基于热质理论的广义热弹性动力学模型

具有微尺度传热特征的超常传热过程中,热流矢与温度梯度之间存在延迟效应,且热流的运动受到空间效应的影响.基于热质概念的普适导热定律,结合Clausius不等式和Helmholtz自由能公式,构建了计及热流矢和温度对时间和空间惯性效应的广义热弹性动力学模型,推导了各向同性材料超常传热行为的热弹性控制方程组.通过与已有广义热弹性动力学模型进行对比分析可得,当热流密度不大的条件下,热流矢与温度对空间的惯性效应可忽略时,基于热质概念的广义热弹性模型可分别退化为L-S,G-L和G-N的模型;对于尺度微观、稳态导热条件时,热流矢与温度对空间的惯性效应不可忽略,此时导热系数将受到热质运动惯性效应的影响,利用所建模型可揭示稳态导热时呈现的非傅里叶现象,并可避免基于已有广义模型得到的导热系数随结构特征尺寸变化的非物理现象.     

热质的运动与传递-热波

根据爱因斯坦狭义相对论,热量具有其对应的相对论质量,并且引入了描述热质(热量)运动的连续方程、动量方程.本文根据热质(热量)运动控制方程组,导出了热质(热量)的波动方程,证明了热量具有波动的传递方式,当热质动能与热质的耗散在同一量级时,得到了有限的热波传播速度.分析了热波产生的物理机制.基于热质理论的热波模型与CV模型进行了比较,指出了CV模型在物理上的缺陷.最后对一维热波的传播过程进行了数值模拟,给出了超快速导热过程的物理图像.     

基于热质理论的热波传递现象研究

基于热质的概念应用牛顿力学原理建屯了热质输运的控制方程,推导得到了普适的导热定律.在惯性力可以忽略时它即退化为傅立叶导热定律,反映出非傅立叶导热现象的本质是热质的惯性引起的.当热流和温度对空间的惯性以及温度对时间的惯性可以忽略时,所得到的导热定律可以退化为CV模型.对热波传递的数值分析表明:当热扰动和热流都比较小时,热流在空间加速的惯性可以忽略,基丁热质理论的热波方程和CV模型符合得很好;但是,在描述较大的热扰动时,由于热流的空间加速惯性不能够被忽略,CV模型的结果在两个温度波峰叠加时会出现负温度的非物理现象,而基于热质理论的普适导热定律的结果则克服了这一缺陷.     

液相工质中热声效应数值模拟研究

基于求解可压缩流体的N-S方程,分别计算水及R134a两种液相工质在二维空间内的热声波产生及传递过程,分析初始压力及左侧壁温阶跃值对两种工质热声压力波产生的幅值及波传递到右边界后与壁面的热流交换影响情况。结果表明,初始压力对两种工质热声波产生的幅值及与向右边界换热的热流影响不大;压力幅值及右边界传热热流强度随左侧壁温度阶跃值增大而增大;在相同边界条件下,R134a可以产生更大幅值的压力波,并且与右边界换热的热流较大。     

超流氦浴中的热波传热研究

热波传热机制是超流氦传热非常重要的一个方面.在小热流密度的情况下,超流氦中的热波完全保持加热热流的波形,热量的传输完全靠热波来完成;随着热流密度的增加到一定程度,会在超流氦浴中激发量子涡旋.量子涡旋使热波发展成为热激波.在开放氦浴中,热波的波形不同于狭窄通道里的热波,在热波的尾部会出现一个冷却波;并且随着加热时间的变化,冷却波的形状和幅度会发生很大的变化.运用二流体模型和涡旋方程对超流氦中的热波进行了计算,实验结果与计算结果吻合得较好. 关键词： 超流氦 热波 量子涡旋 热激波     

热质的运动与传递-微尺度导热中的热质动能效应

基于热质(热量的当量动质量)的概念,通过建立和分析热质的运动方程得到了反映热质动能变化的稳态导热微分方程,表明Fourier导热定律只有在热质的动能变化相对热质势能变化很小而可以忽略时才成立;在高热流密度和低温的情况下热质的动能变化不可忽略,这种动能效应表现为热流密度和温度梯度不再成线性关系.动能效应也导致Fourier导热定律不能通过热流和温度梯度准确地获得物体的导热系数,本文基于热质运动方程给出了导热系数动能效应的修正式.最后针对高热流密度和低温一维稳态导热进行了分子动力学模拟验证.     

基于热质运动概念的普适导热定律

根据爱因斯坦的质能等效关系式,热能具有的等效质量称为热质,从而在固态和气态介质中分别建立了声子气质量和热子气质量的概念.应用牛顿定律建立了含有驱动力、阻力和惯性力的热质(声子气或热子气)运动的动量守恒方程.由于热量在介质中的传递本质上就是热质(声子气和热子气)在介质中的运动,所以热质动量守恒方程就是普适的导热定律,能够统一描述各种条件下的导热规律.当热流密度不是很大从而热质惯性力可以忽略时,热质动量守恒方程就退化为傅里叶导热定律,这表明傅里叶导热定律是特殊条件下的导热定律,对于微纳尺度条件下的导热,热流密度可以极高,由速度空间变化引起的惯性力不能忽略,在稳态导热情况下也将出现非傅里叶导热,此时在计算或者实验中不能用热流密度除温度梯度求导热系数.在超快速加热条件下,必需考虑惯性力,与基于CV导热模型的波动方程相比,普适的导热定律增加了因速度空间变化引起的惯性力项,所以在介质中热波叠加时不会出现产生负温度的非物理现象,表明基于热质运动概念的普适导热定律更为合理. 关键词： 傅里叶导热定律 普适导热定律 热质运动 非傅里叶导热     

新型被动在轨非连接支撑热结构耦合分析

新型被动在轨非连接支撑(简称PODS)发射和在轨时主要功能元件接触状态不同,其传热路径不同,漏热量也就不同。针对支撑结构发射及在轨时,热应力、惯性载荷及贮箱重量对其漏热的影响,利用ANSYS Workbench中热-结构耦合方法对支撑结构进行分析,得到PODS温度分布、热流分布及不同接触状态下的漏热量。结果表明,不同接触状态下,热变形及漏热量均不同。热变形是热应力和结构应力共同作用的结果,其中,热应力是影响热变形的主要因素。     

热学中的新物理量

通过与力学、电学的比拟,在热学中引入了热量的势、势能、速度、动能等新的物理量,从而可建立热量运动的守恒方程组.热量传递是不可逆过程,耗散的是热量的"能量".以耗散最小(热阻最小)为目标函数,就能对传热过程进行优化.傅立叶导热定律是热量运动方程在不计动量变化条件下的简化.在极端(低温、超高速、纳米尺度)条件下不再适用,引入新物理量后,能阐明热波、导热系数尺度效应等"超常"物理现象.     

考虑热波效应的皮肤传热过程解析解

为了研究热松弛时间及血液灌输对皮肤温度场变化影响,运用拉普拉斯方法给出了稳定的第一类条件下考虑一阶热波效应的Pennes方程的解析解.得到了指数形式的温度阶跃量,通常热松弛时间越长阶跃变化量越大,而血液灌输率越大阶跃变化量越小.若忽略血液灌输率,该解退化为普通热波方程的解析解.将皮肤内各点温度变化分为五个阶段,研究表明...     

基于热质理论的Hamilton原理

基于热质理论,类比经典力学,给出了热质运动遵循的Hamilton原理以及相应的导热Lagrange方程.由于考虑了热质动能,热质运动的Hamilton原理有望应用于非Fourier效应的讨论,在忽略热质动能时,回归到Fourier热学.应用Lagrange方程对含内热源一维瞬态导热问题进行了近似求解,计算结果与解析解符合较好.从分析力学的角度对传热理论以及热学与力学的统一做了新的阐释,指出了现有文献中采用分析力学方法讨论导热问题时存在的某些不足,为导热问题的近似求解提供了新的思路,同时也说明了热质和热质能     

Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.     

Viscosity and Diffusion Effects at the Boundary Surface of Viscous Fluid and Thermoelastic Diffusive Solid Medium

This paper concentrates on the wave motion at the interface of viscous compressible fluid half-space and homogeneous isotropic, generalized thermoelastic diffusive half-space. The wave solutions in both the fluid and thermoelastic diffusive half-spaces have been investigated; and the complex dispersion equation of leaky Rayleigh wave motion have been derived. The phase velocity and attenuation coefficient of leaky Rayleigh waves have been computed from the complex dispersion equation by using the Muller's method. The amplitudes of displacements, temperature change and concentration have been obtained. The effects of viscosity and diffusion on phase velocity and attenuation coefficient of leaky Rayleigh waves motion for different theories of thermoelastic diffusion have been depicted graphically. The magnitude of heat and mass diffusion flux vectors for different theories of thermoelastic diffusion have also been computed and represented graphically.     

Exact Solutions and Their Asymptotic Behaviors for the Averaged Generalized Fractional Elastic Models

The generalized fractional elastic models govern the stochastic motion of several many-body systems, e.g., polymers, membranes, and growing interfaces. This paper focuses on the exact formulations and their asymptotic behaviors of the average of the solutions of the generalized fractional elastic models. So we directly analyze the Cauchy problem of the averaged generalized elastic model involving time fractional derivative and the convolution integral of a radially symmetric friction kernel with space fractional Laplacian.     

Flexural and transversal wave motion in homogeneous isotropic thermoelastic plates by using asymptotic method

The present investigation is concerned with the flexural and transversal wave motion in an infinite, transversely isotropic, thermoelastic plate by asymptotic method. The governing equations for the flexural and transversal motions have been derived from the system of three-dimensional dynamical equations of linear theory of coupled thermoelasticity. The asymptotic operator plate model for free vibrations; both flexural and transversal, in a homogenous thermoelastic plate leads to fifth degree and cubic polynomial secular equations, respectively, that governs frequency and phase velocity of various possible modes of wave propagation at all wavelengths. All the coefficients of differential operator have been expressed as explicit functions of the material parameters. The velocity dispersion equations for the flexural and transversal wave motion have been deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate waves. The approximations for long and short waves and expression for group velocity have also been derived. The thermoelastic Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations whose equivalence is established with that of asymptotic method. The dispersion curves for phase velocity, group velocity and attenuation coefficient of various flexural and transversal wave modes are shown graphically for aluminum-epoxy material elastic and thermoelastic plates.     

导热与弹性系统及导电的相似性

本文将导热系统与弹性力学系统以及带电系统类比,发现这三种不同类型的系统在输运方面具有一致的行为特征,有相同的数学表达方式。都是在强度量的作用下,广延量的输运过程。强度量在被传递的广延量上的累积效果由广义功反映,广义功就是传递过程中的传递能力,传递能力在过程中有损耗。定义了导热过程中的热力功,它等于传热温度与传递的热量的乘积,反映了温度在传热量上的累积效果。热力功是传递中的热量传递势容,总热力功等于系统热量传递势容的改变量,热量传递势容表示物体的导热能力。     

Generalized thermoelastic extensional and flexural wave motions in homogenous isotropic plate by using asymptotic method

In this paper the asymptotic method has been applied to investigate propagation of generalized thermoelastic waves in an infinite homogenous isotropic plate. The governing equations for the extensional, transversal and flexural motions are derived from the system of three-dimensional dynamical equations of linear theories of generalized thermoelasticity. The asymptotic operator plate model for extensional and flexural free vibrations in a homogenous thermoelastic plate leads to sixth and fifth degree polynomial secular equations, respectively. These secular equations govern frequency and phase velocity of various possible modes of wave propagation at all wavelengths. The velocity dispersion equations for extensional and flexural wave motion are deduced from the three-dimensional analog of Rayleigh-Lamb frequency equation for thermoelastic plate. The approximation for long and short waves along with expression for group velocity has also been obtained. The Rayleigh-Lamb frequency equations for the considered plate are expanded in power series in order to obtain polynomial frequency and velocity dispersion relations and its equivalence established with that of asymptotic method. The numeric values for phase velocity, group velocity and attenuation coefficients has also been obtained using MATHCAD software and are shown graphically for extensional and flexural waves in generalized theories of thermoelastic plate for solid helium material.     

非平衡热力学中传热过程熵产表达式的修正

熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.     

Size-dependent thermal buckling of heated nanowires with ends axially restrained

Nanowires (NWs) are being actively explored for applications as nanoscale building blocks of sensors, actuators and nanoelectromechanical systems (NEMS). Temperature changes can induce an axial force within NWs due to the thermal expansion and may lead to buckling. The thermal buckling behaviors of ends-axially-restrained nanowires, subjected to a uniform temperature rise, are studied based on Bernoulli–Euler beam theory including the surface thermoelastic effects. Besides the surface elastic modulus, the influences of surface thermal expansion coefficient are incorporated into the model presented herein to describe size-dependent thermoelastic behaviors of nanowires. The results show that the critical buckling temperature and postbuckling deflection are significantly affected by surface thermoelastic effects and the influences become more prominent as the thickness of nanowire decreases. The corresponding influences of the slenderness ratio are also discussed. This research is helpful not only in understanding the thermal buckling properties of nanowires but also in designing the nanowire-based sensor and thermal actuator.     

脉冲热能沉积薄板中热弹性弯曲运动的分析

研究脉冲热能沉积薄板中,由于板厚方向的温度梯度和空间径向温度Gauss分布状态,所产生的辐射热能引起的弯曲运动效应。文章从非耦合的经典的Bernoulli—Euler理论出发,得到热弯曲动力学方程,求解初值问题,利用Laplace变换和Hankel变换,针对短脉冲和连续热辐射进行了分析,并给出热弹性弯曲波的数值计算结果。与文献[8]的实验结果比较,二者是相符的。