Theoretical Analysis and Experimental Evidence of Non-Fourier Heat Conduction Behavior

This paper consists of two parts. (1) For a hollow sphere with sudden temperature changes on its inner and outer surfaces, the hyperbolic heat conduction equation is employed to describe this extreme thermal case and an analytical expression of its temperature distribution is obtained. According to the expression, the non-Fourier heat conduction behavior that will appear in the hollow sphere is studied and some qualitative conditions that will result in distinct non-Fourier behavior in the medium is ultimately attained. (2) A novel experiment to observe non-Fourier heat conduction behavior in porous material (mainly ordinary duplicating paper) heated by a microsecond laser pulse is presented. The conditions for observing distinct non-Fourier heat conduction behavior in the experimental sample agree well with the theoretical results qualitatively.

Two exact solutions of the DPL non-Fourier heat conduction equation with special conditions

This paper presents two exact explicit solutions for the three dimensional dual-phase lag （DLP） heat conduction equation, during the derivation of which the method of trial and error and the authors＇ previous experiences are utilized. To the authors＇ knowledge, most solutions of 2D or 3D DPL models available in the literature are obtained by numerical methods, and there are few exact solutions up to now. The exact solutions in this paper can be used as benchmarks to validate numerical solutions and to develop numerical schemes, grid generation methods and so forth. In addition, they are of theoretical significance since they correspond to physically possible situations. The main goal of this paper is to obtain some possible exact explicit solutions of the dual-phase lag heat conduction equation as the benchmark solutions for computational heat transfer, rather than specific solutions for some given initial and boundary conditions. Therefore, the initial and boundary conditions are indeterminate before derivation and can be deduced from the solutions afterwards. Actually, all solutions given in this paper can be easily proven by substituting them into the governing equation.

Numerical Analysis of Non-Fourier Heat Transfer in a Solid Cylinder with Dual-Phase-Lag Phenomenon

In this study,transient non-Fourier heat transfer in a solid cylinder is analytically solved based on dual-phase-lag for constant axial heat flux condition.Governing equations for the model are expressed in two-dimensional cylindrical coordinates;the equations are nondimensionalized and exact solution for the equations is presented by using the separation of variable method.Results showed that the dual-phase-lag model requires less time to meet the steady temperature compared with single-phase-lag model.On the contrary,thermal wave diffusion speed for the dual-phase-lag model is greater than the single-phase-lag model.Also the effect of relaxation time in dual-phase-lag model has been taken on consideration.

基于Non-Fourier导热模型的多芯片组件基板热分析研究

随着电子产品的尺寸和重量日趋变小,经典Fourier理论已经不能很好地解决实际问题。为了使理论结果尽可能准确地反映实际情况,需要用到Non-Fourier导热模型。首先,建立了三维多芯片组件的Fourier和Non-Fourier导热模型;其次,采用有限差分方法求解相应模型的传热方程,得到了温度分布和温度响应;最后,使用有限元热分析软件ICEPAK建立了相应的热分析模型并进行计算。实验结果表明,与经典的Fourier模型相比,Non-Fourier模型更加接近实际温度,且温度场进入稳态的时间较长,热耦合的现象也更强。

DPL Model Analysis of Non-Fourier Heat Conduction Restricted by Continuous Boundary Interface

Dual-phase lag (DPL) model is used to describe the non-Fourier heat conduction in a finite medium where the boundary at x=0 is heated by a rectangular pulsed energy source and the other boundary is tightly contactal with another medium and satisfies the continuous boundary condition. Numerical solution of thes kind of non-Fourier heat conduction is presented in this paper. The results are compared with those predicted by the hyperbolic heat conduction (HHC) equation.

Nonlinear analysis of a non-Fourier heat conduction problem in a living tissue heated by laser source

The effect of laser, as a heat source, on a one-dimensional finite living tissue was stud- ied in this paper. The dual phase lagging （DPL） non-Fourier heat conduction model was used for thermal analysis. The thermal conductivity was assumed temperature- dependent, resulting in a nonlinear equation. The obtained equations were solved using the approximate-analytical Adomian decomposition method （ADM）. It was concluded that the nonlinear analysis was important in nomFourier heat conduction problems. Moreover, a good agreement between the present nonlinear model and experimental result was obtained.

Non-Fourier heat conduction analysis of a 2-D plate with inner cracks at arbitrary direction angles

This paper investigates the problem of a 2-D plate containing internal cracks at arbitrary angles to the heating surface under thermal shock.The finite difference method is applied to solve the temperature distribution and a difference scheme of the oblique crack is developed.For the first time,a non-Fourier heat transfer analysis method of a 2-D plate with inner cracks at arbitrary direction angles is established.Specifically,for a strip with an inner crack paralleling to the surface,numerical results are compared with the analytical solutions by rotating the boundary,and perfect agreement is obtained.Numerical experiments are further presented to investigate the influence of crack orientation angle and multi-crack distribution on non-Fourier heat conduction.

Non-Fourier Heat Conduction Effects During High-Energy Beam Metalworking

Non-Fourier heat conduction induced by ultrafast heating of metals with a high-energy density beam was analyzed. The non-Fourier effects during high heat flux heating were illustrated by comparing the transient temperature response to different heat flux and material relaxation times. Based on the hyperbolic heat conduction equation for the non-Fourier heat conduction law, the equation was solved using a hybrid method combining an analytical solution and numerical inversion of the Laplace transforms for a semi- infinite body with the heat flux boundary. Analysis of the temperature response and distribution led to a crite- rion for the applicability of the non-Fourier heat conduction law. The results show that at a relatively large heat flux, such as greater than 108 W/cm2, the heat-affected zone in the metal material experiences a strong thermal shock as the non-Fourier effects cause a large step increase in the surface temperature. The results provide a method for analyzing transient heat conduction problems using a high-energy density beam, such as electron beam deep penetration welding.

Numerical Simulation of Dual-Phase-Lag Model and Inverse Fractional Single-Phase-Lag Problem for the Non-Fourier Heat Conduction in a Straight Fin

In recent years,many studies have been done on heat transfer in the fin under unsteady boundary conditions using Fourier and non-Fourier models.In this paper,unsteady non-Fourier heat transfer in a straight fin having an internal heat source under periodic temperature at the base was investigated by solving numerically Dual-Phase-Lag and Fractional Single-Phase-Lag models.In this way,the governing equations of these models were presented for heat conduction analysis in the fin,and their results of the temperature distribution were validated using the theoretical results of Single and Dual-Phase-Lag models.After that,for the first time the order of fractional derivation and heat flux relaxation time of the fractional model were obtained for the straight fin problem under periodic temperature at the base using Levenberg-Marquardt parameter estimation method.To solve the inverse fractional heat conduction problem,the numerical results of Dual-Phase-Lag model were used as the inputs.The results obtained from Fractional Single-Phase-Lag model could predict the fin temperature distribution at unsteady boundary condition at the base as well as the Dual-Phase-Lag model could.

Non-Fourier heat conduction study for steady states in metallic nanofilms

As a fundamental theory of heat transfer, Fourier's law is valid for most traditional conditions. Research interest in non-Fourier heat conditions is mainly focused on heat wave phenomena in non-steady states. Recently, the thermomass theory posited that, for steady states, non-Fourier heat conduction behavior could also be observed under ultra-high heat flux conditions at low ambient temperatures. Significantly, this is due to thermomass inertia. We report on heat conduction in metallic nanofilms from large currents at low temperatures; heat fluxes of more than 1×1010 W m 2 were used. The measured average temperature of the nanofilm is larger than that based on Fourier's law, with temperature differences increasing as heat flux increased and ambient temperature decreased. Experimental results for different film samples at different ambient temperatures reveal that non-Fourier behavior exists in metallic nanofilms in agreement with predictions from thermomass theory.

An analytical solution of non-Fourier Chen-Holmes bioheat transfer equation

An algebraically explicit analytical solution with heat wave effect is derived for the non-Fourier bioheat transfer Chen-Holmes model. Besides its important theoreti-cal meaning (for example, to expand the understanding of heat wave phenomena in living tissues), this analytical solu-tion is also valuable as the benchmark solution to check the numerical calculation and to develop various numerical computational approaches.

Some non-Fourier heat conduction characters under pulsed inlet conditions

Through simulating one-and two-dimensional non-Fourier heat conduction problems under different pulsed inlet conditions, this paper numerically predicts some different non-Fourier heat conduction characters arose from different pulse types and different pulse frequencies. Meanwhile, the differences among thermal wave, non-Fourier and Fourier heat conduction are also showed.

Explicit analytical solutions of non-Fourier heat conduction equation for IC chip

Four basic explicit analytical solutions of non_Fourier heat conduction equation simulating IC chip thermal condition are derived. Some other analytical series solutions can also be derived with the above_mentioned basic solutions. Analytical solution has its own irreplaceable important meaning in theory. In addition, as the standard solution to check the accuracy, convergence and effectiveness of various numerical computational methods and their differencing schemes, grid generation ways and so on, the analytical solution is very useful also for the newly rapidly developing computational heat transfer.

基于相移的三维扫描数据自动配准方法研究

在三维扫描过程中,常因受到设备自身因素与点云丢失的限制而难以一次性完成数据采集。为准确实现物体三维模型重构,提出基于相移的三维扫描数据自动配准方法。首先设置旋转台,利用非接触式结构光方法获得转动轴的有关信息,从而采集目标点云数据。在此基础上,结合任意一点与其周围点曲率信息建立曲率图,对全部顶点做曲率运算,将数据划分为连续子块,计算每个子块中平均值和方差,从而提取关键特征点。然后获取两幅具有部分重叠关系图像的相对位移,采用交叉功率谱的傅里叶变换完成位移估计,再通过构造与组合点对、粗略与精确配准去除噪声点,实现三维扫描数据自动配准。仿真实验表明,该方法能够在确保配准精度的同时提高配准方法的运行效率,可靠性和实用性较强。

基于声子水动力学方程分析全环绕栅极晶体管的瞬态热输运过程

相较于经典的傅里叶定律,声子水动力学模型在描述纳米尺度超快声子热输运中已经展现出显著优势.全环绕栅极晶体管(GAAFET)通过三维沟道设计极大优化了电学性能,但其纳米尺度特征也导致自热问题和局部过热的挑战.基于此,本文针对纳米尺度GAAFET器件内的声子热传输特性开展理论和数值模拟分析.首先,基于声子玻尔兹曼方程严格推导了声子水动力学模型和边界条件,建立了基于有限元的数值求解手段,针对新型的GAAFET器件,分析了表面粗糙度、沟道长度、沟道半径、栅极电介质、界面热阻等因素对其热传输特性的影响规律.研究结果表明,本文构建的连续介质框架下基于声子水动力学模型及温度跳跃条件的非傅里叶热分析方法能够精确预测GAAFET内部非傅里叶声子导热过程,并揭示声子阻尼散射和声子/界面散射的作用机制.这项工作为进一步优化GAAFET的热可靠性设计,提高其热稳定性和工作性能提供了重要的理论支持.

基于DFT的旋转变压器信号偏差矫正方法研究

解码芯片在对旋转变压器输出的位置信号做处理的过程中,芯片在采样时容易产生各种非理想偏差,这会造成转子位置估算精度的急剧下降。针对该问题,分析了电压信号中的幅值偏差和正交偏差会对旋转变压器解码的输出角度叠加一个2倍频的波动,直流偏差会叠加一个同频波动的问题,提出了一种基于离散傅里叶变换(DFT)的输入矫正法用于实现旋转变压器输出信号的偏差矫正,同时有效降低一次二次波动。该方法首先离散采样信号,通过DFT公式提取旋转变压器输出信号的直流信号和基频信号;然后基于直流信号和基频信号先后计算直流偏差、幅值偏差和正交偏差,通过控制器实现偏差值矫正。最后,仿真和试验结果表明,在芯片采样产生偏差时,所提出的偏差提取方法有效,试验中相应的正余弦输出信号指定阶次的波动更小。

非傅里叶效应对Maxwell流体在垂直槽道中热对流不稳定性的影响

基于Maxwell流体在科学、工程和技术等各个领域的重要性,并且结合非傅里叶热传导效应在许多不同研究领域的广泛关注,文章研究了非傅里叶效应对Maxwell流体在垂直槽道中热对流不稳定性的影响.将传统傅里叶热传导模型加入一个包含热松弛时间的新瞬态项,得到了非傅里叶热传导方程.使用切比雪夫配置法数值求解了一个广义特征值问题,得到了时间增长率和中性稳定曲线随各参数的变化情况.结果表明,时间增长率会随着松弛时间参数Λ增加而增加.中性稳定曲线表明,在波数相对较小的范围内,松弛时间的影响几乎可以忽略.但是当波数较大时,松弛时间对热对流不稳定性的影响逐渐加剧.这表明Maxwell流体的弹性效应增强了垂直管道内的热对流不稳定性.对于傅里叶流体,中性稳定性曲线不会随着Prandtl数变化.另一方面,非傅里叶效应增强了热对流不稳定性,并且新的双曲型热传导方程使得中性稳定曲线产生了波动现象.进一步研究表明,这种波动会随着Prandtl数的增加而增强.当Prandtl数超过一定临界值时,中性稳定曲线同时出现稳态分支和振荡分支,而且在振荡分支中,不稳定性显著增强.

基于隐层傅里叶卷积的非平稳纹理合成方法

随着深度学习在计算机视觉领域取得的巨大成功,基于示例的纹理合成研究得到了长足的发展.当下主流纹理合成模型往往采用神经网络方法,其通常包含卷积层和上采样层、下采样层等局部组件,并不适用于捕捉非平稳纹理中的不规则结构特征.受频率域与空间域的对偶性质的启发,提出了一种基于隐层傅里叶卷积的非平稳纹理合成方法.该方法以生成对抗网络为基础架构,沿着隐层通道进行特征拆分,搭建图像域局部分支和频率域全局分支,进而兼顾视觉感知和结构信息.实验表明,该方法能够处理结构上极具挑战的非平稳纹理样本,相较于目前最优方法而言,在大尺度结构的学习与扩展上取得了更好的效果.

面向通感一体化的非均匀感知信号设计

通感一体化被国际电信联盟ITU确定为6G的六大应用场景之一,而感知信号设计是通感一体化研究中的一个重要议题。传统的均匀感知信号设计具有时频资源开销大、信号设计灵活度差等问题,而非均匀感知信号设计能够解决上述问题。首先对三种非均匀信号设计方法的原理进行梳理和对比,给出非均匀信号设计在感知信号时频资源配置中的应用和链路自适应方法。然后基于vivo公司自研的通感一体化样机平台,对三种非均匀感知信号设计进行了初步的测试验证的性能对比。测试结果表明,非均匀感知信号在显著节约时频资源的情况下,能够取得较好的感知性能。

非线性最小二乘法在傅里叶变换红外光谱定量分析中的误差估计

根据统计学的参数估计理论,提出在傅里叶变换红外光谱定量分析中使用非线性最小二乘法进行浓度反演的参数误差估计方法。实验中,通过光谱平均次数来控制噪声水平,以此来评估不同噪声水平下混合气体中各组分反演结果的估计误差。结果表明,对于自研抽取式傅里叶变换红外光谱仪,8次平均光谱即可满足反演误差小于3%的需求,64次平均光谱的反演结果配合估计误差可以实现对平均浓度的覆盖率达到100%。随着噪声水平的降低,仪器、环境等非噪声因素的扰动是估计误差的主要部分。该方法在优化光谱定量分析的参数配置和指导光谱仪器系统设计等诸多方面具有重要的应用前景。