弹道扩散导热的热质模型  

Ballistic-diffusive heat conduction by thermomass theory

作　　者：华钰超 曹炳阳[1] 过增元[1] 

机构地区：[1]清华大学工程力学系,热科学与动力工程教育部重点实验室,北京100084

出　　处：《科学通报》2015年第24期2344-2348,共5页Chinese Science Bulletin

基　　金：国家自然科学基金(51136001,51321002,51322603);新世纪优秀人才支持计划;清华大学自主科研计划资助

摘　　要：经典的傅里叶导热定律只适用于扩散导热.在瞬态导热过程中,为了描述热量的波动输运,基于热质理论建立了普适导热定律.对于微纳尺度的器件,由于弹道输运的作用,傅里叶导热定律也将失效.然而现有普适导热定律尚不能描述由弹道输运引起的非傅里叶导热现象.本文通过边界条件修正的方法将普适导热定律扩展到了弹道扩散导热区域.首先用热质理论的观点分析了弹道扩散导热机理;然后从声子玻尔兹曼方程出发推导了修正边界条件模型;最后数值求解了修正的普适导热定律并与蒙特卡罗模拟进行对比,验证了本文模型的正确性.The classical Fourier heat conduction law only works well for diffusive transport under normal conditions. Several typical non-Fourier models, such as the Cattaneo-Vernotte, dual-phase-lagging, and thermomass models, have been developed for thermal wave transport under transient conditions in recent decades. In addition, some recent studies have shown that the thermal conductivity of lowdimensional systems increases with increasing characteristic length because heat is transported in a ballistic-diffusive manner in nanostructures, in which the phonon mean free path（MFP） is comparable to the characteristic length. However, few models have become available for such thermal transport processes to date. In this work, we show that the general heat conduction law can be extended to phonon ballistic-diffusive transport by modification of the boundary conditions. First, we analyze the diffusive and ballistic transport processes from a thermomass theory viewpoint. Diffusive transport is transport in which thermal mass drifts in a body with a resistance proportional to the drift velocity, similar to fluid flows in porous media, and the current general heat conduction law can be derived from the thermomass balance equations, in which the heat inertia is considered. However, when the MFP is comparable with the characteristic length, the rarefied effect of the thermomass occurs, which corresponds to ballistic heat transport. In this regime, temperature jumps occur at the boundaries. It is noted here that the effects of ballistic heat transport are not covered in the current general heat conduction law. Therefore, modified boundary conditions that consider ballistic transport are applied to extend the general heat conduction law. We derive these modified boundary conditions from the phonon Boltzmann transport equation. The phonon distribution function is expanded with respect to the Knudsen number（Kn）, and the continuous heat flux condition is used to obtain the modified boundary conditions. In addition, heat conductio

关 键 词：热质理论 普适导热定律 弹道扩散导热 玻尔兹曼方程 

分 类 号：TK124[动力工程及工程热物理—工程热物理]