Optimization of the rectification factor of radiative thermal diodes based on two phase-change materials

https://doi.org/10.1016/j.ijheatmasstransfer.2020.119739Get rights and content

Highlights

  • Analytical description and optimization of the rectification factors of the plane, cylindrical, and spherical radiative diodes operating with two phase-change materials.

  • Metal-insulator transition of the emissivity of phase change materials.

  • Rectification of far-field heat currents.

Abstract

We have theoretically studied and optimized the thermal rectification of plane, cylindrical and spherical radiative thermal diodes operating with terminals of two phase-change materials, whose emissivities significantly change within a narrow interval of temperatures. Analytical expressions for the optimal rectification factors of these three diodes are derived and analyzed comparatively. Optimal rectification factors of 82%, 86% and 90.5% are obtained for the plane, cylindrical and spherical diodes made up with terminals of Ge2Sb2Te5 and VO2 operating with a temperature difference of 450300=150 K, respectively. The spherical geometry thus represents a suitable shape to optimize the rectification of radiative heat currents. Furthermore, it is shown that higher rectification factors can potentially be achieved by using phase-change materials with emissivities contrasts higher than those of Ge2Sb2Te5 and VO2. We demonstrate that radiative thermal diodes based on two phase-change materials are able to operate with rectification factors higher than the corresponding ones of diodes involving a single phase-change material. The obtained results thus shed light on the phase-change materials required for optimizing the rectification factor of radiative thermal diodes with different geometries.

Introduction

Thermal diodes transporting heat in a preferred direction and blocking it in the opposite one have recently attracted significant attention due to their promising applications on heat control and nanoscale thermal modulation [1], [2], [3], [4]. The unusual behavior of thermal diodes have paved the way for controlling the rate of heat flows in a similar way as is done with their electric current counterparts in modern electronic devices. Over the last few years, the rectification effect has been theoretically studied through thermal diodes driven by electrons [5], photons [6], [7], [8], [9], [10], phonons [3], [4], [11], [12], [13], [17], [18], quantum dots, hybrid quantum structures [14], [15], [16], and nanoporous silicon devices [17]. The experimental study of the diode effect, on the other hand, was done by using quantum dots [19], carbon nanotubes structures [20], graphene nanoribbons [21], nanoporous graphene [22], solid-liquid phase change thermal diodes [23], as well as electrostatic [24] and bulk oxide materials [25].

One of the main methods to rectify heat flows consists of using phase-change materials (PCMs), whose optical, electrical and thermal properties significantly change with temperature, in a relatively narrow interval of temperatures. These changes are generated by the correlated interactions of phonons and electrons inside a PCM [26] and can be applied for developing thermal memories [27], thermal memristors [28], [29], optical switching [30], thermal rectifier [31], [32], thermal switch [33] radiative thermal diodes [34], [35], [36], [37], and radiative thermal transistors [38], [39] operating in both the near- and far-field regimes [26], [34], [38], [40]. This wide variety of promising applications has motivated the interest on PCMs, such as vanadium dioxide (VO2), nitinol, Ge2Sb2Te5 (GST), whose emissivities can be thermally driven [26], [34], [40]. These three thermochromic materials have recently attracted great attention in both experimental and theoretical studies due to their metal-insulator transition (MIT) at temperatures near room temperature. For example, the emissivities of GST and VO2 undergo the MIT within the temperature ranges of 420 K  < T < 430 K and 340 K  < T < 345 K, respectively [41]. The fact that the MIT of VO2 occurs in a temperature interval of only 5 K has motivated its application as one of the terminals of a radiative thermal diode [34], whose rectification factor can be as high as 90%. This significant rectification is more than four times the typical ones obtained without PCMs [36], which indicates the great potential of these materials to rectify heat flows.

Taking into account that a thermal diode is composed of two terminals and that two PCMs provide more degrees of freedom than a single PCM to tailor the heat transport between them, the rectification factor of radiative thermal diodes is expected to be optimized by the combined effect of two PCMs, as was proposed for conductive thermal diodes [42], [43]. For instance, Yang et al. [44], determined rectification factors up to 50% and 80% for a conductive thermal diode made up of two PCMs, whose thermal conductivities vary linearly and quadratically with temperature, respectively. Furthermore, a high rectification ratio of 147% was also obtained by Kang et al. [45] for a conductive thermal diode operating with two PCMs. These rectification factors are higher than the ones obtained for conductive thermal diodes base on a single PCM [42], [43]. This fact indicates that two PCMs could also be applied to enhance the rectification factor of radiative thermal diodes, which is not reported in the literature yet, to the best of our knowledge

The goal of this work is to theoretically optimize the thermal rectification effect of plane, cylindrical and spherical radiative thermal diodes based on two PCMs. This is comparatively done by considering the temperature dependence of the emissivities of each PCM within their MITs. Simple analytical expressions are derived and analyzed for the optimal rectification factors of these three diodes supporting thermal radiation generated by a relatively narrow temperature difference between their terminals. Our calculations show that the rectification factor can be raised significantly by using two PCMs instead of the single PCM.

Section snippets

Theoretical modeling

Let us consider two semi-infinite plates consisting of GST and VO2 exchanging heat through radiation as a result of their temperature difference ThTc>0, as illustrated in Fig. 1(a) and (b), respectively. The two plates are separated by a vacuum gap of thickness d much longer than the involved thermal wavelengths to ensure the far-field regime of heat transport. In the forward configuration [Fig. 1(a)], the heat flow qF flows from GST to VO2, while in the backward one [Fig. 1(b)], the heat flow

Results and discussions

Fig. 4 (a) shows the heat flows exchanged by the terminals of a plane diode operating in the forward and backward configurations, as functions of the temperature Th. Note that both heat flows qF and qB exhibit a nearly linear increase with Th and change of slope at temperatures around the transition temperatures (Th ≈ T0n with n=1,2) of the PCMs emissivities. According to Fig. 3, the transition of qB at Th=340.6 K is related to the MIT of VO2, while that of qF at Th=343.9 K is driven by the MIT

Conclusion

We have theoretically analyzed and optimized the rectification factors of plane, cylindrical and spherical radiative thermal diodes with terminals made up of two phase-change materials. This has been done by deriving analytical expressions for the optimal rectification factors of these three diodes. It has been shown that combined effect of two phase-change materials along with the geometry of the thermal diode has a significant impact on its rectification factor. Optimal rectification factors

Declaration of Competing Interest

Authors declare that there is no conflict of interest among them.

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