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

机译：纳米级凝固的Guyer-Krumhansl-Stefan模型的渐近分析

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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.
机译：在涉及超快速冷冻过程和纳米技术的应用中，纳米级固化变得越来越重要。但是，纳米级的热传输是由热能载体（称为声子）之间的不频繁碰撞驱动的，傅立叶定律并未对此进行充分描述。在本文中，通过将Stefan条件与Guyer-Krumhansl（GK）方程耦合，研究了非傅立叶热传导在纳米级凝固中的作用，该方程是傅立叶定律的扩展，在纳米级有效，包括记忆和非热定律。 -局部效应。系统的渐近分析表明，凝固过程可以分解为多个时间段，每个时间段的特征都是非经典的热传输模式和独特的凝固动力学。在足够长的时间内，傅立叶定律得以恢复。该模型能够捕获固体生长过程中有效导热系数的变化，这与实验观察结果一致。这项研究的结果提供了关键的定量见解，可用于控制纳米级凝固过程。

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