Thermal rectification device

Abstract

The first and second media are coupled via evanescent waves generated by surface phonon polaritons thermally excited on surfaces of the first and second media. First and second media made of the same material are disposed with a gap formed between for cutting off thermal conduction and the heat transfer between them is performed via the thermally excited evanescent waves. A third medium is provided on a surface of the first medium on a side toward the second medium. Heat flux flows from the second medium to the first medium in a first state wherein the second medium has a first temperature T.sub.H and the first medium has a second temperature T.sub.L lower than the T.sub.H differ in intensity from heat flux which flows from the first to the second medium in a second state wherein the first medium has the T.sub.H and the second medium has the T.sub.L.

Claims

1. A thermal rectification device comprising: a first medium and a second medium, the first medium and the second medium being of the same material, and the first and second media being coupled via evanescent waves generated by surface phonon polaritons thermally excited on surfaces of the first and second media, a third medium provided on a surface of the first medium on a side toward the second medium; a gap formed between the second medium and the third medium for cutting off thermal conduction therebetween, heat transfer between the first and second media being performed mainly via the thermally excited evanescent waves, and the gap comprising a relative permittivity different from each relative permittivity of the second medium and the third medium; wherein heat flux which flows from the second medium to the first medium in a first state in which the second medium has a first temperature T.sub.H and the first medium has a second temperature T.sub.L lower than the first temperature T.sub.H differs in intensity from heat flux which flows from the first medium to the second medium in a second state in which the first medium has the first temperature T.sub.H and the second medium has the second temperature T.sub.L.

2. The thermal rectification device according to claim 1, wherein a fourth medium is provided on a surface of the second medium on a side toward the first medium, the fourth medium comprising a relative permittivity different from the relative permittivity of the gap and the gap formed between the third medium and the fourth medium.

3. The thermal rectification device according to claim 1, wherein the third medium has a relative permittivity and a thickness such that in the first state, there exists a first frequency range in which the resonance frequency of surface phonon polaritons thermally excited at the interface between the first medium and the third medium coincides with the resonance frequency of surface phonon polaritons thermally excited on the surface of the second medium on the side toward the first medium; and in the second state, the first frequency range is wider than a second frequency range in which the resonance frequency of surface phonon polaritons thermally excited at the interface between the first medium and the third medium coincides with the resonance frequency of surface phonon polaritons thermally excited on the surface of the second medium or the second frequency range does not exist.

4. The thermal rectification device according to claim 2, wherein the third medium and the fourth medium have a relative permittivity and a thickness, respectively, such that in the first state, there exists a first frequency range in which the resonance frequency of surface phonon polaritons thermally excited at the interface between the first medium and the third medium coincides with the resonance frequency of surface phonon polaritons thermally excited at the interface between the second medium and the fourth medium; and in the second state, the first frequency range is wider than a second frequency range in which the resonance frequency of surface phonon polaritons thermally excited at the interface between the first medium and the third medium coincides with the resonance frequency of surface phonon polaritons thermally excited at the interface between the second medium and the fourth medium or the second frequency range does not exist.

5. The thermal rectification device according to claim 1, wherein heat flux which flows from the second medium to the first medium in the first state is larger in intensity than heat flux which flows from the first medium to the second medium in the second state.

6. The thermal rectification device according to claim 1, wherein a distance between the first medium and the second medium is 300 nm or less.

7. The thermal rectification device according to claim 1, wherein the relative permittivities of the first and second media have a real part of −1 or less as measured in a temperature range and a frequency band of the evanescent waves when heat transfer is performed via the evanescent waves.

8. The thermal rectification device according to claim 1, wherein the first medium and the second medium are at least one of silicon carbide (SiC), silicon dioxide (SiO.sub.2), and silicon (Si) doped with impurities.

9. The thermal rectification device according to claim 1, wherein, when a direction in which heat flux of high intensity flows is defined as a forward direction and a direction in which heat flux of low intensity flows is defined as a reverse direction, the third medium has such a relative permittivity and thickness as to maximize heat flux of the forward direction.

10. The thermal rectification device according to claim 3, wherein, when a direction in which heat flux of high intensity flows is defined as a forward direction and a direction in which heat flux of low intensity flows is defined as a reverse direction, the third medium has such a relative permittivity and thickness as to maximize heat flux of the forward direction.

11. The thermal rectification device according to claim 2, wherein, when a direction in which heat flux of high intensity flows is defined as a forward direction and a direction in which heat flux of low intensity flows is defined as a reverse direction, the fourth medium has such a relative permittivity and thickness as to maximize heat flux of the forward direction.

12. The thermal rectification device according to claim 4, wherein, when a direction in which heat flux of high intensity flows is defined as a forward direction and a direction in which heat flux of low intensity flows is defined as a reverse direction, the fourth medium has such a relative permittivity and thickness as to maximize heat flux of the forward direction.

13. The thermal rectification device according to claim 1, wherein a thickness t.sub.3 and a relative permittivity ε.sub.3 of the third medium satisfy $\begin{array}{cc}\left[\mathrm{Math}.1\right]& \\ t_3=\frac{1}{2k_m}\ln \frac{\left({\mathrm{.Math.}}_3-1\right)\left({\mathrm{.Math.}}_3^2-{.Math.{\mathrm{.Math.}}_1.Math.}^2\right)}{\left({\mathrm{.Math.}}_3+1\right){.Math.{\mathrm{.Math.}}_3+{\mathrm{.Math.}}_1.Math.}^2}& \left(1\right)\end{array}$ where ε.sub.1 is a relative permittivity of the first medium, k.sub.m is 40k.sub.0 to 50k.sub.0, k.sub.0 =2π/λ.sub.0, and λ.sub.0 is a wavelength of evanescent waves which maximizes heat flux in a forward direction, which is a direction in which heat flux of higher intensity flows as compared with that in the opposite direction.

14. The thermal rectification device according to claim 3, wherein a thickness t.sub.3 and a relative permittivity ε.sub.3 of the third medium satisfy $\begin{array}{cc}\left[\mathrm{Math}.1\right]& \\ t_3=\frac{1}{2k_m}\ln \frac{\left({\mathrm{.Math.}}_3-1\right)\left({\mathrm{.Math.}}_3^2-{.Math.{\mathrm{.Math.}}_1.Math.}^2\right)}{\left({\mathrm{.Math.}}_3+1\right){.Math.{\mathrm{.Math.}}_3+{\mathrm{.Math.}}_1.Math.}^2}& \left(1\right)\end{array}$ where ε.sub.1 is a relative permittivity of the first medium, k.sub.m is 40k.sub.0 to 50k.sub.0, k.sub.0 =2π/λ.sub.0, and λ.sub.0 is a wavelength of evanescent waves which maximizes heat flux in a forward direction, which is a direction in which heat flux of higher intensity flows as compared with that in the opposite direction.

15. The thermal rectification device according to claim 1, wherein the third medium is amorphous silicon and has a thickness t.sub.3 of 1 nm to 2 nm.

16. The thermal rectification device according to claim 2, wherein the third medium is amorphous silicon and has a thickness t.sub.3 of 1 nm to 2 nm.

17. The thermal rectification device according to claim 1, wherein the third medium is a material having a relative permittivity of 1.5 to 2.5 and has a thickness t.sub.3 of 5 nm to 20 nm.

18. The thermal rectification device according to claim 2, wherein the third medium is a material having a relative permittivity of 1.5 to 2.5 and has a thickness t.sub.3 of 5 nm to 20 nm.

19. The thermal rectification device according to claim 1, wherein the third medium is at least one selected from the group consisting of barium fluoride (BaF.sub.2), strontium fluoride (SrF.sub.2), lead fluoride (PbF.sub.2), calcium fluoride (CaF.sub.2), rubidium bromide (RbBr), cesium bromide (CsBr), cesium chloride (CsCl), potassium chloride (KCl), and sodium chloride (NaCl).

20. The thermal rectification device according to claim 2, wherein the fourth medium is at least one selected from the group consisting of barium fluoride (BaF.sub.2), strontium fluoride (SrF.sub.2), lead fluoride (PbF.sub.2), calcium fluoride (CaF.sub.2), rubidium bromide (RbBr), cesium bromide (CsBr), cesium chloride (CsCl), potassium chloride (KCl), and sodium chloride (NaCl).

Description

BRIEF DESCRIPTION OF DRAWINGS

(1) FIG. 1 is a view showing the configuration of a thermal rectification device according to a first embodiment of the present invention;

(2) FIG. 2A is a characteristic diagram showing the forward heat flux spectrum of the heat rectification device of the first embodiment and the blackbody radiation spectrum;

(3) FIG. 2B is a characteristic diagram showing the heat flux spectra of the heat rectification device of the first embodiment in the forward and reverse biased states;

(4) FIG. 3A is a characteristic diagram showing the relationship between the relative permittivity and the thickness of a third medium, which partially constitutes the heat rectification device of the first embodiment;

(5) FIG. 3B is a characteristic diagram showing the relationship between the rectification coefficient and the thickness of the third medium, which partially constitutes the heat rectification device of the first embodiment;

(6) FIG. 4 is a view showing the configuration of a thermal rectification device according to a second embodiment of the present invention; and

(7) FIG. 5 is a view showing the configuration of a conventional thermal rectification device.

DESCRIPTION OF EMBODIMENTS

(8) Embodiments of the present invention will next be described in detail with reference to the drawings. The following embodiments are mere examples, and the present invention is not limited thereto.

(9) First Embodiment

(10) FIG. 1 shows, in (a), the configuration of a thermal control device A10 according to a first embodiment of the present invention. A first medium 11 and a second medium 12 are of silicon carbide. The first medium 11 and the second medium 12 are rectangular parallelepipeds whose square xy planes serve as main surfaces 21 and 22, respectively, and whose thicknesses extend in the z direction. As compared with the area of the xy plane, the thickness is sufficiently thick. The second medium 12 and a third medium 13 are disposed in parallel with each other with a gap 10 formed therebetween so as to separate them from each other by a distance d.sub.0. The gap 10, which provides the fixed distance d.sub.0, is formed by a thermally insulative spacer 15 having a square shape and provided around the main surface 21. The gap 10 is a vacuum layer, but may be an air layer. Also, a thermally insulative material having a sufficiently low thermal conductivity may exist in the entirety or a portion of the gap 10. The main surface 21 of the first medium 11 and the main surface 22 of the second medium 12 face each other with a distance (gap) d therebetween. The third medium 13 is coated on the main surface 21 of the first medium 11. The third medium 13 is of amorphous silicon.

(11) Even when the first medium 11 and the second medium 12 are of the same material, by means of the third medium 13 of amorphous silicon being coated on the surface of the first medium 11, the permittivity of the first medium 11 can be equivalently controlled. Therefore, unidirectional heat flow can be obtained. Specifically, as shown in (b) of FIG. 1, when the temperature T.sub.2 of the second medium 12 is maintained at 500K and the temperature T.sub.1 of the first medium 11 is maintained at 300K, the resonance frequency of surface phonon polaritons thermally excited on the main surface 21 of the first medium 11 coincides with the resonance frequency of surface phonon polaritons thermally excited on the main surfaces 22 of the second medium 12, whereby heat flux of high intensity flows in the forward direction. On the contrary, as shown in (c) of FIG. 1, when the temperature T.sub.2 of the second medium 12 is maintained at 300K and the temperature T.sub.1 of the first medium 11 is maintained at 500K, heat flux is reversed. In this case, since the resonance frequency of surface phonon polaritons thermally excited on the main surface 21 of the first medium 11 does not coincide with the resonance frequency of surface phonon polaritons thermally excited on the main surfaces 22 of the second medium 12, the heat flux flowing in the reverse direction is sufficiently smaller in intensity than the heat flux flowing in the forward direction.

(12) Thermal conduction components are p-polarization and s-polarization of evanescent waves and p-polarization and s-polarization of propagation waves (radiation waves). In the case where the first medium 11 and the second medium 12 face each other with a very small gap therebetween, heat flow is dominated by the p-polarization component of evanescent waves; therefore, attention is focused herein on p-polarization. With the second medium 12 having a high temperature and the first medium 11 having a low temperature, the Poynting vector of p-polarization of evanescent waves in the state in which the net heat flow is directed from the second medium 12 to the first medium 11 (forward temperature biased state) is expressed as follows, where (ε.sub.3).sup.1/2ω/c<β.

(13) $\begin{array}{cc}\left[\mathrm{Math}.2\right]& \\ .Math.S_{\mathrm{Forward}}\left(\omega ,\beta ,T_L,T_H\right).Math.~\left(\theta \left(\omega ,T_H\right)-\theta \left(\omega ,T_L\right)\right){\int }_{\sqrt{{\mathrm{.Math.}}_3}\frac{\omega }{c}}^{+\infty }\frac{4\beta d\beta }{{\pi }^2}[\frac{{\mathrm{.Math.}}_3{\kappa }_0{\kappa }_3}{{\left({\mathrm{.Math.}}_3{\kappa }_0+{\kappa }_3\right)}^2}\mathrm{Im}\left(r_{31,p}\left(\omega ,\beta ,T_L\right)\right)\mathrm{Im}\left(r_{02,p}\left(\omega ,\beta ,T_H\right)\right)\frac{\exp \left(-2{\kappa }_3{t}_3-2{\kappa }_0{d}_0\right)}{{.Math.D_{\mathrm{ee}}\left(\omega ,\beta ,T_L,T_H\right).Math.}^2}]& \left(2\right)\\ \left[\mathrm{Math}.3\right]& \\ \theta \left(\omega ,T\right)=\frac{h{\omega }^{-}}{\exp \left(\frac{h{\omega }^{-}}{k_{B}T}\right)-1}& \left(3\right)\\ \left[\mathrm{Math}.4\right]& \\ D_{\mathrm{ee}}\left(\omega ,\beta ,T_L,T_H\right)=1-r_{31,p}\left(\omega ,\beta ,T_L\right)r_{30,p}\left(\omega ,\beta \right)\exp \left(-2{\kappa }_3{t}_3\right)-r_{03,p}\left(\omega ,\beta \right)r_{02,p}\left(\omega ,\beta ,T_H\right)\exp \left(-2{\kappa }_0{d}_0\right)-r_{31,p}\left(\omega ,\beta ,T_L\right)r_{02,p}\left(\omega ,\beta ,T_H\right)\exp \left(-2{\kappa }_3{t}_3-2{\kappa }_0{d}_0\right)& \left(4\right)\\ \left[\mathrm{Math}.5\right]& \\ {\kappa }_3=\sqrt{{\beta }^2-{{\mathrm{.Math.}}_3\left(\frac{\omega }{c}\right)}^2}\left(\sqrt{{\mathrm{.Math.}}_3}\frac{\omega }{c}<\beta \right)& \left(5\right)\\ \left[\mathrm{Math}.6\right]& \\ {\kappa }_0=\sqrt{{\beta }^2-{\left(\frac{\omega }{c}\right)}^2}\left(\frac{\omega }{c}<\beta \right)& \left(6\right)\end{array}$

(14) Variables T.sub.1 and T.sub.2 of S.sub.Forward (ω,β,T.sub.1,T.sub.2) and S.sub.Reverse (ω,β,T.sub.1,T.sub.2) are the temperatures of the first medium 11 and the second medium 12, respectively. Subscripts 1, 2, 3, and 0 denote the first medium 11, the second medium 12, the third medium 13, and the gap 10, respectively. Also, k is the wavenumber; β is the wavenumber in the xy plane; r.sub.ij,p is the Fresnel coefficient of p-polarization at the interface between a medium i and a medium j; and < > denotes an ensemble average. Silicon carbide varies in permittivity with temperature and frequency. When the temperature T.sub.H is 500K and the temperature T.sub.L is 300K, the resonance wavelength, at which the forward heat flux is maximized, is 10.6 μm. In the vicinity of the resonance wavelength of 10.6 μm, the permittivity of amorphous silicon is 3.742 (no loss).

(15) With the first medium 11 having a high temperature and the second medium 12 having a low temperature, the Poynting vector of p-polarization of evanescent waves in the state in which the net heat flux is directed from the first medium 11 to the second medium 12 (reverse temperature biased state) is expressed as follows, where (ε.sub.3).sup.1/2ω/c<β.

(16) $\begin{array}{cc}\left[\mathrm{Math}.7\right]& \\ .Math.S_{\mathrm{Reverse}}\left(\omega ,\beta ,T_H,T_L\right).Math.~\left(\theta \left(\omega ,T_H\right)-\theta \left(\omega ,T_L\right)\right){\int }_{\sqrt{{\mathrm{.Math.}}_3}\frac{\omega }{c}}^{+\infty }\frac{4\beta d\beta }{{\pi }^2}[\frac{{\mathrm{.Math.}}_3{\kappa }_0{\kappa }_3}{{\left({\mathrm{.Math.}}_3{\kappa }_0+{\kappa }_3\right)}^2}\mathrm{Im}\left(r_{31,p}\left(\omega ,\beta ,T_H\right)\right)\mathrm{Im}\left(r_{02,p}\left(\omega ,\beta ,T_L\right)\right)\frac{\exp \left(-2{\kappa }_3{t}_3-2{\kappa }_0{d}_0\right)}{{.Math.D_{\mathrm{ee}}\left(\omega ,\beta ,T_H,T_L\right).Math.}^2}]& \left(7\right)\end{array}$

(17) Therefore, the forward heat flux and the reverse heat flux are given by the following Eqs. (8) and (9), respectively.
[Math. 8]
φ.sub.Forward=∫.sub.0.sup.+∞<S.sub.Forward(ω,β,T.sub.L,T.sub.H)>dω  (8)
[Math. 9]
φ.sub.Reverse=∫.sub.0.sup.+∞<S.sub.Reverse(ω,β,T.sub.H,T.sub.L)>dω  (9)

(18) FIG. 2A compares the forward heat flux spectrum of the thermal rectification device of the first embodiment with that of blackbody radiation. The distance d between the first medium 11 and the second medium 12 was set to 100 nm, and the thickness t.sub.3 of the third medium 13 (amorphous silicon) was set to 1 nm. For facilitating comparison with blackbody radiation, the vertical axis of FIG. 2A is of logarithmic scale. As is understood from FIG. 2A, evanescent p-polarization provides heat flux whose intensity greatly exceeds that of heat flux provided by blackbody radiation.

(19) FIG. 2B shows heat flux spectra in the forward biased state and the reverse biased state. As is understood from FIG. 2B, in the forward biased state, the heat flux spectrum has a peak at the wavelength of 10.6 μm and, in the reverse biased state, heat flux decays at the position of the peak.

(20) Let us obtain conditions for generation of a forward heat flux peak. With (ε.sub.3).sup.1/2ω/c being sufficiently smaller than β, the imaginary part of the second term, the third term, and the fourth term of Eq. (4) become sufficiently small as compared with the real part of the second term of Eq. (4). Therefore, Eq. (4) can be approximated as follows.
[Math. 10]
D.sub.ee(T.sub.L)˜1−Re(r.sub.31,p(T.sub.L)r.sub.30,pexp(−2k.sub.mt.sub.3)  (10)

(21) The following conditions for maximizing the forward heat flux given by Eq. (8) are obtained by replacing the differential with respect to the thickness t.sub.3 of the third medium in Eq. (8) with zero.

(22) $\begin{array}{cc}\left[\mathrm{Math}.11\right]& \\ 1-\mathrm{Re}\left(r_{31,p}\left(T_L\right)\right)r_{30,p}\exp \left(-2{\kappa }_m{t}_3\right)=0& \left(11\right)\\ \left[\mathrm{Math}.12\right]& \\ 1-\mathrm{Re}\left(\frac{{\mathrm{.Math.}}_1-{\mathrm{.Math.}}_3}{{\mathrm{.Math.}}_1+{\mathrm{.Math.}}_3}\right)\frac{1-{\mathrm{.Math.}}_3}{1+{\mathrm{.Math.}}_3}\exp \left(-2{\kappa }_m{t}_3\right)=0& \left(12\right)\end{array}$

(23) Eq. (12) is solved, thereby yielding Eq. (1) mentioned above.

(24) The rectification coefficient is defined as follows.

(25) $\begin{array}{cc}\left[\mathrm{Math}.13\right]& \\ \mathrm{RF}=\frac{{\varphi }_{\mathrm{Forward}}-{\varphi }_{\mathrm{Reverse}}}{{\varphi }_{\mathrm{Reverse}}}& \left(13\right)\end{array}$

(26) The rectification coefficient was calculated for the case where the temperature T.sub.H was set to 500K, the temperature T.sub.L was set to 300K, and the relative permittivity ε.sub.3 and the thickness t.sub.3 of the third medium 13 were varied. FIG. 3A shows the relationship between the thickness t.sub.3 and the relative permittivity ε.sub.3 for the maximum rectification coefficient. FIG. 3B shows the relationship between the maximum rectification coefficient and the thickness t.sub.3. As is understood from FIGS. 3A and 3B, even though the relative permittivity ε.sub.3 of the third medium is varied in the range of 2 to 14, by means of the thickness t.sub.3 being selected appropriately according to the relative permittivity ε.sub.3 on the basis of the relationship of FIG. 3A, the rectification coefficient becomes constant around 0.7 as shown in FIG. 3B. Also, it is understood that Eq. (1) accurately expresses the relationship between the thickness t.sub.3 and the relative permittivity ε.sub.3 for the maximum rectification coefficient.

(27) Second Embodiment

(28) FIG. 4 shows the configuration of a thermal rectification device A20 according to a second embodiment of the present invention. In the thermal rectification device A10 of the first embodiment, only the first medium 11 is coated with amorphous silicon, thereby having the third medium 13 thereon. In the thermal rectification device A20 of the second embodiment, amorphous silicon is coated on the main surface 22 of the second medium 12 on a side toward the first medium 11, thereby forming a fourth medium 14 having a thickness different from that of the third medium 13. Configurational features identical in function with those of the first embodiment are denoted by like reference numerals or signs. The material of the fourth medium 14 may differ from that of the third medium 13 in temperature and frequency characteristics of permittivity. The employment of the configuration of the second embodiment provides a thermal rectification device whose degree of freedom of design is further improved and whose fabrication is further facilitated.

(29) In the above embodiments, the distance d between the main surface 21 of the first medium 11 and the main surface 22 of the second medium 12 is 100 nm. However, no particular limitation is imposed on the distance d so long as evanescent waves can be efficiently coupled. This is for the following reason: when the distance d is much less than the wavelength (10.6 μm) of evanescent waves generated through excitation of surface phonon polaritons, the evanescent waves are efficiently coupled together, resulting in resonance between surface phonon polaritons on the two interfaces. For example, a distance d of 300 nm or less, 200 nm or less, 100 nm or less, or a 50 nm or less can be used.

(30) In the present invention, the third medium 13 and the fourth medium 14 can be of, in addition to the above-mentioned material, barium fluoride (BaF.sub.2), strontium fluoride (SrF.sub.2), lead fluoride (PbF.sub.2), calcium fluoride (CaF.sub.2), rubidium bromide (RbBr), cesium bromide (CsBr), cesium chloride (CsCl), potassium chloride (KCl), or sodium chloride (NaCl), for use with a material of the first and second media 11 and 12, such as SiC or SiO.sub.2, whose real part of permittivity is −1 or less in the frequency band of evanescent waves generated through thermal excitation of surface phonon polaritons.

(31) Particularly, in the case of the first and second media 11 and 12 of SiC, desirably, the third and fourth media 13 and 14 are of barium fluoride (BaF.sub.2), strontium fluoride (SrF.sub.2), or calcium fluoride (CaF.sub.2). In this case, forward heat flux can be increased in intensity, and the rectification coefficient can be increased.

INDUSTRIAL APPLICABILITY

(32) The present invention can be applied to devices which require unidirectional heat flow, such as heat sinks, heat storage devices, and heat retaining devices.