球对称瞬态非傅里叶热传导分析

基于非傅里叶热传导理论,分别从频域和时域分析了球对称瞬态热传导问题.频域求解时,采用Laplace变换结合状态空间法以及层合近似模型,过程清晰统一.时域求解时采用了分离变量法和叠加法,能减小数值反变换所带来的误差.数值算例比较了两种方法的计算效果,结果表明时域法可清晰捕捉热波传播过程中的前沿波阵面.     

考虑非傅里叶微尺度效应涂层基体复合结构热冲击强度研究

针对在涂层热冲击研究中忽略非傅里叶传热微尺度效应的问题,本文引入一维平板涂层基体复合结构物理模型,建立涂层双曲线型传热、基体抛物线型传热的数学模型Ⅰ,并根据交界面处的传热行为建立合理边界条件.在此基础上,构建了涂层、基体的热弹性力学模型.采用隐式差分法对模型离散化处理,得到温度场的数值解,进而求得应力场,并给出了具体算例.同时,建立涂层和基体均为抛物线型传热的数学模型Ⅱ作为对比研究.结果表明：当初始条件和热扰动均相同,并考虑非傅里叶传热的微尺度效应时,在涂层内,模型Ⅰ热应力表现出变化的延迟性、分布的局域性以及波动性,任意位置热应力都不是从0开始变化,而模型Ⅱ不存在波动性,任意位置热应力从0开始变化.模型Ⅰ热应力产生后,率先达峰且峰值大于模型Ⅱ.在基体内,模型Ⅰ热应力大于模型Ⅱ,且变化梯度较大.在交界面处,模型Ⅰ产生“反射效应”,此处应力值以及应力骤降值均大于模型Ⅱ.对比表明,模型Ⅰ受到的热冲击更加复杂剧烈.该研究为极端热传导环境下确保涂层可靠性提供了有益参考.     

层合材料的非傅里叶热传导及热应力

论文建立了一个双层材料层合板受瞬态加热情况下的非傅里叶热传导分析模型,用向后差分法得到了温度场的数值解,并对该差分格式的稳定性进行了讨论.给出了温度场随导热时间、热扩散率、空间与时间步长之比以及弛豫时间的变化趋势.同时,通过已经求得的温度场,求得了层合板内的应力场,给出了层合板内的热应力随时间的变化.     

功能梯度材料热传导问题的近场动力学模型

当材料中存在不连续性缺陷的时候,传统的基于连续介质理论的方法在研究热传导问题时存在诸多不便．我们基于近场动力学方法(Peridynamics)建立了功能梯度材料的热传导模型,并且研究了在温度荷载作用下功能梯度材料的温度场的变化表现．该文概述了PD方法应用于热传导问题时的详细理论基础,描述了其建模思路以及计算体系,给出了使用PD方法模拟结构承受温度荷载时的计算格式,讨论了不同梯度形式对功能梯度材料内热传导的影响．算例结果表明：通过PD模型所得到的温度场与解析解吻合较好,证明了PD方法在分析功能梯度材料热传导行为等问题时的可行性．     

基于非傅立叶热传导半无限大体热冲击力学分析

在微观尺度下,陶瓷的热传导机理与宏观尺度下的热传导机理有较大的差异,由此产生的热应力与宏观尺度下的不同,本文针对热冲击条件下的半无限大体,基于非傅立叶热传导模型分析了温度场、应力场和单边裂纹的应力强度因子,并与基于傅立叶热传导模型分析的结果进行了比较.研究表明在半无限大体表面附近或裂纹较短时,基于非傅立叶热传导模型得到的应力最大值或应力强度因子最大值比基于傅立叶热传导模型得到的结果大,而在半无限大体内部或裂纹较长时,结果相反.     

电磁发射轨道的非傅里叶热应力分析

电磁轨道发射过程中快速升高的温度会导致热应力的急剧变化,这种变化有可能导致轨道的破坏,对轨道的发射效率和寿命造成影响.为了研究轨道应力场的变化规律,利用电磁发射轨道的轨道热传导方程和数据拟合方法得到了沿轨道方向的温度场变化特性,运用应力场理论分析了非傅里叶热效应对轨道应力场的影响.结果表明:电磁轨道炮发射过程中电枢与轨...     

薄板弯曲问题的复合傅里叶级数方法

解析方法与数值方法有效融合是提高计算效能的重要途径．提出薄板弯曲问题的复合傅里叶级数方法．它以解析方法为融合基体,数值方法为融合增强相,是一种新的融合模式．在这种新的融合模式中,傅里叶级数解析解作为变形场的连续表现形式,摆脱了载荷形式和边界条件的强烈依赖性,表现出良好的收敛性态．     

基于近场动力学微分算子的含裂纹正交各向异性板热传导分析方法

采用近场动力学微分算子(Peridynamic Differential Operator, PDDO)理论建立正交各向异性板热传导的非局部模型。通过构造近场动力学函数,将边界条件和热传导方程由局部微分形式转化为非局部积分形式,引入Lagrange乘子,采用变分分析对含裂纹正交各向异性板温度及裂纹尖端的热通量分布进行求解。通过对比算例,验证了该模型具有较好的收敛性和有效性。分析了正交各向因子、材料铺设角、裂纹倾角及间距对裂纹尖端热通量的影响。结果表明,基于PDDO建立的含裂纹正交各向异性板热传导模型,考虑了热传导问题中的非局部性,能有效提高计算精度,预测含裂纹板中裂纹尖端出现的奇异性。     

条形荷载下梯度非均匀非饱和土的动力响应分析

基于多孔介质混合物理论, 建立了梯度非均匀非饱和土地基模型, 研究了条形荷载作用下梯度非均匀非饱和土地基的动力响应问题. 通过傅里叶积分变换和Helmholtz矢量分解原理, 获得频域内非饱和土地基动力响应问题的通解, 结合回传射线矩阵法和边界条件, 求解获得了非均匀非饱和土层中位移、应力以及孔隙压力的计算列式. 假设沿深度方向梯度非均匀非饱和土的物理力学性质按幂函数连续变化, 通过数值傅里叶逆变换得到了非均匀非饱和土地基中的应力、位移以及孔隙压力等物理量的数值解, 分析讨论了土体非均匀性对非饱和土介质动力响应的影响规律. 结果表明: 土体非均匀性显著改变了非饱和土中竖向位移、正应力和孔隙压力在其深度方向上的振动模态, 其中孔隙气压在其深度方向的振动频率随着梯度因子的增加而不断增大, 波峰值不断靠近地表处附近; 竖向位移随着梯度因子的增大不断减小; 正应力和孔隙水压随着梯度因子的增大先增大后减小, 并且土体非均匀程度越高, 正应力与孔隙水压的幅值越大.      

基于纯声子辐射模型的超薄绝缘夹层结构

在复合材料结构中起绝热、增韧作用的绝缘夹层,其加工厚度现在已达到纳米量级,原有的傅立叶热传导定律已无法描述其热能的传递行为,需从分子动力学、量子力学从发,针对不同研究对象建立相应的热传导模型．针对超薄绝缘夹层结构,将纯声子辐射模型和傅立叶热传导模型相结合数值求解热冲击条件下的温度场,并作为热载荷,用于求解结构上表面应力和夹层裂纹驱动力,其结果与只采用傅立叶热传导模型计算的结果相比较, 分析了物理参数对温度、应力和裂纹驱动力的影响．结果表明：与只采用傅立叶热传导模型计算的结果相比,按EPRT计算的热传导明显变慢,其表面剥离应力偏大,而夹层裂纹驱动力偏小．同时随着松弛时间增大和声子速度的降低,热传导减缓,表面横向剥离应力增大,超薄绝缘夹层内裂纹尖端驱动力减小．     

非傅立叶导热的最新研究进展

对迄今为止有关非傅立叶导热的研究成果进行了全面的综述,其中包括作者在该领域的最新研究进展:空心球体介质双曲线非傅立叶导热模型的分析求解,室温条件下多孔材料内非傅立叶导热的实验结果及数值模拟,非傅立叶导热的“瞬时薄层”模型,非傅立叶导热和非费克质量传递的耦合分析,非傅立叶导热的分子动力学模拟等．文中还对下一步的研究工作进行了展望.      

Wave propagation model of heat conduction and group speed

In view of the finite relaxation model of non-Fourier’s law, the Cattaneo and Vernotte (CV) model and Fourier’s law are presented in this work for comparing wave propagation modes. Independent variable translation is applied to solve the partial differential equation. Results show that the general form of the time spatial distribution of temperature for the three media comprises two solutions: those corresponding to the positive and negative logarithmic heating rates. The former shows that a group of heat waves whose spatial distribution follows the exponential function law propagates at a group speed; the speed of propagation is related to the logarithmic heating rate. The total speed of all the possible heat waves can be combined to form the group speed of the wave propagation. The latter indicates that the spatial distribution of temperature, which follows the exponential function law, decays with time. These features show that propagation accelerates when heated and decelerates when cooled. For the model media that follow Fourier’s law and correspond to the positive heat rate of heat conduction, the propagation mode is also considered the propagation of a group of heat waves because the group speed has no upper bound. For the finite relaxation model with non-Fourier media, the interval of group speed is bounded and the maximum speed can be obtained when the logarithmic heating rate is exactly the reciprocal of relaxation time. And for the CV model with a non-Fourier medium, the interval of group speed is also bounded and the maximum value can be obtained when the logarithmic heating rate is infinite.     

Rational design of thermoelastic damping in microresonators with phase-lagging heat conduction law

The design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging the quality factor of widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method for designing the TED in the framework of non-Fourier heat conduction law. This work, therefore, proposes a design framework to achieve low thermoelastic dissipation of microresonators governed by the phase-lagging heat conduction law. The equation of motion and the heat conduction equation for phase-lagging TED microresonators are derived first, and then the non-Fourier TED design problem is proposed. A topology optimization-based rational design method is used to resolve the design problem. What is more, a two-dimensional (2D) plain-strain-based finite element method (FEM) is developed as a solver for the topology optimization process. Based on the suggested rational design technique, numerical instances with various phase lags are investigated. The results show that the proposed design method can remarkably reduce the dissipation of microresonators by tailoring their substructures.     

基于时域间断有限元方法的生物组织非傅立叶热行为数值分析

在热传导分析中,当热流与温度梯度存在时间延迟时,需采用非傅立叶热传导模型进行分析。生物组织具有较强的热松弛时间系数,承受激光、微波及烧烫等作用时,其呈现出较强的非傅立叶行为。本文对脉冲热源作用下生物组织的非傅立叶热传导进行研究,针对强脉冲引起的温度场在空间域的高梯度变化、波阵面的间断行为以及通用传统时域数值方法会带来虚假数值振荡的特点,提出采用所发展的时域间断Galerkin有限元法（DG-FEM ）进行求解计算。对多种脉冲热源作用下的非傅立叶热传导过程进行数值模拟,通过考量强脉冲作用下温度场分布和热致生物组织损伤行为的影响,表明了本文所发展的DGFEM 能够有效、准确地描述温度场空间分布和热传导过程以及非傅立叶行为下的生物热损伤更为明显,在生物组织热行为分析中应该受到重视。     

Multiple spatial and temporal scales method for numerical simulation of non-classical heat conduction problems: one dimensional case

A multiple spatial and temporal scales method is studied to simulate numerically the phenomenon of non-Fourier heat conduction in periodic heterogeneous materials. The model developed is based on the higher-order homogenization theory with multiple spatial and temporal scales in one dimensional case. The amplified spatial scale and the reduced temporal scale are introduced respectively to account for the fluctuations of non-Fourier heat conduction due to material heterogeneity and non-local effect of the homogenized solution. By separating the governing equations into various scales, the different orders of homogenized non-Fourier heat conduction equations are obtained. The reduced time dependence is thus eliminated and the fourth-order governing differential equations are derived. To avoid the necessity of C¹ continuous finite element implementation, a C⁰ continuous mixed finite element approximation scheme is put forward. Numerical results are shown to demonstrate the efficiency and validity of the proposed method.     

Axisymmetric non-fourier temperatures in cylindrically bounded domains

Heat conduction solutions are presented for the case where the material obeys a non-Fourier conduction law. In contrast to the Fourier law which predicts an infinite speed of heat propagation, the non-Fourier theory implies that the speed of thermal signals are finite. Axisymmetric problems for regions interior and exterior to a circular cylinder are investigated by using methods of Laplace transformation and asymptotic analysis. Comparisons of the temperature profiles are made with Fourier theory for the case of step function temperature boundary conditions.     

Solution and analysis of hyperbolic heat propagation in hollow spherical objects

The hyperbolic heat conduction process in a hollow sphere with its two boundary surfaces subject to sudden temperature changes is solved analytically by means of integration transformation. An algebraic analytical expression of the temperature profile is obtained. Accordingly, the non-Fourier hyperbolic heat propagation in hollow spherical medium is analyzed and possible hyperbolic anomalies are discussed.     

Experimental evidence about the controversy concerning Fourier or non-Fourier heat conduction in materials with a nonhomogeneous inner structure

Distinct non-Fourier behavior in terms of finite propagation velocity and a hyperbolic wave like character of heat conduction has been reported for certain materials in several studies published recently. However, there is some doubt concerning these findings. The objective of this paper is to present experimental evidence for a perfectly Fourier-like behavior of heat conduction in those materials with nonhomogeneous inner structure that have been under investigation in the other studies. This controversy needs to be settled in order to understand the physics of heat conduction in these materials.     

THERMAL SHOCK OF SEMI-INFINITE BODY WITH MULTI-PULSED INTENSE LASER RADIATION

In order to investigate the thermal shock and the heat conduction property of a target under multi-pulsed laser radiation, analytic expressions of both temperature and thermal stress fields in the target are deduced on the basis of the non-Fourier conduction law and the thermo-elastic theory. Taking a stainless steel target as an example, we can solve the analytic expressions under appropriate boundary conditions by using the finite difference method and MATLAB software, and then reveal the evolution law of both surplus temperaturt, and thermal stress in the target. The results indicate that the temperature curves in the target irradiated by a multi-pulsed laser take on a delayed character in different sections away from the boundary, which is only affected by its relaxation time. The front of the stress wave is very steep in the non-Fourier numerical solutions, which presents an obvious thermal shock, so it is necessary to consider the non-Fourier effect of semi-infinite body under the high energy laser radiation.     

Non-Fourier heat conduction in an exponentially graded slab

The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.