Constraints,dissipation functions and cholesteric liquid crystals

Our recently introduced dissipation function theory of molecular liquids and solids is extended to include constrained motions. Lagrangian multipliers are used in the reversible parts of the field equations of motion. Conservation laws of mass, momentum, energy and angular momentum are derived (in both the material and spatial frames) and shown to hold under the same general conditions as in the unconstrained case. Our theory is then applied to liquid crystals. Within our formalism, constitutive relations characterizing linear and nonlinear liquid crystals are given. In the linear regime, for cholesterics, depending on whether the heat flux or the temperature gradient is used in the dissipation function we show that different reciprocal relations follow. Our results for incompressible nematics and cholesterics are compared with the Ericksen-Leslie theory and others.     

(火积)耗散理论在换热器设计中的应用

本文首先说明(火积)耗散理论避免了最小熵产原理和傅里叶定律间的矛盾,显示了其在处理导热问题上的优越性.然后利用热力学(火积)和熵的关系,推出了换热器中由流体阻力引起的(火积)耗散表达式.     

Onsager-Machlup Theory for Nonequilibrium Steady States and Fluctuation Theorems

A generalization of the Onsager-Machlup theory from equilibrium to nonequilibrium steady states and its connection with recent fluctuation theorems are discussed for a dragged particle restricted by a harmonic potential in a heat reservoir. Using a functional integral approach, the probability functional for a path is expressed in terms of a Lagrangian function from which an entropy production rate and dissipation functions are introduced, and nonequilibrium thermodynamic relations like the energy conservation law and the second law of thermodynamics are derived. Using this Lagrangian function we establish two nonequilibrium detailed balance relations, which not only lead to a fluctuation theorem for work but also to one related to energy loss by friction. In addition, we carried out the functional integral for heat explicitly, leading to the extended fluctuation theorem for heat. We also present a simple argument for this extended fluctuation theorem in the long time limit. PACS numbers: 05.70.Ln, 05.40.-a, 05.10.Gg.     

Reciprocal relations based on the non-stationary Boltzmann equation

The reciprocal relations for open gaseous systems are obtained on the basis of main properties of the non-stationary Boltzmann equation and gas-surface interaction law. It is shown that the main principles to derive the kinetic coefficients satisfying the reciprocal relations remain the same as those used for time-independent gaseous systems [F. Sharipov, Onsager-Casimir reciprocal relations based on the Boltzmann equation and gas-surface interaction law single gas, Phys. Rev. 73 (2006) 026110]. First, the kinetic coefficients are obtained from the entropy production expression; then it is proved that the coefficient matrix calculated for time reversed source functions is symmetric. The proof is based on the reversibility of the gas-gas and gas-surface interactions. Three examples of applications of the present theory are given. None of these examples can be treated in the frame of the classical Onsager-Casimir reciprocal relations, which are valid only in a particular case, when the kinetic coefficients are odd or even with respect to the time reversion. The approach is generalized for gaseous mixtures.     

Reflection and transmission of plane electromagnetic waves in uniaxial bianisotropic materials

Electromagnetic waves in the most general linear reciprocal uniaxial media are considered. The theory is appropriate for novel reciprocal microwave materials which have properties of chiral composites and omega structures (or both) and can be modeled by uniaxial bianisotropic constitutive relations. Field coupling terms in the media equations are assumed to be the most general uniaxial dyadics with symmetric and antisymmetric components. Plane eigenwaves in unbounded media are studied and the theory of reflection and transmission in plane layers is constructed.     

换热器性能分析新方法

鉴于以加热或冷却为目的的热量传递过程,其不可逆性应以NFDA1的耗散率来度量,为此可以用换热器中的NFDA1耗散率定义换热器的当量热阻,它既包含换热器中的传热热阻,还包含了由非逆流形式和非平衡流引起的附加热阻. 换热器当量热阻的倒数称之为换热器的当量热导. 通过NFDA1耗散定义的换热器当量热阻建立了传热不可逆性与有效度的联系,并导得了换热器有效度与当量热导（热阻）和热容量流比的统一函数关系式,它适用于不同流程布置的换热器. 因此,有效度-热导（热阻）方法能更方便于不同类型换热器性能的分析和比 关键词： 换热器 热阻 耗散 熵产     

A Rather General Variational Principle for Purely Dissipative Non-Stationary Processes

A general variational principle concerning non-stationary purely dissipative phenomena, obeying ONSAGER 's reciprocal relations, is presented. The principle expresses that the variation of the sum of the total entropy production and the time derivative of the MASSIEU function is equal to zero. It is shown that the EULER -LAGRANGE equations corresponding to arbitrary variations of the state variables yield the conservation laws. Other general criteria for non-stationary processes have been given by GLANSDORFF -PRIGOGINE and GYARMATI . They are compared with our principle. Two illustrative examples are considered: coupled heat and electrical conduction in an isotropic medium and chemical reactions coupled with diffusion of matter and heat conduction in a multi-component fluid.     

Properties of hydrodynamic nuclei for quantum field models

The transition to the hydrodynamic limit for a many-particle quantum system withN local conservation laws is made in a specified class of external effects. It is shown that the hydrodynamic equations are nonlocal in time and space and the hydrodynamic model is equivalent to the initial quantum statistical model. The nuclei appearing in the material relations are expressed in terms of the Green functions for the currents. It follows from the properties of the Green functions that the hydrodynamic model satisfies the dissipation conditions. When the quantum field model isT-invariant, the nuclei are related by reciprocal relations (analogous to the Onsager relations).Institute of Earth Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 34–38, July, 1995.     

Heat transfer coefficients in two-dimensional Yukawa systems (numerical simulations)

New data on heat transfer in two-dimensional Yukawa systems have been obtained. The results of a numerical study of the thermal conductivity for equilibrium systems with parameters close to the conditions of laboratory experiments in dusty plasma are presented. The Green-Kubo relations are used to calculate the heat transfer coefficients. The influence of dissipation (internal friction) on the heat transfer processes in nonideal systems is studied. New approximations are proposed for the thermal conductivity and diffusivity for nonideal dissipative systems. The results obtained are compared with the existing experimental and numerical data.     

基于(火积)理论的“+”形高导热构形通道实验研究

基于构形理论和■理论,对"+"形高导热通道的方形构造体开展导热实验研究,并对不同优化目标和不同高导热通道布置形式下的构造体导热性能进行比较.结果表明:对于"+"形高导热通道的方形构造体,实验和数值计算所得到的构造体最高温度点均位于"+"形高导热通道两分支之间,实验和数值计算所得到的构造体平均温差和■耗散率的误差均在可接受范围内,这从定性和定量的角度证明了导热构形优化结果的正确性.与"H"形高导热通道的方形构造体相比,构造体内高导热通道采用一级"+"形布置使得其导热■耗散率得到降低.■耗散率最小的一级"+"形高导热通道构造体最优构形与最大温差最小的构造体最优构形相比,前者的导热■耗散率降低了5.98%,但最大温差提高了3.57%.最大温差最小目标有助于提高构造体的热安全性,■耗散率最小目标有助于提高构造体的整体导热性能.在保证热安全性能的前提下,实际微电子器件设计中可采用■耗散率最小的构造体最优构形以提高其整体导热性能.     

Out‐of‐Equilibrium Fluctuation‐Dissipation Relations Verified by the Electrical and Thermoelectrical AC‐Conductances in a Quantum Dot

The electrical and heat currents flowing through a quantum dot are calculated in the presence of a time‐modulated gate voltage with the help of the out‐of‐equilibrium Green function technique. From the first harmonics of the currents, we extract the electrical and thermoelectrical trans‐admittances and ac‐conductances. Next, by a careful comparison of the ac‐conductances with the finite‐frequency electrical and mixed electrical‐heat noises, we establish the fluctuation‐dissipation relations linking these quantities, which are thus generalized out‐of‐equilibrium for a quantum system. It is shown that the electrical ac‐conductance associated to the displacement current is directly linked to the electrical noise summed over reservoirs, whereas the relation between the thermoelectrical ac‐conductance and the mixed noise contains an additional term proportional to the energy step that the electrons must overcome when traveling through the junction. A numerical study reveals however that a fluctuation‐dissipation relation involving a single reservoir applies for both electrical and thermoelectrical ac‐conductances when the frequency dominates over the other characteristic energies.     

微方肋冷却系统的换热特性

采用去离子水为冷却介质,对自行设计的不同结构微方肋散热器内的换热特性进行实验研究,结果表明:在进口温度为20 ℃、进口流量为57.225 L/h、底面平均温度为73.4 ℃时,散热器散热量可达2.83106 W/cm2,可以满足当前高热流密度散热需求;当散热面温度一定时,散热量随着散热器进口流量的增加而增加,但增速随散热器底面温度的增加变缓;努谢尔特数随雷诺数的增加而成幂次方增加,常规针肋结构和微针肋结构换热关系式不满足微方肋散热器特性。为了更好地表达微方肋散热器内的换热特性,拟合了微方肋散热器内对流换热关系式。     

离散发热器件基于(火积)耗散率最小和最高温度最小的构形优化比较

建立了导热基座上圆柱体离散发热器件的三维湍流散热模型,基于构形理论,考虑空气变物性及可压缩性和黏性耗散,研究了器件材料的热导率、热源强度和流体流速对器件最高温度、基于(火积)耗散定义的当量热阻和平均Nu数的影响.结果表明:在总发热功率一定的条件下,以器件最高温度和当量热阻为性能指标进行热设计,均存在最优热源强度分布使得散热性能最优.当各热源强度相同且热源热导率小于基座热导率时,提高热源热导率可明显改善散热性能;将热源热导率沿流动方向从低到高布置可降低器件最高温度,而将热源热导率均匀布置可使当量热阻最小.所得结果可为实际热设计中不同材质和不同发热率的电子器件最优布置提供理论支撑.     

基于(火积)理论的轧钢加热炉壁变截面绝热层构形优化

基于绝热过程(火积)耗散极值原理, 分别在对流传热和复合传热(对流和辐射传热)边界条件下, 对轧钢加热炉壁变截面绝热层进行构形优化, 得到(火积)耗散率最小的绝热层最优构形. 结果表明: 与等截面绝热层相比, (火积)耗散率最小的变截面绝热层整体绝热性能更优. 热损失率最小和(火积)耗散率最小的绝热层最优构形是不同的. 热损失率最小的绝热层最优构形使得其能量损失减小, 而(火积)耗散率最小的绝热层最优构形使得其整体绝热性能提高. (火积)耗散率最小和最大温度梯度最小的变截面绝热层最优构形差别较小, 此时(火积)耗散率最小的绝热层最优构形在提高绝热层整体绝热性能的同时也提高了其热安全性. 基于(火积)理论的绝热层构形优化为绝热系统的优化设计提供了新的指导.     

合成双射流与小型复合结构翅片组合散热参数影响

为了保证电子设备能有足够长的工作寿命并可以在高热流下安全运行, 必须可靠而经济地解决高温设备的散热冷却问题. 为解决狭小空间板翅式翅片强化换热能力有限的问题, 基于纵向涡强化换热理论, 提出了合成双射流与表面微凸起复合结构翅组合散热方法. 利用Fluent数值模拟软件对合成双射流作用下的复合结构翅片内部气体流动特性及其强化换热特性进行了研究. 仿真结果表明表面微凸起复合结构翅片的肋片附近Y方向涡量是传统光滑肋片的2倍以上, 换热性能增加10%. 合成双射流驱动频率在500 Hz时, 具有均匀的温度分布以及更好的散热效果; 合成双射流峰值速度下散热效率更好.      

Statistical mechanics of thermal diffusion

Expressions of the flows of atoms A and B of a binary system in a crystal are derived as the response to the imposed gradients of temperature and chemical potentials. The formulation is done using the pair approximation of the Path Probability Method of irreversible statistical mechanics and atomic migration is assumed to be via the vacancy mechanism. The energy carried by photons (and electrons) under the temperature gradient is assumed to be independent of the atomic flux. For the case near equilibrium, linear relations are derived among the atomic fluxes, the energy flux (associated with atomic flux) and the gradients. The Onsager reciprocal relations are proved to hold among the coefficients, including those related to energy flows. The heat of transport (energy carried by a diffusing atom) and the heat conduction due to atomic flux are thus unambigously derived.     

导热系数测定过程中下铜板散热速率的理论计算

采用传热学的相关理论,对稳态法测量导热系数实验过程中下铜板的散热速率进行了计算,并与实测结果进行对比分析。     

Irreversibility and entropy production in transport phenomena,III—Principle of minimum integrated entropy production including nonlinear responses

A new variational principle of steady states is found by introducing an integrated type of energy dissipation (or entropy production) instead of instantaneous energy dissipation. This new principle is valid both in linear and nonlinear transport phenomena. Prigogine’s dream has now been realized by this new general principle of minimum “integrated” entropy production (or energy dissipation). This new principle does not contradict with the Onsager–Prigogine principle of minimum instantaneous entropy production in the linear regime, but it is conceptually different from the latter which does not hold in the nonlinear regime. Applications of this theory to electric conduction, heat conduction, particle diffusion and chemical reactions are presented.     

对流换热中的准(火积)耗散函数

通过分析对流换热过程中微元控制体内的(火积)流动平衡,得到类似于热传导过程中(火积)耗散函数表达形式的对流换热准(火积)耗散函数,表明对流换热过程中的(火积)耗散由热传导和对流形成的耗散共同构成。并通过分析对流换热过程的特点,对准(火积)耗散函数中对流项的影响进行了修正,使用圆管内热充分发展流动与无限宽平行通道内的对流换热过程检验,控制体内准(火积)耗散函数的计算结果与边界(火积)流的结果一致,表明文中提出的准(火积)耗散函数是可靠的。     

Heat dissipation in two-terminal Benzene junction

We investigate the heat dissipation mechanism in the Benzene molecular junctions. Using the tight-binding model and the generalised Green’s function formalism, heat dissipation in the electrodes is studied numerically. Results reveal a strong dependence of heat dissipation on the transmission characteristics and the bill polarity. For a pure Benzene molecular junctions, regardless the electrodes positions, namely meta, ortho and para configurations, heat dissipates in a symmetric fashion at both electrodes and does not rely on the bias polarity. This feature is a consequence of a symmetric transmission function over the energy spectrum of incoming electrons. Introducing a single impurity on the Benzene molecule, we force the model to lose its particle-hole symmetry and a drastic change occurs in the heat dissipation of the junction.