Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties

Abstract

Topology optimization approaches for thermal transport problems generally rely on the presence of high contrast in thermal conductivity between constituent materials. Even though this might result in topological configurations that are optimal according to some desired thermal metric, the resulting systems might be impractical from a mechanical standpoint: high contrast in thermal conductivity generally translates into disparate ranges of thermal expansion, which in turn may lead to mechanical failure. In this paper, we focus on the combination of multi-scale modeling and topology optimization techniques for the design of polycrystalline single-material systems with enhanced thermal transport properties. Spatial variation of the length-dependent thermal conductivity is achieved by grading the characteristic grain size of the microstructure. We adopt a multi-scale approach to compute the attainable range of thermal conductivity due to grain-size effect, given maximum and minimum grain sizes and an operating temperature range. Then, we utilize an adaptive topology optimization technique to obtain an optimal grain size distribution, while accounting for manufacturing constraints. Through a series of specific examples, we demonstrate the extent to which thermal transport properties can be optimized without resorting to the adoption of multi-material systems.