabled solutions with a main application field in medicine. Technical challenges include the low output voltage of around 0.2–0.4 V and the size, stability and nontoxicity of the cathodes. A review of the design, the current state-of-the-art and challenges in biofuel cells has been provided by Zebda et al. [38].
2.5 Electromagnetic Transmission
Other than all other forms of energy, electromagnetic emission, including within the optical range, can be sent on purpose for charging applications, as outlined in the introduction of this book by Joe Paradiso. This section focuses on the use of radio frequencies (RF) based on antennas (radio frequency harvesting).
In a simplified model, the efficiency εRF of these systems is calculated from
(2.14)
The output power thus depends on the emitted power, its distance to the RF harvester, and amount of damping in between. How much power the harvester can receive and convert to usable electric power, depends on the specific antenna design, its damping, and the rectification losses. Recent reviews on this topic have been provided by Serdijn et al. and Cansiz et al. [39, 40].
The inductive charging of electric toothbrushes is a daily life example of such systems.
2.6 Atomic Batteries
Atomic batteries use the energy of the decay of a radioactive isotope. This energy is converted to electrical energy by different types of generators, such as thermoelectric or optical. Therefore, these systems can be defined as semi-ambient systems. The applied radioisotopes, such as Plutonium-238, are unstable. Their resulting continuous heat emission is used for electric conversion. In the early seventies, some implanted pacemakers were powered by radioisotope batteries based on Plutonium-238 and a TEG. About ten years later, Lithium-ion batteries superseded atomic pacemakers. Lal and coworkers demonstrated the excitation of a piezoelectric converter with radioisotopes [41]. Currently, atomic batteries have their main application field in space. A review on the topic has been published by Kumar [42].
