A generalized model of an irreversible thermal Brownian refrigerator and its performance

A generalized model of an irreversible thermal Brownian refrigerator, which consists of Brownian particles moving in a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate, is established in this paper. The heat flows driven by both potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs are taken into account. The optimum performance of the generalized model is analyzed using the theory and method of finite time thermodynamics. The analytical expressions for cooling load, coefficient of performance (COP) and power input of the Brownian refrigerator are derived. It is shown by numerical examples that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, the Brownian refrigerator is always irreversible and the COP can never attain the Carnot COP. The influences of the heat leakage, the external force, barrier height of the potential, asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs on the performance of the Brownian refrigerator are also investigated in detail. The effective regions of external force and barrier height of the potential in which the Brownian motor can operate as a refrigerator are determined. It is found that the performance of the Brownian refrigerator depends strictly on the design parameters. If these design parameters are properly chosen, the Brownian refrigerator can be controlled to operate in the optimal regimes. The results obtained herein about the general Brownian refrigerator model include those obtained in many previous literatures.     

Heating load density optimization of an irreversible simple Brayton cycle heat pump coupled to counter-flow heat exchangers

This paper presents a theoretical investigation on the finite time thermodynamic performance for an irreversible Brayton cycle heat pump (BCHP) coupled to counter-flow heat exchangers. The heating load density, i.e. the ratio of heating load to the maximum specific volume in the cycle, is taken as the optimization objective. Relations between heating load density and pressure ratio and between COP (coefficient of performance) and pressure ratio for BCHP in which the irreversibilities of heat resistance losses in the hot and cold-side heat exchangers and non-isentropic losses in the compression and expansion processes are derived. The analytical expression obtained for the cycle performance enabled its optimization through addressing the effects of mechanical and thermal inefficiencies of all components comprising the cycle. The influences of the temperature ratio of the reservoirs, the efficiencies of the compressor and expander and the effectiveness of the heat exchangers on the heating load density are provided. The cycle performance optimizations are performed by searching the optimum distribution of heat conductance of the hot- and cold-side heat exchangers for the fixed total heat exchanger inventory and the optimum heat capacity rate matching between the working fluid and the heat reservoirs. The BCHP design with heat loading density optimization leads to a smaller size of all equipments comprising the heat pump.     

Exergetic efficiency optimization for an irreversible quantum Brayton refrigerator with spin systems

The purpose of this paper is to study the optimal performance for an irreversible quantum Brayton refrigerator with spin systems, which consists of two isomagnetic field branches connected by two irreversible adiabatic branches. The time evolution of the total magnetic moment M is determined by solving the generalized quantum master equation of an open system in the Heisenberg picture. The time of two irreversible adiabatic processes is considered based on finite-rate evolution in this paper. The optimization region (or criteria) for an irreversible quantum Brayton refrigerator with spin systems is obtained. The relationship between the exergetic efficiency ε_E and dimensionless cooling load R for the irreversible quantum Brayton refrigerator with heat leakage and other irreversibility losses are derived.     

电渗流中传热传质过程与熵的分析

在壁面存在恒定热通量条件下,分析微通道内电渗流中传热传质过程与熵的生成.建立数值计算模型,分别采用Poisson-Boltzmann方程、Navier-Stokes方程、Nernst-Planck方程和能量方程来描述微通道内双电层电势、流场、离子浓度和温度的分布情况.引入熵产生,进一步研究不同流动参数对流体传热过程的作用,讨论不同流动参数下各热效应的变化规律,并具体分析热效应参数对流体总熵增加及各部分热效应对总熵比重的影响.结果表明,动电参数与Joule(焦耳)热系数的增大会使得传热性能减弱,动电参数对传热性能影响更为明显;流体的总熵为动电参数、传质系数和质量弥散系数的增函数.     

Researches on operating region of Tokamak device with soft X-ray tomography

The structures of three operating regions in HT-6B Tokamak have been studied by soft X-ray tomographic system with high sensibility and high time-space resolution. One of the requisites for forming sawtooth discharge is the effective heating action in the central region. In the sawtooth region there are five evolutional phases and five types of magnetic surface structures correspondingly; that is, the concentric, the eccentric, the double-core, the “MHD-type” and the “ultra-MHD type” magnetic surface structures. In the MHD oscillation region, there is a stable “MHD-type” magnetic surface structure. It consists of a crescent “hot core” and a circular “cold bubble” and rotates in the diamagnetic direction of electrons. In the resonant region, the resonant helical field improves the heating status and suppresses the MHD disturbances; therefore the single “MHD-type” magnetic surface changes into a sawtooth type one.     

Coagulation, diffusion and the continuous Smoluchowski equation

The Smoluchowski equations are a system of partial differential equations modelling the diffusion and binary coagulation of a large collection of tiny particles. The mass parameter may be indexed either by positive integers or by positive reals, these corresponding to the discrete or the continuous form of the equations. For dimension d≥3, we derive the continuous Smoluchowski PDE as a kinetic limit of a microscopic model of Brownian particles liable to coalesce, using a method similar to that used to derive the discrete form of the equations in [A. Hammond, F. Rezakhanlou, The kinetic limit of a system of coagulating Brownian particles, Arch. Ration. Mech. Anal. 185 (2007) 1–67]. The principal innovation is a correlation-type bound on particle locations that permits the derivation in the continuous context while simplifying the arguments of the cited work. We also comment on the scaling satisfied by the continuous Smoluchowski PDE, and its potential implications for blow-up of solutions of the equations.     

On a Heat Exchange Problem under Sharply Changing External Conditions

The heat exchange problem between carbon particles and an external environment (water) is stated and investigated based on the equations of heat conducting compressible fluid. The environment parameters are supposed to undergo large and fast variations. In the time of about 100 μs, the temperature of the environment first increases from the normal one to 2400 K, is preserved at this level for about 60 μs, and then decreases to 300 K during approximately 50 μs. At the same periods of time, the pressure of the external environment increases from the normal one to 67 GPa, is preserved at this level, and then decreases to zero. Under such external conditions, the heating of graphite particles of various sizes, their phase transition to the diamond phase, and the subsequent unloading and cooling almost to the initial values of the pressure and temperature without the reverse transition from the diamond to the graphite phase are investigated. Conclusions about the maximal size of diamond particles that can be obtained in experiments on the shock compression of the mixture of graphite with water are drawn.     

Optimum work in real systems with a class of finite thermal capacity reservoirs

The optimum work in real systems with two finite thermal capacity reservoirs is determined. It is obtained by using optimal control theory. It is shown that the temperature of external working fluid changes exponentially with respect to flow velocity and process duration. The analysis proves that the optimum work is different for heat engine mode and heat pump mode. The recently obtained results are compared with those obtained previously. The models and results in this paper provide an approach to improve calculations of energy limits in real systems.     

Brownian motion, quantum corrections and a generalization of the Hermite polynomials

The nonequilibrium evolution of a Brownian particle, in the presence of a “heat bath” at thermal equilibrium (without imposing any friction mechanism from the outset), is considered. Using a suitable family of orthogonal polynomials, moments of the nonequilibrium probability distribution for the Brownian particle are introduced, which fulfill a recurrence relation. We review the case of classical Brownian motion, in which the orthogonal polynomials are the Hermite ones and the recurrence relation is a three-term one. After having performed a long-time approximation in the recurrence relation, the approximate nonequilibrium theory yields irreversible evolution of the Brownian particle towards thermal equilibrium with the “heat bath”. For quantum Brownian motion, which is the main subject of the present work, we restrict ourselves to include the first quantum correction: this leads us to introduce a new family of orthogonal polynomials which generalize the Hermite ones. Some general properties of the new family are established. The recurrence relation for the new moments of the nonequilibrium distribution, including the first quantum correction, turns out to be also a three-term one, which justifies the new family of polynomials. A long-time approximation on the new three-term recurrence relation describes irreversible evolution towards equilibrium for the new moment of lowest order. The standard Smoluchowski equations for the lowest order moments are recovered consistently, both classically and quantum-mechanically.     

Transient conduction in a plate with counteracting convection and thermal radiation at the boundaries

During the flash dehydroxylation of powdered kaolinite it is desirable that a rapidly propagating thermal wave penetrates the cold powder particles in a way that raises the particle interior to the reaction temperature of 600°C without the particle exterior being heated beyond 1000°C. In a production unit this is achieved by performing the heat treatment in a device where particles are heated by convection from hot gas and are subject to heat loss by thermal radiation to cool walls. This paper concerns the fundamental heat transfer problem of the process, decoupled from the thermal effects of the dehydroxylation reaction. Using a plate as the approximation for the particle shape a semi-analytical solution for the plate temperature distribution is obtained as a function of the five dimensionless process parameters: Biot number, radiation number, wall/gas and particle/gas temperature ratios and mode of convection. Accuracy is demonstrated by comparison with an existing numerical solution for the limiting case of pure radiative heating of a plate initially at absolute zero.     

热泳和Brown运动对太阳能辐射下热分层纳米流体边界层流动的影响

在太阳辐射下的纳米流体中,数值地研究竖向延伸壁面具有可变流条件时的层流运动.使用的纳米流体模型为,在热分层中综合考虑了Brown运动和热泳的影响.应用一个特殊形式的Lie群变换,即缩放群变换,得到相应边值问题的对称群.对平移对称群得到一个精确解,对缩放对称群得到数值解.数值解依赖于Lewis数、Brown运动参数、热分层参数和热泳参数.得到结论:上述参数明显地影响着流场、温度和纳米粒子体积率的分布.显示出纳米流体提高了基流体热传导率和对流的热交换性能,基流体中的纳米粒子还具有改善液体辐射性能的作用,直接提高了太阳能集热器的吸热效率.     

On the potential in non‐Gaussian chain polymer models

In this paper, we investigate the potential for a class of non‐Gaussian processes so‐called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M‐Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution.     

Exergoeconomic optimal performance of an irreversible closed Brayton cycle combined cooling,heating and power plant

A combined cooling, heating and power (CCHP) plant model composed of an irreversible closed Brayton cycle and an endoreversible four-heat-reservoir absorption refrigeration cycle is established by using finite time thermodynamics. The irreversibilities considered in the CCHP plant include heat-resistance losses in the hot-, cold-, thermal consumer-, generator-, absorber-, condenser- and evaporator-side heat exchangers as well as non-isentropic losses in the compression and expansion processes. Equations of exergy efficiency and profit rate of the CCHP plant are derived. Based on the finite time exergoeconomic analysis method, profit rate optimization is carried out by searching the optimal compressor pressure ratio and the optimal heat conductance distributions of the seven heat exchangers for a fixed total heat exchanger inventory and with the help of Powell arithmetic. The effects of some design parameters, including compressor and gas turbine efficiencies, ratio of heat demanded by the thermal consumer to power output, heat reservoir temperature ratios and price ratios on the optimal heat conductance distributions, optimal compressor pressure ratio, maximum profit rate and finite time exergoeconomic performance bound of the CCHP plant are discussed by numerical examples. The results obtained may provide some theoretical guidelines for the designs and operations of the practical CCHP plants.     

Esscher变换下扩展的欧式交换期权定价

文章研究Esscher变换下标的资产价格服从几何布朗运动的扩展的几种欧式交换期权(包括广义交换期权,复合交换期权,障碍交换期权,红绿灯期权)定价问题.首先,给出了带漂移布朗运动的反射原理和性质;其次,借助Gerber和Shiu (1994)给出了多维独立平稳增量过程和二维带漂移布朗运动的Esscher变换定义及其性质;最后,应用Esscher变换的相关理论给出了标的资产价格服从几何布朗运动的扩展的多种欧式交换期权定价公式.特别,本文所得到的期权定价公式与以往文献中给出的结果是一致的.     

Tanaka Formula for Multidimensional Brownian Motions

We study the Tanaka formula for multidimensional Brownian motions in the framework of generalized Wiener functionals. More precisely, we show that the submartingale U(B _t –x) is decomposed in the sence of generalized Wiener functionals into the sum of a martingale and the Brownian local time, U being twice of the kernel of Newtonian potential and B _t the multidimensional Brownian motion. We also discuss on an aspect of the Tanaka formula for multidimensional Brownian motions as the Doob–Meyer decomposition.     

广义布朗单的容度估计

研究了既没有平稳增量性,也没有scaling性质的N指标d维广义布朗单的容度问题．证明了广义布朗单“好象”一个局部平稳增量过程,应用Cairoli极大不等式和多参数鞅的方法得到了广义布朗单的碰撞概率与容度之间的关系,给出了其碰撞概率的确切容度估计．所得结果包含了布朗单和可加布朗运动的相应结果．     

A Central Limit Theorem for the Generalized Quadratic Variation of the Step Fractional Brownian Motion

This paper gives a central limit theorem for the generalized quadratic variation of the step fractional Brownian motion. We first recall the definition of this process and the statistical results on the estimation of its parameters.