Conductive thermal diode based on two phase-change materials

doi:10.1016/j.ijthermalsci.2020.106393

International Journal of Thermal Sciences

Volume 153, July 2020, 106393

https://doi.org/10.1016/j.ijthermalsci.2020.106393 Get rights and content

Abstract

The thermal rectification of a conductive thermal diode made up of two phase-change materials, whose thermal conductivities significantly change within a narrow interval of temperatures, is theoretically studied and optimized. This is done by deriving analytical expressions for the temperature profiles, heat fluxes and rectification factor. An optimal rectification factor of 60% is obtained for a thermal diode operating with terminals of VO $_{2}$ and Polyethylene with a temperature difference of 250 K spanning the metal–insulator transition of both materials. It is shown that this high rectification of a conductive thermal diode could be maximized even more by increasing the thermal conductivity variations of both diode terminals. The obtained results can thus be useful to guide the development of phase-change materials capable of optimizing the rectification of conductive heat fluxes.

Introduction

Thermal diodes allowing the heat exchange between two terminals in a given direction and blocking it in the opposite one, have attracted significant attention over the past decade, due to their potential applications in heat control [1], [2], [3]. This thermal rectification is analogous to the electrical one driven by electronic diodes and has been studied through thermal diodes operating with photons [4], [5], [6], [7], phonons [3], [8], [9], [10], [11], [12], electrons [13] and quantum structures [14], [15]. This phenomenon was first experimentally observed by Starr [16] at the interface between copper/cuprous oxide and then observed in carbon nanotubes structures [17], [18], dielectric quantum dots [19], phase-change materials (PCMs) [20], [21], [22], [23] and bulk materials [24].

Thermal rectification of conductive heat fluxes is generally generated by the temperature dependence of the thermal conductivities of the diode terminals [25] and therefore it can, in principle, be achieved with arbitrary solid materials subjected to a sufficiently large temperature gradient. Based on the Fourier’s law of heat conduction, Yang et al. [26] modeled and optimized the rectification ratio of a conductive thermal diode made up of two terminals, whose thermal conductivities follow either a linear or a quadratic dependence on temperature. For the linear variation, they obtained a maximum rectification ratio of 0.5, which increases to 0.86, for the quadratic dependence. These relatively high rectification ratios required a temperature difference greater than $100$ K between the diode terminals, which could be difficult and expensive to achieve in practice. This drawback can be overcome by means of PCMs, such as vanadium dioxide (VO $_{2}$ ), nitinol, and polyethylene (PE), whose thermal conductivities strongly change in a relatively narrow interval of temperatures [27], [28], [29], [30], [31], [32], [33]. These PCMs with a strong phonon–electron correlation have recently attracted a lot of experimental and theoretical interest, due to their metal–insulator transition (MIT) at temperatures close to room temperature. For instance, the thermal conductivities of VO $_{2}$ and PE typically change within a relatively small ranges of temperature $340$ K $<$ $T < 345$ K and $395$ K $<$ $T < 400$ K, respectively [34], [35]. The fact that the MIT of VO $_{2}$ occurs in a temperature range of only $5$ K has motivated its application in combination with a non-PCM, as the terminal of a conductive thermal diode, however, the maximal rectification factor obtained was lower ( $\sim 20 %$ ) [35] than that reported by Yang et al. [26] This indicates that the operation of a conductive thermal diode with both terminals made up of PCMs could enable not only to maximize its rectification factor, but also to reduce the temperature difference between its terminals, as was recently proposed [36]. Based on an alternative definition of the rectification factor, Hyungmook et al. [37] recently determined a rectification factor of $147 %$ for a thermal diode with the terminals of VO $_{2}$ and PE, whose thermal conductivities significantly change with temperatures. This relatively high rectification was obtained by describing the thermal conductivities of both PCMs as step functions, which is similar but not equal to their real behaviors, as the phase transitions of VO $_{2}$ and PE occur in a temperature interval greater than 5 K. Therefore, a more realistic description of the thermal conductivities of the rectification of thermal diodes based on two PCMs is thus required.

In this work, we theoretically study the optimization of the rectification factor of a conductive thermal diode made up of a junction of VO $_{2}$ and PE. This is done by taking into account the temperature dependence of the thermal conductivities of these PCMs within their phase transitions. Simple analytical expressions for the temperature profiles, heat fluxes and optimal rectification factor are derived and analyzed for the steady-state heat conduction. The present study is thus based on the combination of two PCMs, which are expected to yield higher rectification factors than a thermal diode based on a single PCM, which we addressed in a previous work [35].

Section snippets

Theoretical modeling

Let us consider a system of two phase change materials exchanging heat through steady-state conduction as a result of their temperature difference $T_{h} - T_{c} > 0$ , as illustrated in Fig. 1(a) and (b), respectively. In the forward configuration [Fig. 1(a)], the heat flux $q_{F}$ flows from PCM1 to PCM2, while in the backward one [Fig. 1(b)], the heat flux $q_{B}$ occurs in the opposite direction, as a result of the interchange of the temperatures $T_{h}$ and $T_{c}$ . The values of $q_{F}$ and $q_{B}$ are driven by the thermal

Results and discussion

Fig. 3 shows the temperature evolution of the forward ( $q_{F}$ ) and backward ( $q_{B}$ ) heat fluxes of a conductive thermal diode operating with terminals of VO $_{2}$ and PE. Note that both $q_{F}$ and $q_{B}$ exhibit a nearly linear increase with $T_{h}$ , such that their difference is positive ( $q_{F} - q_{B} > 0$ ), for most temperatures higher than the VO $_{2}$ transition one ( $T_{01} = 342.5$ K). The slope change of $q_{F}$ is due to the MIT transition of VO $_{2}$ at $T_{h} = T_{01}$ , such that the difference $q_{F} - q_{B}$ increases for $T_{h} ≫ T_{01}$ . The heat fluxes $q_{F}$ and $q_{B}$

Conclusions

We have theoretically analyzed and optimized the rectification factor of a conductive thermal diode made up of a junction between two phase-change materials, whose thermal conductivities significantly change in a narrow interval of temperatures. This has been done by deriving analytical expressions for the temperature profiles, heat fluxes and rectification factor. A rectification factor up to $60 %$ have been determined for a conductive thermal diode operating with terminals of VO $_{2}$ and

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

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Conductive thermal diode based on two phase-change materials

Abstract

Introduction

Section snippets

Theoretical modeling

Results and discussion

Conclusions

Declaration of Competing Interest

Int. J. Therm. Sci.

Nanosci. Microsc. Therm.

Int. J. Therm. Sci.

Int. J. Thermal Sci.

Int. J. Heat Mass Transfer

Front. Energy Res.

Carbon

Int. J. Thermal Sci.

Maximal rectification ratios for idealized bi-segment thermal rectifiers

Sci. Rep.

Colloquium: Phononics: Manipulating heat flow with electronic analogs and beyond

Rev. Modern Phys.

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Phys. Rev. Lett.

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J. Appl. Phys.

Near-field radiative transfer based thermal rectification using doped silicon

Appl. Phys. Lett.

Thermal diode: Rectification of heat flux

Phys. Rev. Lett.

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Phys. Rev. E

Thermal conduction and rectification in few-layer graphene y junctions

Nanoscale

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Phys. Rev. Lett.

Sufficient conditions for thermal rectification in hybrid quantum structures

Phys. Rev. Lett.

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Phys. Rev. E

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J. Appl. Phys.

Thermal rectification in carbon nanotube intramolecular junctions: Molecular dynamics calculations

Phys. Rev. B