Performance improvement of a four-terminal thermal amplifier with multiple energy selective tunnels
Introduction
Thermoelectric devices [1], [2], [3], [4] may be used as both refrigerators and power generators [5], [6], [7]. The problem how to enhance the conversion efficiency of thermoelectric devices has attracted great attention. With the development of nanotechnology in recent years, many new appearing materials [8], [9], [10] with nanostructure can effectively improve the conversion efficiency of thermoelectric devices [11], [12]. On the other hand, novel concepts [13], [14], [15], [16] were constantly used in the design and fabrication of thermoelectric devices. For example, energy selective electron (ESE) devices [17], [18], [19] are a class of the thermoelectric devices with innovative design. By using an appropriate energy filter, it was predicted that ESE engines can be reversibly operated with the Carnot efficiency [17], [18], [19]. A series of experimental [20], [21], [22], [23] and theoretical [24], [25], [26] works related to ESE devices were carried out.
At present the ESE devices [27], [28], [29] consisting of two heat reservoirs with two different chemical potentials connected by an energy filter is a class of the most studied ESE devices. It was found that the performance of a two-terminal ESE engine can be greatly improved by adding an electron reservoir and an energy selective tunnel [13]. When such a design concept was used in ESE refrigerators [30], [31], the performance of refrigerators can be also improved effectively. It will be found that such a design concept is very significant for an ESE thermal amplifier [32].
In this paper, a new model of the thermal amplifier consisting of four electron reservoirs connected by four energy selective tunnels is proposed. It is expounded that such a thermal amplifier may be equivalent to a coupling system consisting of two three-electron-reservoir heat pumps. It is proved that the heat-pumping rate (HPR) of the coupling system can be doubled while the coefficient of performance (COP) of the coupling system is still maintained to be equal to that of a three-electron-reservoir thermal amplifier. Such a property of the thermal amplifier is similar to that of the electronic cooling device proposed in Ref. [33], in which the cooling power is doubled without reducing the COP of the cooling device. Moreover, the effects of some parameters on the HPR and COP of the amplifier are discussed in detail. The maximum HPR and COP of the thermal amplifier are determined. The selective criteria of main parameters, which are helpful to the design and operation of the thermal amplifier, are provided.
Section snippets
Model description
The ESE device considered here is composed of four electron reservoirs marked by H, C, L, and R and four ESE tunnels labeled as , , , and , as shown in Fig. 1(a), where the temperatures and chemical potentials of electron reservoirs H and C are, respectively, (, ) and (, ), electron reservoirs L and R have the same temperature but different chemical potentials and , and the temperatures of electron reservoirs satisfy a relation: . Electron reservoirs can
Results and discussion
When is very small, Eqs. (5), (6), (7), (8) can be, respectively, simplified asandwhere , , , and . In such a case, , , , , and .It is very
Conclusions
We have systemically evaluated the performance characteristics of a four-terminal ESE device and obtained some important results, which are summarized as follows.
- (i)
The four-terminal thermal amplifier composed of four electron reservoirs and four energy filters may be equivalent to a coupling system consisting of two three-electron-reservoir heat pumps.
- (ii)
Both and are the necessary conditions that the HPR and COP attain their respective maxima. At the states of the
Acknowledgments
This work has been supported by the National Natural Science Foundation (No. 11675132), People’s Republic of China.
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