On the Effective Thermophysical Properties of Phase Change Materials Embedded in Metallic Lattice Structures with Generic Topological Parameters

The recent literature has introduced the use of architected materials with a metallic lattice structure-based topology to enhance the thermal conductivity of phase change materials (PCM). The potential of such structures lies in the freedom of design with complex geometries. This, however, has introduced novel challenges regarding the analytical description of these materials’ effective thermophysical properties, which are used in order to treat the composite as a homogenized material. Only a few limited works have been presented thus far that have holistically addressed the calculation of such properties. The wide variety of possible geometric parameters in these materials can only be appropriately treated via an adaptable approach that can be extended to upcoming lattice geometries. With this aim in mind, the present work introduces a method to calculate the effective thermal conductivity of the discussed composite PCM. A cell-based approach to calculate the effective thermal conductivity is introduced. The method makes use of Steinmetz’s solids as a basis from which one can derive the porosity of unit cells with variable geometric parameters. Empirical factors are introduced to account for limitations due to the complex geometry and eventual manufacturing imperfections of these structures. Thus, semi-analytical formulae to describe the effective thermal conductivity of the lattice cells are derived for a variety of cuboid and hexagonal prismatic unit cells with generic topological parameters. The formulae are validated against the models and experimental results present in the literature. Finally, an analysis and discussion of the limited validity of homogenization techniques for lattice structures is presented.