Metal frame structures with controlled anisotropic thermal conductivity

The summation law (k_xx+k_yy+k_zz=(1−ε)k_s) for those structures made of the same metal frames has been generalized in terms of the thermal conductivity tensor k_ij=∑_n=1 ^Ns_nk_s(g→_n·e→_i)(g→_n·e→_j) in order to identify the conditions for orthotropic thermal conductivity and the level of the anisotropy of thermal conductivity in metal frame structures. A novel design strategy was proposed for controlling the anisotropy of the effective thermal conductivity tensors in various metal frame structures. Both three-dimensional lattice frame structurers and two-dimensional prismatic cellular honeycomb structures were considered to achieve their desired levels of the anisotropy in the thermal conductivity tensors. The relationships between the level of the anisotropy and frame design parameters are found for rectangular frame structures, deformed octet-truss structures, deformed tetrakaidecahedron structures and various kinds of honeycomb structures. The relationships analytically obtained for these structures agree well with the full 3D numerical results, and thus can serve as a theoretical basis to design the anisotropy of the effective thermal conductivity in metal frame structures according to their particular thermal applications.