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.     

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.     

热质的运动和传递-最低热质能耗散原理和热质运动方程

过增元基于质能方程提出了热质的概念.在非平衡热力学中,存在最低能量耗散原理,根据该原理可以导出热传导,扩散及粘性流动等不可逆输运过程的方程式.当采用热质模型对传热现象进行描述时,发现热质的运动也满足最小作用量原理:最低热质能耗散原理,根据该原理可以推导得出热质运动的动量守恒方程。     

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     

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     

热质的运动和传递——热子气的守恒方程和傅立叶定律

本文在热质和热子气概念的基础上建立了热子气的质量、动量、能量守恒方程.基于傅立叶导热定律求得了热子气粘性系数和粘性力的近似表达式.分析了傅立叶定律的物理意义:傅立叶定律是在忽略惯性力的条件下对热子气动量方程的近似.在极低温度或极高热流密度条件下傅立叶定律不再适用.     

金属中的热质运动—电子气的热质状态方程

根据热质运动理论可以得到普适导热定律,适用于极高热流密度以及超快速加热的极端导热条件。已有的理论研究得到了声子气状态方程,适用于非金属材料中的普适导热模型。而在金属材料中电子是热量传递的主要载体,声子气状态方程将不再适用。本文推导出热质理论中的电子气状态方程,并得到金属中的普适导热定律,为金属材料中极端条件下非Fourier导热现象的研究提供了理论基础。     

热波传递过程中的熵产分析

傅里叶导热定律导出的温度演化方程将得出无限大的热扰动传播速率。为了克服这个问题,一些修正导热模型被提出,可以得到双曲型温度方程,保证有限的热波传播速率。但是,新的传热模型得出的温度演化将使现有的不可逆热力学中熵产不能保持正定。拓展不可逆热力学通过修正熵以及熵产的表达式,使双曲导热也能得到正定的熵产率。热质理论用力学的概...     

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.     

Gauge Theory Gravity with Geometric Calculus

A new gauge theory of gravity on flat spacetime has recently been developed by Lasenby, Doran, and Gull. Einstein’s principles of equivalence and general relativity are replaced by gauge principles asserting, respectively, local rotation and global displacement gauge invariance. A new unitary formulation of Einstein’s tensor illuminates long-standing problems with energy–momentum conservation in general relativity. Geometric calculus provides many simplifications and fresh insights in theoretical formulation and physical applications of the theory.     

On the concepts of mass and linear momentum in Galilean thermodynamics

The paper presents a systematic treatment of the consequences of the first law of thermodynamics and of the Galilean principle of relativity for continuous bodies. It is shown that these two principles, when combined, imply not only the existence of energy, but also the existence of linear momentum. Both these quantities are represented by extensive state functions satisfying the equations of balance of energy and linear momentum, respectively. The linear momentum doesnot generally have the usual classical Newtonian form (mass times velocity). If, additionally, an assumption is made that the linear momentum is a function of velocity only, then the classical expression is recovered. The general equation of balance of linear momentum reduces then to Cauchy's equations of motion of continuum mechanics. But even without this additional assumption the concept of mass emerges as a derived concept in the theory: it figures in the transformation law for linear momentum under Galilean transformations.     

The action principle for generalized fluid motion including gyroviscosity

A general set of fluid equations that allow for energy-conserving momentum transport by gyroscopic motion of fluid elements is obtained. The equations are produced by a class of action principles that yield a large subset of the known fluid and magnetofluid models, including gyroviscosity. Analysis of the action principle yields broad, model-independent results regarding the conservation laws of energy and linear and angular momenta. The formalism is illustrated by studying fluid models with intrinsic angular momentum that may appear in the contexts of condensed matter, biological, and other areas of physics.     

Dynamic transport simulation code including plasma rotation and radial electric field

A new one-dimensional transport code named TASK/TX, which is able to describe dynamic behavior of tokamak plasmas, has been developed. It solves simultaneously a set of flux-surface averaged equations composed of Maxwell’s equations, continuity equations, equations of motion, heat transport equations, fast-particle slowing-down equations and two-group neutral diffusion equations. The set of equations describes plasma rotations in both toroidal and poloidal directions through momentum transfer and evaluates the radial electric field self-consistently. The finite element method with a piecewise linear interpolation function is employed with a fine radial mesh near the plasma surface. The Streamline Upwind Petrov–Galerkin method is also used for robust calculation. We have confirmed that the neoclassical properties are well described by the poloidal neoclassical viscous force. The modification of density profile during neutral beam injection is presented. In the presence of ion orbit loss, the generation of the inward radial electric field and torque due to radial current is self-consistently calculated.     

Massive String Cloud Cosmologies in Saez-Ballester Theory of Gravitation

String cloud cosmological models are studied using spatially homogeneous and anisotropic Bianchi type VI₀ metric in Saez-Ballester Scalar-Tensor theory of gravitation. The field equations are solved for massive string cloud with particles attached to them. A more general linear equation of state of the cosmic string tension density with the proper energy density of the universe is considered instead of taking any particular relationships like pure geometric string or the case of the p-string. The pure geometric string and p-string solutions can be easily inferred from the models. For all viable models the possible limiting values of the linear connection between the proper energy density and string tension density have been calculated. The physical and kinematical properties of the models have been discussed in detail.     

A Cosmological Model with Negative Constant Deceleration Parameter in a General Scalar-Tensor Theory of Gravitation

Spatially homogeneous and anisotropic LRS Bianchi type-I metric is considered in the framework of Nordtvedt-Barker’s general scalar-tensor theory of gravitation when the source for the energy momentum tensor is a perfect fluid. With the help of a special law of variation for Hubble’s parameter proposed by Berman (Nuovo Cim. B. 74:182, 1983) a cosmological model with negative constant deceleration parameter is obtained. Some physical and kinematical properties of the model are also discussed.     

Electro-osmotically actuated oscillatory flow of a physiological fluid on a porous microchannel subject to an external AC electric field having dissimilar frequencies

Electro-osmotic flow of a physiological fluid with prominent micropolar characteristics, flowing over a microchannel has been analyzed for a situation, where the system is subject to the action of an external AC electric field. In order to account for the rotation of the micro-particles suspended in the physiological fluid, the fluid has been treated as a micropolar fluid. The microchannel is considered to be bounded by two porous plates executing oscillatory motion. Such motion of the plates will normally induce oscillatory flow of the fluid. The governing equations of the fluid include a second-order partial differential equation depicting Gauss’s law of electrical charge distributions and two other partial differential equations of second order that arise out of the laws of conservation of linear and angular momenta. These equations have been solved under the sole influence of electrokinetic forces, by using appropriate boundary conditions. This enabled us to determine explicit analytical expressions for the electro-osmotic velocity of the fluid and the microrotation of the suspended micro-particles. These expressions have been used to obtain numerical estimates of important physical variables associated with the oscillatory electro-osmotic flow of a blood sample inside a micro-bio-fluidic device. The numerical results presented in graphical form clearly indicate that the formation of an electrical double layer near the vicinity of the wall causes linear momentum to reduce. In contrast, the angular momentum increases with the enhancement of microrotation of the suspended microparticles. The study will find important applications in the validation of results of further experimental and numerical models pertaining to flow in micro-bio-fluidic devices. It will also be useful in the improvement of the design and construction of various micro-bio-fluidic devices.     

A conservative numerical scheme for solving an autonomous Hamiltonian system

A new numerical scheme is proposed for solving Hamilton’s equations that possesses the properties of symplecticity. Just as in all symplectic schemes known to date, in this scheme the conservation laws of momentum and angular momentum are satisfied exactly. A property that distinguishes this scheme from known schemes is proved: in the new scheme, the energy conservation law is satisfied for a system of linear oscillators. The new numerical scheme is implicit and has the third order of accuracy with respect to the integration step. An algorithm is presented by which the accuracy of the scheme can be increased up to the fifth and higher orders. Exact and numerical solutions to the two-body problem, calculated by known schemes and by the scheme proposed here, are compared.     

Approximation of the inductionless MHD problem using a stabilized finite element method

In this work, we present a stabilized formulation to solve the inductionless magnetohydrodynamic (MHD) problem using the finite element (FE) method. The MHD problem couples the Navier–Stokes equations and a Darcy-type system for the electric potential via Lorentz’s force in the momentum equation of the Navier–Stokes equations and the currents generated by the moving fluid in Ohm’s law. The key feature of the FE formulation resides in the design of the stabilization terms, which serve several purposes. First, the formulation is suitable for convection dominated flows. Second, there is no need to use interpolation spaces constrained to a compatibility condition in both sub-problems and therefore, equal-order interpolation spaces can be used for all the unknowns. Finally, this formulation leads to a coupled linear system; this monolithic approach is effective, since the coupling can be dealt by effective preconditioning and iterative solvers that allows to deal with high Hartmann numbers.     

Viscous effects on motion and heating of electrons in inductivelycoupled plasma reactors

A transport model is developed for nonlocal effects on motion and heating of electrons in inductively coupled plasma reactors. The model is based on the electron momentum equation derived from the Boltzmann equation, retaining anisotropic stress components which in fact are viscous stresses. The resulting model consists of transport equations for the magnitude of electron velocity oscillation and terms representing energy dissipation due to viscous stresses in the electron energy equation. In this model, electrical current is obtained in a nonlocal manner due to viscous effects, instead of Ohm's law or the electron momentum equation without viscous effects, while nonlocal heating of electrons is represented by the viscous dissipation. Computational results obtained by two-dimensional numerical simulations show that nonlocal determination of electrical current indeed is important, and viscous dissipation becomes an important electron heating mechanism at low pressures. It is suspected that viscous dissipation in inductively coupled plasma reactors in fact represents stochastic heating of electrons, and this possibility is exploited by discussing physical similarities between stochastic heating and energy dissipation due to the stress tensor