Key Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi'an Jiaotong University, Xi'an, 710049, P.R. China.
Sci Rep. 2017 Aug 29;7(1):9568. doi: 10.1038/s41598-017-10416-9.
Guyer-Krumhansl (G-K) equation is a promising macroscopic model to explore heat transport in nanoscale. In the present work, a new nonlocal characteristic length is proposed by considering the effects of heat carriers-boundaries interactions to modify the nonlocal term in G-K equation, and a slip heat flux boundary condition is developed based on the local mean free path of heat carriers. Then an analytical solution for heat flux across 2-D nanolayers and an in-plane thermal conductivity model are obtained based on the modified G-K equation and the slip heat flux boundary. The predictions of the present work are in good agreement with our numerical results of direct simulation Monte Carlo (DSMC) for argon gas nanolayer and the available experimental data for silicon thin layers. The results of this work may provide theoretical support for actual applications of G-K equation in predicting the thermal transport properties of nanolayers.
盖尔-克伦汉斯（G-K）方程是一种很有前途的宏观模型，可用于研究纳米尺度的热输运。在本工作中，通过考虑热载体-边界相互作用的影响，提出了一个新的非局域特征长度，以修正 G-K 方程中的非局域项，并基于热载体的局部平均自由程，提出了一个滑移热流边界条件。然后，基于修正后的 G-K 方程和滑移热流边界条件，得到了二维纳米层间的热流解析解和平面热导率模型。本工作的预测结果与我们对氩气纳米层的直接模拟蒙特卡罗（DSMC）数值结果以及硅薄膜的现有实验数据吻合较好。本工作的结果可为 G-K 方程在预测纳米层热输运性质中的实际应用提供理论支持。
