The design of a thermal rectifier

– The idea that one can build a solid-state device that lets heat flow more easily in one way than in the other, forming a heat valve, is counter-intuitive. However the design of a thermal rectifier can be easily understood from the basic laws of heat conduction. Here we show how it can be done. This analysis exhibits several ideas that could in principle be implemented to design a thermal rectifier, by selecting materials with the proper properties. In order to show the feasibility of the concept, we complete this study by introducing a simple model system that meets the requirements of the design. While electronics has been able to control the flow of charges in solids for decades, the control of heat flow still seems out of reach, and this is why, when a paper showed for the first time how to build a “thermal rectifier” [1], the thermal analogue of the electrical diode, it attracted a great deal of attention [2]. The idea that one can build a solid-state device that lets heat flow more easily in one way than in the other, forming a heat valve, is counterintuitive and may even appear in contradiction with thermodynamics. Actually this is not the case, and the design of a thermal rectifier can be easily understood from the basic laws of heat conduction. Here we show how it can be done. This analysis exhibits several ideas that could in principle be implemented to design a thermal rectifier, by selecting materials with the proper properties. In order to show the feasibility of the concept, we complete this study by introducing a simple model system that meets the requirements of the design. Such devices could be useful in nanotechnology, and particularly to control he heat flow in electronic chips. Let us consider the heat flow along the x direction, in a material in thermal contact with two different heat baths at temperatures T1 for x = 0 and T2 for x = L (Fig. 1-a). We consider the general case of an inhomogeneous material with a local thermal conductivity λ(x, T ) which depends not only on space but also on temperature. To discuss the main ideas only the x dependence is introduced, but the same analysis can be extended to a more general case, at the expense of heavier calculations. The heat flow Jf is given by Jf = −λ[x, T (x)] dT (x) dx , (1)