Analysis of a trilayer thermal cloak

An analytical solution exists for a circular bilayer cloak against a background of linearly varying temperature distribution and under steady state. In particular, the ratio of the outer-layer and background conductivity is fixed, given the inner and outer radius of the outer layer. This conductivity ratio could be large, thus limiting the selection of bulk materials for the outer layer. This study reports a different design by adding a third layer of known conductivity between the inner and the outer layer of the bilayer cloak. The analysis extends the analytical solution of the bilayer cloak. For the same outer layer geometry between the bilayer and trilayer cloak, the proposed trilayer design gives a less limiting conductivity ratio between the outer layer and the background material than the bilayer design. Consequently, the trilayer design can enhance the selection of natural materials for the outer layer of the thermal cloak.