Attaining Prescribed Isotropic Effective Thermal Conductivity via Topology Optimization and Symmetry Exploitation

The geometry of a nanostructure significantly impacts thermal transport because of the interaction between phonons with relatively large mean-free-paths and the boundaries. Shape optimization has the potential to enable applications where ballistic transport plays a crucial role, such as thermal energy harvesting and management. To this end, we recently introduced an inverse design framework based on density-based topology optimization and the adjoint Boltzmann transport equation (BTE). In this talk, we will apply this method to design materials with prescribed effective thermal conductivity, where isotropy is ensured via symmetry exploitation. optimizing the material in terms of the irreducible wedge avoids solving the BTE for multiple perturbations at each iteration, thus enhancing computational efficiency.