Cold Heat Reservoir Research Articles

Performance of Quantum Heat Engines Enhanced by Adiabatic Deformation of Trapping Potential.

We present a quantum Otto engine model alternatively driven by a hot and a cold heat reservoir and consisting of two isochoric and two adiabatic strokes, where the adiabatic expansion or compression is realized by adiabatically changing the shape of the potential. Here, we show that such an adiabatic deformation may alter operation mode and enhance machine performance by increasing output work and efficiency, even with the advantage of decreasing work fluctuations. If the heat engine in the sudden limit operates under maximal power by optimizing the control parameter, the efficiency shows certain universal behavior, η*=ηC/2+ηC2/8+O(ηC3), where ηC=1-βhr/βcr is the Carnot efficiency, with βhr(βcr) being the inverse temperature of the hot (cold) reservoir. However, such efficiency under maximal power can be produced by our machine model in the regimes where the machine without adiabatic deformation can only operate as a heater or a refrigerator.

Comparative analysis and optimization of one- and two-stage cooling systems with thermoelectric cells with respect to supercooling

The paper discusses issues related to the modelling of a cooling system equipped with thermoelectric modules to achieve the lowest possible temperature of the cooled space. Considerations were made for both the steady state and the momentary capability to reach the lowest possible temperatures. The analysis concerns modules arranged as the in-series thermal connection in a sandwich configuration and the parallel connection in a single layer. It was assumed that in each case the modules worked with identical heat exchangers. Optimal sizes were found for the modules in each of the analysed configurations, both considering and omitting in the model the thermal resistance between the system elements. Taking resistance into account results in an almost 50% increase in the module dimensions to 90/250, compared to 60/170, and also in the minimum temperature rise by even up to 20K. Inducing higher currents in the circuits of the modules can cause momentary supercooling of the cold heat reservoir significantly below the temperature achievable in the steady state. The highest values of momentary drops in temperature can be achieved through current pulse in the circuits, and also for higher thermal capacities of the upper and additional internal reservoir in a sandwich system. To determine optimal supply currents for the modules, optimization was carried out. In the considered configurations this made it possible to achieve momentary supercooling temperatures by about 18K lower compared to the steady state. The most essential design variables are the number of thermoelectric legs, the shape of the thermal capacity of the current pulse shape and the internal reservoir.

Performance prediction of a new solar-driven electrochemical refrigerator

A new solar-driven electrochemical refrigerator model is proposed by integrating a dye-sensitized solar cell with a thermally regenerative electrochemical refrigerator. Considering various irreversible losses within the dye-sensitized solar cell, thermally regenerative electrochemical refrigerator as well as between them, mathematical formulas for the performance parameters of dye-sensitized solar cell and thermally regenerative electrochemical refrigerator as well as the solar-driven electrochemical refrigerator are derived. Based on the energy balance equation, the electric current relation between the dye-sensitized solar cell and the thermally regenerative electrochemical refrigerator are derived. The maximum cooling rate density and maximum coefficient of performance of the solar-driven electrochemical refrigerator could reach 800.47 W m−2 and 0.8, respectively. There exists an optimum thin film thickness of DSSC to optimize the system performance. A larger photoelectron absorption coefficient, specific charge capacity, isothermal coefficient or regenerative efficiency positively improves the solar-driven electrochemical refrigerator performance. However, a larger Schottky barrier, internal resistance of TRER and temperature difference between hot and cold heat reservoirs is unfavorable for the solar-driven electrochemical refrigerator performance. The obtained results may offer some guidance for the design and optimization of such an actual refrigerator.

Power efficiency characteristics of MHD thermodynamic gas cycle

In this study, the performance of a thermodynamic gas cycle of magnetohydrodynamic (MHD) power generation is considered and presented in terms of power efficiency curves. The dissipation mechanisms considered include: fluid friction modeled by means of the isentropic efficiency of the compressor, heat transfer leakage directly from the hot reservoir to the cold heat reservoir, and constant velocity of the MHD generator. The study demonstrates that power and efficiency vanish at the extremes of both slow and fast operating conditions. These points are demonstrated on power efficiency curves and the locus of efficiency at maximum power and the locus of maximum efficiency. Qualitatively, the considered loss mechanisms have a similar effect on the efficiency at maximum power operation and on maximum efficiency operation, thus these efficiencies are reduced, even for small values of the loss mechanisms.

Attainability of Maximum Work and the Reversible Efficiency of Minimally Nonlinear Irreversible Heat Engines

Abstract We use the general formulation of irreversible thermodynamics and study the minimally nonlinear irreversible model of heat engines operating between a time-varying hot heat source of finite size and a cold heat reservoir of infinite size. We find the criterion under which the optimized efficiency obtained by this minimally nonlinear irreversible heat engine can reach the reversible efficiency under the tight coupling condition: a condition of no heat leakage between the system and the reservoirs. We assume the rate of heat transfer from the hot to the cold heat reservoir obeys Fourier’s law and discuss physical conditions under which one can obtain the reversible efficiency in a finite time with finite power. We also calculate the efficiency at maximum power for the minimally nonlinear irreversible heat engine under the nontight coupling condition.

Coefficient of performance and its bounds of minimally nonlinear irreversible refrigerator at arbitrary optimal value

We study the performance of minimally nonlinear irreversible refrigerators which works between a hot and cold heat reservoir of constant temperatures [Formula: see text] and [Formula: see text], respectively. Applying optimization criterion [Formula: see text] or [Formula: see text], we analyze the coefficient of performance (COP) at arbitrary value of [Formula: see text] or [Formula: see text] and thus obtain the upper and lower bounds of the COP. Our results show that, for the optimized, tightly-coupled refrigerators, a small loss away from the maximum value of either [Formula: see text] or [Formula: see text] figure of merit means a larger gain in the COP.

Optimization of power generating thermoelectric modules utilizing LNG cold energy

A theoretical investigation to optimize thermoelectric modules, which convert LNG cold energy into electrical power, is performed using a novel one-dimensional analytic model. In the model the optimum thermoelement length and external load resistance, which maximize the energy conversion ratio, are determined by the heat supplied to the cold heat reservoir, the hot and cold side temperatures, the thermal and electrical contact resistances and the properties of thermoelectric materials. The effects of the thermal and electrical contact resistances and the heat supplied to the cold heat reservoir on the maximum energy conversion ratio, the optimum thermoelement length and the optimum external load resistance are shown.

Energetics of a heat engine: a molecular dynamics simulation study

We perform a classical molecular dynamics simulation study of a heat engine operating between two heat reservoirs and performing a Carnot-like cycle in a finite time over a wide range of process rates. The working substance of the heat engine is made of highly concentrated interacting Lennard-Jones particles with the aim to simulate a real gas. The piston speed and temperature ratio of the cold and hot heat reservoirs are used as control parameters whereas efficiency and power output per cycle are the physical quantities of interest. The variation of these quantities as a function of the independent parameters is studied with the objective to investigate the validity of relevant theoretical predictions. For instance, for small process rates, the linear dependence of the heat engine efficiency with temperature ratio, in agreement with theory, has been demonstrated. Finally, a unified optimization criterion is applied to determine optimum operation conditions of the engine that make the best trade-off between efficiency and power output.

Four-level refrigerator driven by photons.

We propose a quantum absorption refrigerator driven by photons. The model uses a four-level system as its working substance and couples simultaneously to hot, cold, and solar heat reservoirs. Explicit expressions for the cooling power Q̇(c) and coefficient of performance (COP) η(COP) are derived, with the purpose of revealing and optimizing the performance of the device. Our model runs most efficiently under the tight coupling condition, and it is consistent with the third law of thermodynamics in the limit T→0.

Work output and efficiency at maximum power of linear irreversible heat engines operating with a finite-sized heat source.

We formulate the work output and efficiency for linear irreversible heat engines working between a finite-sized hot heat source and an infinite-sized cold heat reservoir until the total system reaches the final thermal equilibrium state with a uniform temperature. We prove that when the heat engines operate at the maximum power under the tight-coupling condition without heat leakage the work output is just half of the exergy, which is known as the maximum available work extracted from a heat source. As a consequence, the corresponding efficiency is also half of its quasistatic counterpart.

Onsager coefficients of a finite-time Carnot cycle

We study a finite-time Carnot cycle of a weakly interacting gas which we can regard as a nearly ideal gas in the limit of T(h)-T(c) --> 0 where T(h) and T(c) are the temperatures of the hot and cold heat reservoirs, respectively. In this limit, we can assume that the cycle is working in the linear-response regime and can calculate the Onsager coefficients of this cycle analytically using the elementary molecular kinetic theory. We reveal that these Onsager coefficients satisfy the so-called tight-coupling condition and this fact explains why the efficiency at the maximal power eta(max) of this cycle can attain the Curzon-Ahlborn efficiency from the viewpoint of the linear-response theory.

Numerical Experiments of a Finite-Time Thermodynamic Cycle

Heat engines are ubiquitous in our industrial society and are also crucially important to the basis of thermodynamics. They allow us to extract useful work from the heat flowing from a hot heat reservoir into a cold heat reservoir by expanding and compressing the working substance. We have already known that the upper bound of the efficiencies of all the existing heat engines is limited by the Carnot efficiency ηC ≡ 1− Tc/Th where Th and Tc are the temperatures of the hot and the cold reservoirs, respectively. ηC can be realized only when heat engines are working infinitely slowly (quasistatic limit). This implies that the heat engine working in the quasistatic limit produces zero power because it takes infinite time to produce a finite amount of work. Though the Carnot efficiency is a fundamental result which manifests the natural law of the heat energy conversion and supplies certain guidance for designing efficient heat engines, it is not useful for describing the realistic heat engines which should produce finite power. Therefore, it is important to question: Are there any physical laws which can be applied to finite-time heat engines? Motivated by the above considerations, Curzon and Ahlborn studied the efficiency of a finite-time Carnot cycle and derived the result that the efficiency at the maximal power output ηmax becomes

Optimizing miniature thermoacoustic coolers

Because of limited sound intensity output from commercial drivers at midaudio and ultrasonic frequency ranges used in thermoacoustic coolers, it is important to optimize their performance. To achieve this, studies were conducted on heat transfer at the cold heat exchanger and at the hot heat exchanger. Measurements were taken on stray heat influx to the cooler by mechanisms of convection, conduction, radiation, and streaming, and from the driver. PIV studies show the contributions of streaming, both from the driver and other parts of the devices. A special 4-layer copper mesh heat exchanger was designed and tested to cope with heat pumped acoustically from the cold heat reservoir as well as the streaming from the piezoelectric driver. For typical sound levels of 155–160 dB achieved inside the resonator by commercial bimorph piezoelectric drivers, a cooling power density of 0.5 watts/cm2 was achieved with air at 1 atm. Pressurizing the working gas to 17 atm raises the cooling density. The choice of working gas provides a increase in power density. With the above optimizing approaches, a cooling power density of over 50 watts/cm2 appears feasible for the frequency range of 4 to 24 kHz. [Work supported by a grant from the ONR and the State of Utah.]

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.

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.

Performance analysis for an irreversible variable temperature heat reservoir closed intercooled regenerated Brayton cycle

In this paper, the theory of finite time thermodynamics is used in the performance analysis of an irreversible closed intercooled regenerated Brayton cycle coupled to variable temperature heat reservoirs. The analytical formulae for dimensionless power and efficiency, as functions of the total pressure ratio, the intercooling pressure ratio, the component (regenerator, intercooler, hot and cold side heat exchangers) effectivenesses, the compressor and turbine efficiencies and the thermal capacity rates of the working fluid and the heat reservoirs, the pressure recovery coefficients, the heat reservoir inlet temperature ratio, and the cooling fluid in the intercooler and the cold side heat reservoir inlet temperature ratio, are derived. The intercooling pressure ratio is optimized for optimal power and optimal efficiency, respectively. The effects of component (regenerator, intercooler and hot and cold side heat exchangers) effectivenesses, the compressor and turbine efficiencies, the pressure recovery coefficients, the heat reservoir inlet temperature ratio and the cooling fluid in the intercooler and the cold side heat reservoir inlet temperature ratio on optimal power and its corresponding intercooling pressure ratio, as well as optimal efficiency and its corresponding intercooling pressure ratio are analyzed by detailed numerical examples. When the heat transfers between the working fluid and the heat reservoirs are executed ideally, the pressure drop losses are small enough to be neglected and the thermal capacity rates of the heat reservoirs are infinite, the results of this paper replicate those obtained in recent literature.

Transport Induced by Dichotomic Temperature Fluctuations**The project supported by National Natural Science Foundation of China under Grant No. 19605002 and the Excellent Young Teachers' Foundation of the Ministry of Education of China

The transport process of a Brownian particle in a ratchet-like potential subjected to two exchanging Gaussian white noises is studied. The change of the temperatures is described by a stochastic dichotornic process. By making use of the perturbation method the probability current up to second order in small correlation time is obtained, and time-averaged current is evaluated numerically for a whole region of the parameters. For asymptotically fst temperature cycles, the present model yields larger current in comparison with the periodical temperature cycles. Depending on the temperature of cold heat reservoir, the current changes sign as a function of .

Tandem magnetic refrigerator for 1.8 K

A tandem magnetic refrigerator has been developed for continuous operation between 4.2 and 1.8 K. This paper presents the design, computer simulation and construction of the prototype machine. The regenerative concept is employed in the magnetic refrigerator to obtain a cascaded magnetic Carnot cycle effect along the temperature axis from the cold end to the warm end. Entropy pumping action from the cold heat reservoir to the warm heat reservoir occurs in the active magnetic regenerator. The inherent sources of irreversibility in regenerative magnetic refrigerators, i.e. heat capacity imbalance between magnetic refrigerant and heat transport medium, helium entrainment and dead volume effect, have been minimized by design optimization of the system components. The magnetic system of the tandem refrigerator has two virtually identical units, each consisting of a gadolinium gallium garnet (GGG; Gd 3Ga 5O 12) magnetic core, a superconducting magnet, a warm end heat exchanger and a cold end heat exchanger. These components are united by a cryogenic displacer which shuttles the heat transport medium, subatmospheric 3He gas, between the two units. The prototype of the designed magnetic refrigerator has operated continuously, producing a net refrigeration rate of 12 mW per magnetic core at 1.8 K.

Redefining cooling rate in terms of ice front velocity and thermal gradient: First evidence of relevance to freezing injury of lymphocytes

A freezing process and the resulting injury or survival of biological cells is commonly characterized in terms of the cooling rate, B. Under certain circumstances, the cooling rate can be expressed as B = G · v, where G denotes the thermal gradient at the ice-liquid interface and v its velocity, respectively. To determine the influence of G and v on the morphology of the ice-liquid interface and on cell survival, a gradient freezing stage was designed. Flat capillaries could be pushed with constant velocity from a warm to a cold heat reservoir. With this setup both parameters, G and v, are independently adjustable and the resulting process of directional solidification can be observed dynamically in a light microscope. Human lymphocytes in phosphate-buffered saline with 10 vol% of dimethyl sulfoxide were used as biological test material. Viability was assessed by a membrane integrity test with fluorescein diacetate and ethidium bromide. All cells were cooled down to a final temperature of −196 °C and then rapidly thawed. The results obtained with this technique show that the viability determined after freezing and thawing with a certain cooling rate, B = G · v, may vary considerably depending on the imposed values of the thermal gradient, G, and the ice front velocity, v. In addition, the data seem to suggest that, first, the maximum viability which can be reached is governed by the cooling rate, and, second, this maximum for a given cooling rate could be achieved by establishing small temperature gradients and high interface velocities (about 30 ° K/cm and 500 (μm/sec, respectively, for the range of values of G and v tested).

The Temperature Coefficients of Electrode Potentials: The Isothermal and Thermal Coefficients—The Standard Ionic Entropy of Electrochemical Transport of the Hydrogen Ion

The temperature coefficient of the potential of an electrode can be defined experimentally by reference to (a) the potential of the SHE at the same temperature, (b) the potential of the same electrode at some fixed temperature. These two definitions give rise to the “isothermal” and “thermal” temperature coefficients of electrode potentials. The isothermal coefficient is where ΔS is the reaction entropy of the “SHE//Electrode” cell. The thermal coefficient is where is the entropy transported from the hot to the cold heat reservoir by the passage of n faradays of positive electricity through the cell from the cold to the hot electrode (before the onset of thermal diffusion). The entropy is divided into an entropy of electrochemical transport which determines the electrode temperature effect, and an entropy of migration transport which determines the thermal liquid junction potential.By assuming that is negligible in a saturated potassium chloride bridge, we have deduced that the thermal temperature coefficient of the SHE is +0.871 mv/°C [hot electrode (+) terminal] at 25°C. The standard ionic entropy of electrochemical transport of hydrogen ion is −4.48 cal/deg. Thermal temperature coefficients are computed for calomel, silver chloride, and copper sulfate electrodes and are compared with experiment. Thermal and isothermal temperature coefficients are computed and tabulated for nearly 300 standard electrode potentials.