Perspective on multi-scale simulation of thermal transport in solids and interfaces.

Phonon-mediated thermal transport is inherently multi-scale. The wave-length of phonons (considering phonons as waves) is typically at the nanometer scale; the typical size of a phonon wave energy packet is tens of nanometers, while the phonon mean free path (MFP) can be as long as microns. At different length scales, the phonons will interact with structures of different feature sizes, which can be as small as 0D defects (point defects), short to medium range linear defects (dislocations), medium to large range 2D planar defects (stacking faults and twin boundaries), and large scale 3D defects (voids, inclusions, and various microstructures). The nature of multi-scale thermal transport is that there are different heat transfer physics across different length scales and in the meantime the physics crossing the different scales is interdependent and coupled. Since phonon behavior is usually mode dependent, thermal transport in materials with a combined micro-/nano-structure complexity becomes complicated, making modeling this kind of transport process very challenging. In this perspective, we first summarize the advantages and disadvantages of computational methods for mono-scale heat transfer and the state-of-the-art multi-scale thermal transport modeling. We then discuss a few important aspects of the future development of multi-scale modeling, in particular with the aid of modern machine learning and uncertainty quantification techniques. As more sophisticated theoretical and computational methods continue to advance thermal transport predictions, novel heat transfer physics and thermally functional materials will be discovered for the pertaining energy systems and technologies.