Thermal-Wave Diode

Based on the spatiotemporal modulation of thermal conductivity and volumetric heat capacity, we propose a thermal-wave diode characterized by the rectification of the heat currents carried by thermal waves. By transforming Fourier’s law for the heat flux and the diffusion equation for the temperature into equations with constant coefficients, it is shown that: (i) the rectification effect is generated by the simultaneous wavelike modulation of both thermal properties, such that it disappears in the absence of either of them, and (ii) the rectification factor can be optimized and tuned by means of the speed and phase difference of the variations of the heat capacity and thermal conductivity. High rectification factors, greater than 86%, are obtained for lower frequencies driving the propagation of thermal waves. The proposed thermal-wave diode is thus analogous to its electronic counterpart operating with modulated electrical currents and can open a vista for developing different types of thermal-wave logic components.

Figure 1

Scheme of a thermal-wave diode operating in the (a) forward and (b) backward configurations. Arrows along with their amplitudes indicate the propagation direction and intensity of the thermal waves generated by the excitation $\delta T\cos (\omega t)$.

Figure 2

(a) Propagation length of a thermal wave propagating in the $+x$ (${\mathrm{\Lambda }}_{+}$) and $-x$ (${\mathrm{\Lambda }}_{-}$) directions as a function of the normalized speed $\mathrm{\Gamma }$, for three phase shifts. (b) Amplitude profiles of the temperature field for the forward and backward configurations. Calculations are done for $f=f_c={\alpha }_0/\pi d^2$ and the dashed lines in (b) represent the numerical solution of Eq. (2) obtained through the finite difference method (FDM) [46].

Figure 3

Speed $\mathrm{\Gamma }$ dependence of the heat flux amplitudes at the (a) arrival and (b) departure positions for the forward and backward configurations. Calculations are done for $f=f_c$ and three representative phase shifts. Points represent the numerical solution of Eq. (2) obtained using the FDM [46].

Figure 4

Rectification factors for the heat fluxes carried by thermal waves at the (a) arrival and (b) departure positions, as functions of the normalized speed and frequency, respectively. Points represent the FDM numerical solution of Eq. (2) [46].