Structural Optimization for nanoscale heat conduction problems

Abstract

Heat conduction in nano or submicron structures is quite different from macroscale conduction. Nanoscale heat conduction has ballistic process, whereas macroscale one is diffusive, and when a system is a two-phase domain, temperature discontinuities occur on the material interfaces. High-performance devices have been developed by utilizing these nanoscale unique phenomena, especially temperature jumps. However, few reports have focused on optimum design methods for nanoscale heat conduction problems except heuristic or experimental approaches. In this paper, we propose a level set-based structural optimization method for heat conduction problems in nanostructures. The level-set method is an appropriate method for our design problems, since it can precisely consider the discontinuities on material interfaces. We first formulate an optimization problem with general objective functional, then compute a shape sensitivity for the problems. Next, we expand the level set-based structural optimization method proposed by Allaire et al. to our design problem. Then, we confirm the validity of our proposed method through numerical examples. Finally, we conclude this paper with future plans.