Thermal and shape topological robustness of heat switchers using nematic liquid crystals

One interesting way to control heat is to use devices designed by transformation thermics, where artificial media are used. However, once manufactured (either repelling or concentrating heat, for example), besides being mono-purpose, such devices are designed according to a specific geometric boundary conditions. Another problem is the temperature dependence of the materials employed, since their properties are sometimes considered temperature-invariant. In this paper, we show that a previously proposed bi-objective heat switcher (Phys. Rev. E 89, 020501(R) (2014)) is in fact robust against temperature and geometric deformations, due to the topological properties of the molecular nematic orientation. Using a geometrical approach for heat propagation, by performing finite element simulations, we show that a device made by concentric cylinders with thermotropic nematic liquid crystal between them, sustains its functionality even with their molecular thermal conductivities depending on the temperature, achieving a 60% increase and a 44% decrease in the heat flux for each mode. Utilizing topological arguments we show that deformations on the surface of the outer cylinder do not break the operating mode (repeller or concentrator). We present a comparison between our geometrical approach and the transformation thermodynamics to give an additional explanation for the obtained results. We hope the presented device is useful for heat control under mechanical and thermal influence of the external environment.