Size-dependent heat conduction of thermal cellular structures: A surface-enriched multiscale method

This paper examined how microstructure influences the homogenized thermal conductivity of cellular structures and revealed a surface-induced size-dependent effect. This effect is linked to the porous microstructural features of cellular structures, which stems from the degree of porosity and the distribution of the pores. Unlike the phonon-driven surface effect at the nanoscale, the macro-scale surface mechanism in thermal cellular structures is found to be the microstructure-induced changes in the heat conduction path based on fully resolved 3D numerical simulations. The surface region is determined by the microstructure, characterized by the intrinsic length. With the coupling between extrinsic and intrinsic length scales under the surface mechanism, a surface-enriched multiscale method was developed to accurately capture the complex size-dependent thermal conductivity. The principle of scale separation required by classical multiscale methods is not necessary to be satisfied by the proposed multiscale method. The significant potential of the surface-enriched multiscale method was demonstrated through simulations of the effective thermal conductivity of a thin-walled metamaterial structure. The surface-enriched multiscale method offers higher accuracy compared with the classical multiscale method and superior efficiency over high-fidelity finite element methods.