Reprint of : Three-terminal heat engine and refrigerator based on superlattices

We propose a three-terminal heat engine based on semiconductor superlattices for energy harvesting. The periodicity of the superlattice structure creates an energy miniband, giving an energy window for allowed electron transport. We find that this device delivers a large power, nearly twice than the heat engine based on quantum wells, with a small reduction of efficiency. This engine also works as a refrigerator in a different regime of the system's parameters. The thermoelectric performance of the refrigerator is analyzed, including the cooling power and coefficient of performance in the optimized condition. We also calculate phonon heat current through the system and explore the reduction of phonon heat current compared to the bulk material. The direct phonon heat current is negligible at low temperatures, but dominates over the electronic at room temperature and we discuss ways to reduce it.     

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     

Effect of thermal inhomogeneity on the performance of a Brownian heat engine

We explore the effect of thermal inhomogeneity on the performance of a Brownian heat engine by considering exactly solvable models. We first consider a Brownian heat engine which is modeled as a Brownian particle in a ratchet potential moving through a highly viscous medium driven by the thermal kick it receives from a linearly decreasing background temperature. We show that even though the energy transfer due to kinetic energy is neglected, Carnot efficiency cannot be achieved at quasistatic limit. At quasistatic limit, the efficiency for such a Brownian heat engine approaches the efficiency of endoreversible engine η = 1 ? √T _c /T _h [F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)]. Moreover, the dependence of the current, the efficiency and the coefficient of performance of the refrigerator on the model parameters is also explored via Brownian dynamic simulations and analytically. 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 [M. Asfaw, M. Bekele, Eur. Phys. J. B 38, 457 (2004), M. Asfaw, M. Bekele, Physica A 384, 346 (2007)]. Furthermore, for a Brownian heat engine driven by a piecewise constant temperature, we show that systematic removal of the inhomogeneous medium leads to a homogeneous medium with a uniform temperature where the effect of temperature inhomogeneity is replaced by an effective load.     

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.     

Effects of dark energy on the efficiency of charged AdS black holes as heat engines

In this paper, we study the heat engine where a charged AdS black hole surrounded by dark energy is the working substance and the mechanical work is done via the PdV term in the first law of black hole thermodynamics in the extended phase space. We first investigate the effects of a kind of dark energy (quintessence field in this paper) on the efficiency of the RN-AdS black holes as the heat engine defined as a rectangular closed path in the P–V plane. We get the exact efficiency formula and find that the quintessence field can improve the heat engine efficiency, which will increase as the field density \(\rho _q\) grows. At some fixed parameters, we find that a larger volume difference between the smaller black holes(\(V_1\)) and the bigger black holes(\(V_2\) ) will lead to a lower efficiency, while the bigger pressure difference \(P_1-P_4\) will make the efficiency higher, but it is always smaller than 1 and will never be beyond the Carnot efficiency, which is the maximum value of the efficiency constrained by thermodynamics laws; this is consistent to the heat engine in traditional thermodynamics. After making some special choices for the thermodynamical quantities, we find that the increase of the electric charge Q and the normalization factor a can also promote the heat engine efficiency, which would infinitely approach the Carnot limit when Q or a goes to infinity.     

Heat flow and efficiency in a microscopic engine

We study the energetics of a thermal motor driven by temperature differences, which consists of a Brownian particle moving in a sawtooth potential with an external load where the viscous medium is periodically in contact with hot and cold heat reservoir along space coordinate. The motor can work as a heat engine or a refrigerator under different conditions. The heat flow via both potential and kinetic energy is considered. The former is reversible when the engine works quasistatically and the latter is always irreversible. The efficiency of the heat engine can never approach Carnot efficiency.     

Heat Modulation on Target Thermal Bath via Coherent Auxiliary Bath

We study a scheme of thermal management where a three-qubit system assisted with a coherent auxiliary bath (CAB) is employed to implement heat management on a target thermal bath (TTB). We consider the CAB/TTB being ensemble of coherent/thermal two-level atoms (TLAs), and within the framework of collision model investigate the characteristics of steady heat current (also called target heat current (THC)) between the system and the TTB. It demonstrates that with the help of the quantum coherence of ancillae the magnitude and direction of heat current can be controlled only by adjusting the coupling strength of system-CAB. Meanwhile, we also show that the influences of quantum coherence of ancillae on the heat current strongly depend on the coupling strength of system—CAB, and the THC becomes positively/negatively correlated with the coherence magnitude of ancillae when the coupling strength below/over some critical value. Besides, the system with the CAB could serve as a multifunctional device integrating the thermal functions of heat amplifier, suppressor, switcher and refrigerator, while with thermal auxiliary bath it can only work as a thermal suppressor. Our work provides a new perspective for the design of multifunctional thermal device utilizing the resource of quantum coherence from the CAB.     

Efficiency of Inefficient Endoreversible Thermal Machines

We present a study of the performance of endoreversible thermal machines optimized with respect to the thermodynamic force associated with the cold bath in the regime of small thermodynamic forces. These thermal machines can work either as an engine or as a refrigerator. We analyze how the optimal performances are determined by the dependence of the thermodynamic flux on the forces. The results are motivated and illustrated with a quantum model, the three level maser, and explicit analytical expressions of the engine efficiency as a function of the system parameters are given.     

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.     

Dynamic properties in an endoreversible Curzon-Ahlborn engine using a van der Waals gas as working substance

In this work we analyze the stability of an endoreversible Curzon-Ahlborn engine, using a van der Waals gas as working substance and the corresponding efficiency for such an engine. From the local stability analysis we find that a critical point of an almost linear system is stable. After arbitrary small perturbation, the system state exponentially decays to a critical point with either of two characteristic relaxation times that are a function of the thermal conductance (α), heat capacity (C) and τ=T2/T1. The behavior of relaxation times and solution of the systems are shown qualitatively by sketching its phase portrait. Finally we discuss the local stability and steady state energetic properties of the endoreversible engine.     

The Spectral Zeta Function for Laplace Operators on Warped Product Manifolds of the type I × f N

In this work we study the spectral zeta function associated with the Laplace operator acting on scalar functions defined on a warped product of manifolds of the type I × _f N, where I is an interval of the real line and N is a compact, d-dimensional Riemannian manifold either with or without boundary. Starting from an integral representation of the spectral zeta function, we find its analytic continuation by exploiting the WKB asymptotic expansion of the eigenfunctions of the Laplace operator on M for which a detailed analysis is presented. We apply the obtained results to the explicit computation of the zeta regularized functional determinant and the coefficients of the heat kernel asymptotic expansion.     

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.     

Heat transistor: demonstration of gate-controlled electronic refrigeration

We present experiments on a superconductor-normal-metal electron refrigerator in a regime where single-electron charging effects are significant. The system functions as a heat transistor; i.e., the heat flux out from the normal-metal island can be controlled with a gate voltage. A theoretical model developed within the framework of single-electron tunneling provides a full quantitative agreement with the experiment. This work serves as the first experimental observation of Coulombic control of heat transfer and, in particular, of refrigeration in a mesoscopic system.     

Size dependence of efficiency at maximum power of heat engine

We perform a molecular dynamics computer simulation of a heat engine model to study how the engine size difference affects its performance. Upon tactically increasing the size of the model anisotropically, we determine that there exists an optimum size at which the model attains the maximum power for the shortest working period. This optimum size locates between the ballistic heat transport region and the diffusive heat transport one. We also study the size dependence of the efficiency at the maximum power. Interestingly, we find that the efficiency at the maximum power around the optimum size attains a value that has been proposed as a universal upper bound, and it even begins to exceed the bound as the size further increases. We explain this behavior of the efficiency at maximum power by using a linear response theory for the heat engine operating under a finite working period, which naturally extends the low-dissipation Carnot cycle model [M. Esposito, R. Kawai, K. Lindenberg, C. Van den Broeck, Phys. Rev. Lett. 105, 150603 (2010)]. The theory also shows that the efficiency at the maximum power under an extreme condition may reach the Carnot efficiency in principle.     

线性不可逆热力学框架下一个无限尺寸热源而有限尺寸冷源的制冷机的性能分析

如何优化工作在有限尺寸的热源与冷源之间的热设备的性能是有限时间热力学领域的一个重要课题.本文在线性不可热力学框架下,结合有限时间热力学理论,研究了一个无限尺寸热源而有限尺寸冷源的制冷机的工作过程,解析性地推导了紧耦合条件下平均输入功率以及制冷系数表达式,并且进一步讨论了该制冷机的性能.发现平均输入功率与制冷时间不存在明确的优化关系,而且输入功率的增加导致制冷系数单调减小,但辐射能的增加致使制冷系数增强.研究结果对于深入理解实际的热力学过程具有一定的工程实践性价值.     

Feynman's ratchet and pawl: an exactly solvable model

We introduce a simple, discrete model of Feynman's ratchet and pawl, operating between two heat reservoirs. We solve exactly for the steady-state directed motion and heat flows produced, first in the absence and then in the presence of an external load. We show that the model can act both as a heat engine and as a refrigerator. We finally investigate the behavior of the system near equilibrium, and use our model to confirm general predictions based on linear-response theory.     

Experimental investigation of a thermoacoustic-Stirling refrigerator driven by a thermoacoustic-Stirling heat engine

In this paper, a thermally-driven thermoacoustic refrigerator system without any moving part is reported. This refrigeration system consists of a thermoacoustic-Stirling heat engine and a thermoacoustic-Stirling refrigerator; that is, the former is the driving source for the latter. Both the subsystems are designed to operate on traveling-wave mode. In the experiment, it was found that the DC-flows had significant negative effect on the heat engine and the refrigerator. To suppress these DC-flows, two flexible membranes were inserted into the two subsystems and worked very well. Then extensive experiments were made to test the influence of different parameters on refrigeration performance of the whole system. The system has so far achieved a no-load temperature of -65 degrees C, a cooling capacity of about 270 W at -20 degrees C and 405 W at 0 degrees C; in fact, the result showed a good prospect of the refrigeration system in room-temperature cooling such as food refrigeration and air-conditioning.     

两级烟气废热热管溴化锂发生器的动态特性

利用热管废热溴化锂制冷机不仅能够回收工业过程的大量废热、余热,而且可以提高整个工业系统的能源利用效率。针对两级烟气废热热管溴化锂制冷机发生器的结构特征,建立了动态数学模型,进行了数值求解,得出了机组启动过程中发生器的各参数的变化规律。结果表明:蒸汽发生量与溶液出口温度基本同步稳定,烟气中间为250℃左右,出口温度为200℃左右。此研究对减短启动时间、节约能源具有一定的积极意义。     

Influence of stack geometry and resonator length on the performance of thermoacoustic engine

Thermoacoustic engines convert heat energy into high amplitude sound waves, which is used to drive thermoacoustic refrigerator or pulse tube cryocoolers by replacing the mechanical pistons such as compressors. The increasing interest in thermoacoustic technology is of its potentiality of no exotic materials, low cost and high reliability compared to vapor compression refrigeration systems. The experimental setup has been built based on the linear thermoacoustic model and some simple design parameters. The engines produce acoustic energy at the temperature difference of 325–450 K imposed along the stack of the system. This work illustrates the influence of stack parameters such as plate thickness (PT) and plate spacing (PS) with resonator length on the performance of thermoacoustic engine, which are measured in terms of onset temperature difference, resonance frequency and pressure amplitude using air as a working fluid. The results obtained from the experiments are in good agreement with the theoretical results from DeltaEc.     

Holographic heat engine efficiency of hyperbolic charged black holes

We consider a four-dimensional charged hyperbolic black hole as working matter to establish a black hole holographic heat engine, and use the rectangular cycle to obtain the heat engine efficiency. We find that when the increasing of entropy is zero, the heat engine efficiency of the hyperbolic black hole becomes the well-known Carnot efficiency. We also find that less charge corresponds to higher efficiency in the case of $\tilde{q}>0$. Furthermore, we study the efficiency of the flat case and spherical case and compare the efficiency with that of the hyperbolic charged black holes. Finally, we use numerical simulation to study the efficiency in benchmark scheme.