Performance improvement of a four-terminal thermal amplifier with multiple energy selective tunnels

https://doi.org/10.1016/j.enconman.2018.04.026Get rights and content

Highlights

  • A new model of the thermal amplifier connected by four energy filters is established.

  • The equivalently coupling system proposed consists of two three-terminal heat humps.

  • The maximum coefficient of performance and rate of heat-pumping are calculated.

  • The operating regions of the amplifier are optimally determined.

  • The optimum selection criteria of main parameters are provided.

Abstract

A new model of the energy selective electron (ESE) device composed of four electron reservoirs and four energy filters is proposed. The device can work as a thermal amplifier, which may be equivalent to a coupling system consisting of two three-electron-reservoir heat pumps. Expressions for the heat-pumping rate (HPR) and coefficient of performance (COP) of the device are analytically derived through the heat flows of two-terminal ESE devices. The maximum HPR and COP are calculated. It is found that the maximum HPR of the coupling system can attain 2 times of that of a three-electron-reservoir heat pump while its COP is still equal to that of a three-electron-reservoir heat pump. Moreover, the effects of the chemical potentials of electron reservoirs, central levels of energy filters, half width at half maximum of energy filters on the HPR and COP of the device are discussed in detail. The optimal configuration of the device is determined. The cut-off value of the half width at half maximum of energy filters is calculated. The optimum selection criteria of main parameters are provided.

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 εHL, εHR, εLC, and εRC, as shown in Fig. 1(a), where the temperatures and chemical potentials of electron reservoirs H and C are, respectively, (TH, μH) and (TC, μCμ0), electron reservoirs L and R have the same temperature TP but different chemical potentials μL and μR, and the temperatures of electron reservoirs satisfy a relation: TH>TP>TC. Electron reservoirs can

Results and discussion

When δ is very small, Eqs. (5), (6), (7), (8) can be, respectively, simplified asqP=2πδh(fH-fR)(ΔεH+ΔεC)=4πδh(fH-fR)(ΔH-ΔC-εHL+εLC)=4πδh(fH-fR)(-ΔH+ΔC+εHR-εRC),ψ=ΔεH+ΔεCΔεH=ΔH-ΔC+εLC-εHLΔH+μ0-εHL=ΔH-ΔC-εHR+εRCΔH+μ0-εHR,Ṡ=2πδh(fH-fR)ΔεH+ΔεCT0-ΔεHTH-ΔεCTC,andfH-fR=fR-fC=fC-fL=fL-fH,where ΔεHεHR-εHL, ΔεCεLC-εRC, ΔH(εHR+εHL)/2-μ0, and ΔC(εLC+εRC)/2-μ0. In such a case, qL=2πδh(fH-fR)(εLC-εHL), qR=2πδh(fH-fR)(εHR-εRC), α=εHL-μHεHL-εHR, ψL=εHL-εLCεHL-μH, and ψR=εHR-εRCεHR-μH.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 εHR+εHL=εLC+εRC=2μ0 and μL+μR=2μ0=2μH 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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