| Summary: | Thermal design is essential when developing various types of technological devices, especially miniaturized electronic devices. Conventional thermal design methods that only focus on macrostructures can provide only limited improvements in electronic device performance. On the other hand, in recent years, the implementation of nanostructural designs that take advantage of the unique properties of heat conduction at the nanoscale has resulted in electronic devices offering unprecedentedly high performance. Nanoscale heat conduction is a ballistic process, whereas heat conduction at the macroscale is diffusive. When a system is a two-phase domain, temperature discontinuities occur on the material interfaces. High-performance devices have been developed by utilizing these unique phenomena, especially the interface effect. However, few reports have proposed thermal design criteria, and thermal designs have been dependent on heuristic approaches. The development of design guidelines applicable to nanoscale thermal problems is a fundamental requirement, and one of the most effective design criteria is shape sensitivity, which indicates how to deal with material interfaces based on physics and mathematics. In this paper, we propose a shape sensitivity analysis method for a two-phase thermal design problem considering temperature discontinuities. We first explain the difference between nanoscale and macroscale heat conduction and introduce a numerical analysis method for nanoscale heat conduction based on the Boltzmann transport equation. Next, we construct a method for shape sensitivity analysis for a heat conduction problem considering two-phase nanoscale effects such as temperature discontinuities, by expanding the work of Pantz, based on Céa’s method. The validity of our shape sensitivity analysis is demonstrated through two numerical examples.
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