Effective medium theory for thermal scattering off rotating structures

Controlling heat transfer with artificial functional materials has been a promising route towards the efficient and smart utilization of thermal energy in modern society. At the macroscopic scale, thermal metamaterials have demonstrated versatile functionalities in manipulating thermal conduction. One major method is the effective medium theory, which provides a reliable approximation for the material parameters of the composite. Although most of thermal metamaterials use static components, recent devices with integrated moving parts are attracting great interest thanks to their high efficiency and flexibility. However, the effective medium theory for thermal scattering off such devices has not been well established, due to the fundamental difference between thermal convection and conduction. Here, we provide a thorough study on heat transfer through mechanically rotating structures. It is shown that the effective thermal conductivity of a rotating structure can be rigorously described in a complex plane. The analytical expressions of the effective thermal conductivity for structures with rotating multiple layers are formulated, which explicitly capture their influences on the surrounding temperature field. We validate the theory and numerically demonstrate the rotated and unrotated temperature distributions generated around a single structure. Our theory is expected to become a design recipe for novel thermal metamaterials and meta-devices.