Optimal design of maximally amplified thermal concentrators with homogeneous and isotropic materials

In recent years, thermal metamaterials have garnered significant interest due to their remarkable potential for manipulating thermal fields, leading to the development of thermal metadevices. However, most thermal metadevices are based on coordinate transformation theory, which associates spatial distortions and transformations with material parameters, resulting in inhomogeneous and anisotropic properties that complicate practical applications. In this study, we present matching relations and the particle swarm optimized inverse design methodology for the design of maximally amplified thermal concentrators with elliptical-cylinder and circularcylinder geometries, which possess thermally-hidden Venturi effects and are made of homogeneous and isotropic materials. To achieve the optimal design, the bilayer thermal concentration issue is converted into an optimization problem that the amplification performance guides the design process. Thus, the orientations of concentrators, the thermal conductivities of concentrators, as well as the thickness ratio of the inner and outer layers required to achieve the maximum amplification performance on the premise of minimum disturbance to the external temperature fields are obtained. Finally, the proposed optimization method is not limited to thermal concentrators and can be extended to other physical fields, such as acoustic concentrators, electromagnetic concentrators, and hydrodynamic concentrators, among others.