Optimization Method for Practical Design of Planar Arbitrary-Geometry Thermal Cloaks Using Natural Materials

This study proposes an optimization method for the design of planar arbitrary-geometry thermal cloaks using natural materials based on the bilayer theory in thermal-cloaking studies. Our objective is to provide a practical design method for bilayer thermal cloaks of arbitrary shapes by determining the optimal outer-layer conductivity of the bilayer yielding the best thermal-cloaking performance. The method accounts for a potentially conducting inner layer, which is deemed more realistic from a practical standpoint as opposed to an ideal bilayer having a perfectly insulated inner layer. The proposed method is applied to solve thermal-cloaking problems involving not only conventional circular and elliptical geometries but also arbitrary-geometry thermal cloaks, as well as nonlinear background temperature distributions. For the ideal circular and elliptical bilayer cloaks, the proposed method yields the same analytical results as reported in the literature. For those cases where an analytical solution is not known to exist, the results demonstrate that excellent thermal-cloaking performance can be achieved on the basis of the bilayer design using the optimal outer-layer conductivity determined from the optimization method for a given set of background, inner-layer, and cloaked-region conductivities.