Asymptotic analysis of the Guyer-Krumhansl-Stefan model for nanoscale solidification

• Published in: arXiv.org
• Main Authors: Hennessy, Matthew G, Marc Calvo Schwarzwälder, Myers, Timothy G
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 17.04.2018
• Subjects: Asymptotic properties; Conduction heating; Conductive heat transfer; Fourier law; Freezing; Nanotechnology; Physics - Mesoscale and Nanoscale Physics; Solidification; Thermal conductivity; Thermal energy
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1804.06448

Nanoscale solidification is becoming increasingly relevant in applications involving ultra-fast freezing processes and nanotechnology. However, thermal transport on the nanoscale is driven by infrequent collisions between thermal energy carriers known as phonons and is not well described by Fourier's law. In this paper, the role of non-Fourier heat conduction in nanoscale solidification is studied by coupling the Stefan condition to the Guyer--Krumhansl (GK) equation, which is an extension of Fourier's law, valid on the nanoscale, that includes memory and non-local effects. A systematic asymptotic analysis reveals that the solidification process can be decomposed into multiple time regimes, each characterised by a non-classical mode of thermal transport and unique solidification kinetics. For sufficiently large times, Fourier's law is recovered. The model is able to capture the change in the effective thermal conductivity of the solid during its growth, consistent with experimental observations. The results from this study provide key quantitative insights that can be used to control nanoscale solidification processes.