一维热波晶体的热传导特性研究

发布时间：2018-03-11 15:10

本文选题：非傅里叶导热　切入点：传递矩阵法　出处：《北京交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：在急速传热的系统中,由于时间尺度或空间尺度及其微小,这使得傅里叶导热定律在这些极端条件下不在适用。且傅里叶导热定律暗含的假设是热量传播的速度是无穷大。因此,为了解决上述问题,Cattaneo和Vernotte对傅里叶导热定律进行了修正提出了非傅里叶导热的单相弛豫模型(Cattaneo-Vernotte模型,CV模型)。CV模型的引入,使得传统的温度扩散方程转化为一个双曲的波动方程,即热波波动方程。CV模型暗含的假设为热流产生的温度梯度的传播速度为无穷大,这显然不符合实际,为了解决这一问题,Tzou于1995年提出了双相弛豫模型(Dual Phase Lag模型,DPL模型)。若热量是以波的形式传播,就不得不提在经典波(电磁波、弹性波、声波、格波等)领域,抑或是非经典波领域(de Broglie波)领域,一个极端重要而又极具挑战性的问题,波的调控。借助于光子晶体、声子晶体的研究,本文从波的调控角度入手,提出一种可以调控热量传播行为的人工周期结构-热波晶体。分别基于CV和DPL模型,利用传递矩阵法、时域有限差分方法研究一维热波晶体中的非傅里叶导热问题。计算了热波在其中传播时的频散曲线,初步探讨了热波晶体控制热量传播行为的机理,并分析了结构参数、材料参数对热波能带结构的影响。为了能够将理论结果应用于实际,本文将实际生活中常见的界面热阻引入热波晶体,并分析了其影响。主要的研究结果表明:1、影响带隙的结构参数和材料参数为填充率、无量纲长度、导热率比、体积热比、弛豫时间比。其中,导热率比和弛豫时间比为控制带隙产生的主要参数,两者为一定值时带隙接近消失。除无量纲长度结构外,其他的参数和材料均能影响带隙内热波的衰减速度,其中对衰减速度最大的为弛豫时间比、体积热比。2、用以表示结构尺寸和声子自由程的无量纲长度和导热率比成为控制带隙频率范围高低的主要因素,其中如果无量纲长度过大即结构尺寸远远大于声子自由程时,带隙被淹没。3、界面热阻会使热波衰减更快,且令CV模型和DPL模型频散曲线趋近一致。基于傅里叶定律的热阻会在低频率处增加一条带隙。
[Abstract]:In a system of rapid heat transfer, due to the small scale of time or space, This makes the Fourier law of heat conduction not applicable under these extreme conditions, and the implicit assumption of the law of Fourier heat conduction is that the speed of heat propagation is infinite. In order to solve the above problems, Cattaneo and Vernotte have modified the Fourier heat conduction law. The introduction of Cattaneo-Vernotte model and CV model makes the traditional temperature diffusion equation transform into a hyperbolic wave equation. That is, the thermal wave wave equation .CV model implies that the temperature gradient generated by the heat flux is infinitely fast, which is obviously not in line with the reality. In order to solve this problem, Tzou put forward the dual Phase Lag model in 1995. If the heat is propagated in the form of waves, it has to be mentioned in the field of classical waves (electromagnetic wave, elastic wave, acoustic wave, lattice wave, etc.). Or in the field of nonclassical wave field de Broglie wave, a very important and challenging problem, wave regulation. With the help of the study of photonic crystal and phonon crystal, this paper starts from the angle of wave regulation. A kind of artificial periodic structure-thermal wave crystal, which can regulate the heat transfer behavior, is proposed, based on CV and DPL models, the transfer matrix method is used. The finite difference time-domain (FDTD) method is used to study the non-Fourier heat conduction in one-dimensional thermal wave crystals. The dispersion curves of the thermal waves propagating in the crystals are calculated, the mechanism of controlling the heat propagation behavior of the thermal wave crystals is preliminarily discussed, and the structural parameters are analyzed. The influence of material parameters on the structure of the thermal wave band. In order to apply the theoretical results to the practical application, the common interface thermal resistance in real life is introduced into the thermal wave crystal in this paper. The main results show that the structural and material parameters affecting the band gap are filling ratio, dimensionless length, thermal conductivity ratio, volumetric heat ratio, relaxation time ratio. The ratio of thermal conductivity and relaxation time are the main parameters to control the generation of band gap. The band gap is nearly disappeared when they are two values. Except for dimensionless length structure, other parameters and materials can affect the attenuation rate of thermal wave in band gap. The biggest attenuation velocity is relaxation time ratio and volume-heat ratio, which is used to express the dimensionless length and the thermal conductivity ratio of the structure size and the free path of phonon, which are the main factors controlling the frequency range of band gap. If the dimensionless length is too large, the structure size is much larger than the free path of the phonon, the band gap is submerged. 3, the thermal resistance of the interface will make the thermal wave decay faster. The dispersion curves of CV model and DPL model are consistent. The thermal resistance based on Fourier law increases a band gap at low frequency.
【学位授予单位】：北京交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O736

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