Irreversible Brownian Heat Engine

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine \(\eta =1-\sqrt{{T_{c}/T_{h}}}\) [23]. On the other hand, the maximum power efficiency of the engine approaches \(\eta ^{MAX}=1-({T_{c}/T_{h}})^{1\over 4}\). It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.     

Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine

Brownian particles moving in a spatially asymmetric but periodic potential (ratchet), with an external load force and connected to an alternating hot and cold reservoir, are modeled as a microscopic heat engine, referred to as the Brownian heat engine. The heat flow via both the potential energy and the kinetic energy of the particles are considered simultaneously. The forward and backward particle currents are determined using an Arrhenius' factor. Expressions for the power output and efficiency are derived analytically. The maximum power output and efficiency are calculated. It is expounded that the Brownian heat engine is always irreversible and its efficiency cannot approach the efficiency η_C of the Carnot heat engine even in quasistatic limit. The influence of the main parameters such as the load, the barrier height of the potential, the asymmetry of the potential and the temperature ratio of the heat reservoirs on the performance of the Brownian heat engine is discussed in detail. It is found that the Brownian heat engines may be controlled to operate in different regions through variation of some parameters.     

Modeling and Performance Optimization of an Irreversible Two-Stage Combined Thermal Brownian Heat Engine

Based on finite time thermodynamics, an irreversible combined thermal Brownian heat engine model is established in this paper. The model consists of two thermal Brownian heat engines which are operating in tandem with thermal contact with three heat reservoirs. The rates of heat transfer are finite between the heat engine and the reservoir. Considering the heat leakage and the losses caused by kinetic energy change of particles, the formulas of steady current, power output and efficiency are derived. The power output and efficiency of combined heat engine are smaller than that of single heat engine operating between reservoirs with same temperatures. When the potential filed is free from external load, the effects of asymmetry of the potential, barrier height and heat leakage on the performance of the combined heat engine are analyzed. When the potential field is free from external load, the effects of basic design parameters on the performance of the combined heat engine are analyzed. The optimal power and efficiency are obtained by optimizing the barrier heights of two heat engines. The optimal working regions are obtained. There is optimal temperature ratio which maximize the overall power output or efficiency. When the potential filed is subjected to external load, effect of external load is analyzed. The steady current decreases versus external load; the power output and efficiency are monotonically increasing versus external load.     

周期性双势垒锯齿势中温差驱动的布朗热机

研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明：当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率. 关键词： 布朗热机 双势垒锯齿势 热漏 热力学性能     

Bound on Efficiency of Heat Engine from Uncertainty Relation Viewpoint

Quantum cycles in established heat engines can be modeled with various quantum systems as working substances. For example, a heat engine can be modeled with an infinite potential well as the working substance to determine the efficiency and work done. However, in this method, the relationship between the quantum observables and the physically measurable parameters—i.e., the efficiency and work done—is not well understood from the quantum mechanics approach. A detailed analysis is needed to link the thermodynamic variables (on which the efficiency and work done depends) with the uncertainty principle for better understanding. Here, we present the connection of the sum uncertainty relation of position and momentum operators with thermodynamic variables in the quantum heat engine model. We are able to determine the upper and lower bounds on the efficiency of the heat engine through the uncertainty relation.     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.     

Thermodynamic Performance Characteristics of a Brownian MicroscopicHeat Engine Driven by Discrete and Periodic Temperature Field

A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by a discrete and periodic temperature field in a periodic sawtooth potential is investigated. In order to clarify the underlying physical pictures of the heat engine, the heat flow via the potential energy and the kinetic energy of the particles are considered simultaneously. Based on describing the jumps among the three states, the expressions of theefficiency and power output of the heat engine are derived analytically. The general performance characteristic curves are plotted by numerical calculation. It is found that the power output-efficiency curve is a loop-shaped one, which is similar to one for a real irreversible heat engine. The influence of the ratioof the temperature of the hot and cold reservoirs and the sawtooth potential on the maximum efficiency and power output is analyzed forsome given parameters. When the heat flows via the kinetic energy isneglected, the power output-efficiency curve is an open-shaped one,which is similar to one for an endroeversible heat engine.     

以广义Redlich-Kwong气体为工质的不可逆回热式斯特林热机循环输出功率和效率

研究了热阻、回热损失和热漏等多种不可逆因素对以广义Redlich-Kwong气体为工质的斯特林热机性能的影响,给出了斯特林热机输出功率和效率的具体表达式并分析非理想回热特性及循环主要性能参数(如循环体积比及工质高低温比等)对循环输出功率和效率的影响.同时指出,只有在理想回热及无热漏的情况下,气体斯特林热机的效率才能达到卡诺效率.     

以一维谐振子势阱中的单粒子为工质的量子热机性能分析

建立了以一维谐振子势阱中的单粒子为工质的量子热机模型.当势阱壁宽度和粒子的量子态缓慢改变时, 该热机类似于经典卡诺热机对外做功.假设势阱壁移动速度非常缓慢并且考虑热漏, 推导出量子热机循环的输出功率和效率等重要性能参数的一般表达式.通过优化分析, 获得了热机循环中各主要性能参数的最佳优化值和优化区间.     

线性与非线性传热过程的Curzon-Ahlborn热机在任意功率时的效率

热机性能的优化是热力学领域的一个重要问题,而工质与热源之间的传热过程是热机工作时产生不可逆的主要来源.本文在引入功率增益和效率增益两个重要参数的基础上,基于一个简化的Curzon-Ahlborn热机模型并利用合比分比原理,给出了线性与非线性传热过程的热机在任意功率输出时的效率表达式,结合数值计算详细讨论了热机在任意功率输出时的特性.研究表明,参数ξ作为功率增益δP的函数存在两个分支:在第一分支上(不利情形),效率呈现出单调变化特征;在第二分支上(有利情形),效率随着的δP变化是非单调的且有最大值.随着传热指数的增加,热机的工作区域减小,这源于非线性传热过程包含热辐射所致.进一步发现功率-效率关系曲线存在权衡工作点,热机在该点附近工作能够实现最有效的热功转换.研究结果有助于深入理解具有不同传热过程热机的优化执行.     

Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Reprint of : Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Performance analysis of a tunneling thermoelectric heat engine with nano-scaled quantum well

A numerical model of a nano-scaled thermoelectric heat engine with InP/InAs/InP trilayer quantum well (QW) is investigated. The expressions of those performance parameters, such as current, power output, and efficiency are expressed. By numerical calculation, the resonant tunneling behavior of electrons in the QW is described, which seems like a very good energy selective electron mechanism for the heat engine. After considering the radiation heat leakage, for fixed layer thicknesses of the QW, the optimum working regions of the heat engine with respect to the chemical potentials and the bias voltage are obtained numerically under the economic criterion. From these results, the power output can be increased by narrowing down the layer thicknesses. In addition, owing to the radiant heat leakage, the efficiency initially increases in the working regions and then decreases when the layer thicknesses increase gradually, from which one can obtain a maximum efficiency by optimizing layer thicknesses of QW. These results calculated here may provide a guide for the optimum designs of tunneling thermoelectric devices.     

多孔介质(PM)发动机理想循环热力学分析

本文论述了基于多孔介质燃烧技术的超绝热发动机的原理及其工作过程,建立了PM发动机的热力学模型,对 PM发动机内的PM回热循环进行热力学分析,列出了循环参数如压缩比、预胀比、预压比等对发动机效率、循环功的影响,确定了PM回热循环的两种极限状态。将PM回热循环与发动机的Otto循环、Diesel循环进行比较,结果表明: PM回热循环在保证效率的同时,可以大幅度提高循环功。     

Isolated quantum heat engine

We present a theoretical and numerical analysis of a quantum system that is capable of functioning as a heat engine. This system could be realized experimentally using cold bosonic atoms confined to a double well potential that is created by splitting a harmonic trap with a focused laser. The system shows thermalization, and can model a reversible heat engine cycle. This is the first demonstration of the operation of a heat engine with a finite quantum heat bath.     

Implementing Black Hole as Efficient Power Plant *

Treating the black hole molecules as working substance and considering its phase structure, we study the black hole heat engine by a charged anti-de Sitter black hole. In the reduced temperature-entropy chart, it is found that the work, heat, and efficiency of the engine are free of the black hole charge. Applying the Rankine cycle with or without a back pressure mechanism to the black hole heat engine, the compact formula for the efficiency is obtained. And the heat, work and efficiency are worked out. The result shows that the black hole engine working along the Rankine cycle with a back pressure mechanism has a higher efficiency. This provides a novel and efficient mechanism to produce the useful mechanical work, and such black hole heat engine may act as a possible energy source for the high energy astrophysical phenomena near the black hole.     

A thermoacoustic-Stirling heat engine: detailed study

A new type of thermoacoustic engine based on traveling waves and ideally reversible heat transfer is described. Measurements and analysis of its performance are presented. This new engine outperforms previous thermoacoustic engines, which are based on standing waves and intrinsically irreversible heat transfer, by more than 50%. At its most efficient operating point, it delivers 710 W of acoustic power to its resonator with a thermal efficiency of 0.30, corresponding to 41% of the Carnot efficiency. At its most powerful operating point, it delivers 890 W to its resonator with a thermal efficiency of 0.22. The efficiency of this engine can be degraded by two types of acoustic streaming. These are suppressed by appropriate tapering of crucial surfaces in the engine and by using additional nonlinearity to induce an opposing time-averaged pressure difference. Data are presented which show the nearly complete elimination of the streaming convective heat loads. Analysis of these and other irreversibilities show which components of the engine require further research to achieve higher efficiency. Additionally, these data show that the dynamics and acoustic power flows are well understood, but the details of the streaming suppression and associated heat convection are only qualitatively understood.     

Current,maximum power and optimized efficiency of a Brownian heat engine

A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs with maximum power and with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines.Received: 28 December 2003, Published online: 28 May 2004PACS: 05.40.Jc Brownian motion - 05.60.-k Transport processes - 05.70.-a ThermodynamicsMesfin Asfaw: Present address: Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany     

Efficiency bounds for nonequilibrium heat engines

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples.