Thermal Metamaterials. Form factors for effective thermal conductivity calculations.

Abstract We present a general derivation of the form factors for two-phase composites needed in the calculation of the effective thermal conductivity. The composite is made of a homogeneous matrix with a random distribution of inclusions with regular shapes, both isotropic. The method is tested with known inclusion geometries such as spheres, ellipsoids, and circular fibers. The form factor for fibers with elliptical cross-sections is also presented. The method is applied to toroidal inclusions, and we show that in this case, it is not possible to relate the effective thermal conductivity to the volume fraction of the inclusions. This paper explores the concept of thermal metamaterials, their properties, fabrication techniques, and potential applications. Despite its regular use, we show that homogenization procedures, such as the Maxwell-Garnett model, are valid only if the system can be described as a separable-coordinate system.