An Analytical and Numerical Estimation of the Effective Thermal Conductivity of Complex Metal Frame Core Structures

An analytical and numerical study was conducted for estimation of the effective thermal conductivities of curved metal frame core structures, which can replace metal foams, in views of their advantages over the metal foams for both load bearing and heat dissipation. The trajectory of the frame ligament and its cross-sectional area were allowed to vary arbitrarily in the three-dimensional (3D) space. The analytical formula obtained by extending the formula previously proposed by Bai et al. (2017, “A General Expression for the Stagnant Thermal Conductivity of Stochastic and Periodic Structures,” ASME J. Heat Transfer, 140(5), p. 052001) was examined by comparing it with the numerical results directly obtained from full 3D numerical computations. An air layer partially filled with a collection of coiled circular rods was treated both analytically and numerically. Furthermore, the effect of lattice nodes on the effective thermal conductivity was investigated by introducing an analytical model with the lattice ligaments merging together at one nodal point. The analytical expressions thus derived for the lattice structures with nodes were applied to tetrahedral structure and octet-truss structure to find their effective thermal conductivities, which are found to agree closely with the 3D numerical results. Thus, the present analytical expressions can be used to customize the structure to meet its desired thermal performance.