Energy Selective Electron Heat Research Articles

Optimal performance regions of an irreversible energy selective electron heat engine with double resonances

A theoretical model for irreversible double resonance ESE (energy selective electron) device with phonon induced bypass heat leakage which is operating as heat engine system is proposed. The thermodynamic performance is optimized and the impacts of heat leakage and structure parameters of the electron system on its performance are discussed in detail by using FTT (finite time thermodynamics). Moreover, performances of the ESE system with multiple optimization objective functions, including power output, thermal efficiency, ecological function and efficient power, are explored by numerical examples. New optimal performance regions and the selection plans of optimization objective functions of the ESE system are obtained. It reveals that the characteristic of power versus efficiency behave as loop-shaped curves in spite of the heat leakage which will always decrease the efficiency of the electron engine. By properly choosing the design parameters, the ESE engine can be designed to operate at optimal conditions according to different design purpose. The preferred design area should be located between the optimal effective power condition and the optimal ecological function condition.

Performance evaluation and comparison of three-terminal energy selective electron devices with different connective ways and filter configurations

Three-terminal energy selective electron (ESE) devices consisting of three electronic reservoirs connected by two energy filters and an electronic conductor with negligible resistance may work as ESE refrigerators and amplifiers. They have three possible connective ways for the electronic conductor and six electronic transmission forms. The configuration of energy filters may be described by the different transmission functions such as the rectangular and Lorentz transmission functions. The ESE devices with three connective ways can be, respectively, regarded as three equivalent hybrid systems composed of an ESE heat engine and an ESE refrigerator/heat pump. With the help of the theory of the ESE devices operated between two electronic reservoirs, the coefficients of performance and cooling rates (heat-pumping rates) of hybrid systems are directly derived. The general performance characteristics of hybrid systems are revealed. The optimal regions of these devices are determined. The performances of the devices with three connective ways of the electronic conductor and two configurations of energy filters are compared in detail. The advantages and disadvantages of each of three-terminal ESE devices are expounded. The results obtained here may provide some guidance for the optimal design and operation of three-terminal ESE devices.

Parametric selection criteria of thermal electron-tunneling amplifiers operating at optimum states

A new model of the thermal amplifier consisting of three electronic reservoirs connected by two energy filters and an electronic conductor with negligible resistance is proposed. The thermal amplifier may have two different connective methods and can be regarded as the equivalent system composed of an energy selective electron (ESE) heat engine and an ESE heat pump. With the help of the theory of the ESE devices operating between two electronic reservoirs, the coefficient of performance and rate of heat-pumping of the thermal amplifier are directly derived. The effects of the center energy levels and the half width (or the half width at the half maximum) of two energy filters on the performance of the thermal amplifier are discussed. The maximum coefficient of performance and rate of heat-pumping are calculated. The optimally operating regions of the thermal amplifier are determined. Moreover, the optimum performance characteristics of the thermal amplifier with two configurations of energy filters are compared.

Analysis and optimization with ecological objective function of irreversible single resonance energy selective electron heat engines

Ecological performance of a single resonance ESE heat engine with heat leakage is conducted by applying finite time thermodynamics. By introducing Nielsen function and numerical calculations, expressions about power output, efficiency, entropy generation rate and ecological objective function are derived; relationships between ecological objective function and power output, between ecological objective function and efficiency as well as between power output and efficiency are demonstrated; influences of system parameters of heat leakage, boundary energy and resonance width on the optimal performances are investigated in detail; a specific range of boundary energy is given as a compromise to make ESE heat engine system work at optimal operation regions. Comparing performance characteristics with different optimization objective functions, the significance of selecting ecological objective function as the design objective is clarified specifically: when changing the design objective from maximum power output into maximum ecological objective function, the improvement of efficiency is 4.56%, while the power output drop is only 2.68%; when changing the design objective from maximum efficiency to maximum ecological objective function, the improvement of power output is 229.13%, and the efficiency drop is only 13.53%.

Power and efficiency optimization for an energy selective electron heat engine with double-resonance energy filter

Theoretical modeling for a microscopic ESE (energy selective electron) heat engine with double-resonance energy filters is performed in this paper. The heat flow characteristics and performance parameters are discussed in two different cases according to the positions for central energy level of double resonances. It is found that the analytical expressions for performance parameter such as power output or efficiency in the two cases share the identical form. The optimal performance for the ESE heat engine system is analyzed by using finite time thermodynamic theory. The performance curves and fundamental optimal relation for the system's output power and efficiency are explored with numerical examples. The fundamental optimal relation of power and efficiency is an open loop-shaped curve. There exist a maximum efficiency and a maximum power output. The optimal operating regions of the power and efficiency are determined and the influences of the system's design parameters are discussed. Finally, a comparison of the ESE engine system with double- and single-resonance filters is carried out in order to show the performance differences and the effect of the newly adopted double resonances. The utilization of double-resonance energy filter leads to increased power output while decreased efficiency for the electron heat engine device.

Performance optimization of total momentum filtering double-resonance energy selective electron heat pump

A theoretical model for energy selective electron (ESE) heat pumps operating with two-dimensional electron reservoirs is established in this study. In this model, a double-resonance energy filter operating with a total momentum filtering mechanism is considered for the transmission of electrons. The optimal thermodynamic performance of the ESE heat pump devices is also investigated. Numerical calculations show that the heating load of the device with two resonances is larger, whereas the coefficient of performance (COP) is lower than the ESE heat pump when considering a single-resonance filter. The performance characteristics of the ESE heat pumps in the total momentum filtering condition are generally superior to those with a conventional filtering mechanism. In particular, the performance characteristics of the ESE heat pumps considering a conventional filtering mechanism are vastly different from those of a device with total momentum filtering, which is induced by extra electron momentum in addition to the horizontal direction. Parameters such as resonance width and energy spacing are found to be associated with the performance of the electron system.

Heating load and COP optimization of a double resonance energy selective electron (ESE) heat pump

A model of a double resonance energy selective electron (ESE) heat pump in one-dimensional system with two idealized energy filters is established in this paper. The analytical expressions of heating load and coefficient of performance (COP) for the ESE heat pump are derived. The optimum heating load and COP performances of the double resonance ESE heat pump are analyzed by using the theory of finite time thermodynamics. The effective regions of central energy level and heating load are obtained. The influences of energy space as well as resonance width of the two resonances on the performance of the ESE heat pump are discussed by detailed numerical examples. The values of some important performance parameters are also obtained by numerical calculations. The performance of the double resonance device is compared with that of the single resonance device. It is found that the maximum heating load decreases with the increase of energy space or the decrease of resonance width, while the maximum COP decreases with the increase of energy space or resonance width. By reasonable choices of the first resonance energy level, the energy space and the resonance width, the heat pump can be controlled to operate under the maximum COP condition. The results obtained herein can provide some theoretical guidelines for the design of practical multi-barrier nanostructured devices.

The impact of energy spectrum width in the energy selective electron low-temperature thermionic heat engine at maximum power

Abstract A model of thermionic heat engine with the energy selective electron mechanism is studied. Analytical expressions of the power output and efficiency of this device are derived at low temperature, where the chemical potentials of the reservoirs are assumed to be constant. After discussing the impact of the energy spectrum width of the energy selective electron mechanism, we find two bounds ( η ± ) of efficiency at maximum power exist naturally. When the energy spectrum width increases gradually from zero and then to the semi-infinite case with the infinite upper limit, the efficiency at maximum power decreases monotonously from the upper bound η + to the lower bound η − at a given temperature ratio of the cold and hot reservoirs. The two bound are given by numerical simulation and by an analytical expression respectively. These results may provide some guidance for the application of the practical energy selective electron heat engines.

Performance analysis of irreversible energy selective electron (ESE) heat pump with heat leakage

A model of an irreversible energy selective electron (ESE) heat pump with heat leakage is established in this paper. The general expressions for heating load and coefficient of performance (COP) of the ESE heat pump in the maximum heating load operation regime and the intermediate operation regime are derived respectively. The optimum performances of the ESE heat pump in these two different operation regimes are analysed by detailed numerical examples. The characteristic curves of COP versus heating load considering heat leakage in maximum heating load operation regime are parabolic-like ones, and the COP will approach a fixed value as the heating load increases. This is due to the fact that electrons that contribute positively to heat pumping are all transmitted through the energy filter in this regime. The characteristic curves of COP versus heating load with and without considering heat leakage in intermediated operation regime are all parabolic-like ones, and the COP will be below unity as the heating load increases, which results from the mixing of heat pump behaviour and heat engine behaviour of the electron system in this regime. The influence of the resonance widths on the heating load and COP performances of the ESE heat pump is discussed. Selecting the reasonable ranges of the central energy and resonance width, the ESE heat pump can be controlled to operate in the optimal COP condition. The results obtained herein can provide theoretical guidelines for analysing and improving the performance of micronanothermionic devices.

Performance optimum analysis and load matching of an energy selective electron heat engine

A new model of the energy selective electron (ESE) heat engine with a variable bias voltage resulting from a variable load resistance is established. Analytical expressions for the power output and efficiency of the system are derived, based on the Fermi–Dirac distribution of electrons. The general performance characteristics of the system are revealed. The effects of the energy level of the central position of the filter, chemical potential, and load resistance on the performance of the system are discussed in detail. It is found that as long as the position of the filter is suitably designed, the maximum electric current may be obtained at zero load. The optimal values of two important parameters, the energy level of the central position of the filter and chemical potential or load resistance, are calculated for differently operating states, and consequently, two important criteria on the parametric optimum design are obtained. These results obtained here may provide some guidance for the optimum design of ESE heat engines.

Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics

A total momentum filtered energy selective electron (ESE) heat pump model with heat leakage is established in this paper. The analytical expressions of heating load and coefficient of performance (COP) for both the total momentum filtered ( k r -filtered) ESE heat pump and the conventionally filtered ( k x -filtered) ESE heat pump in which the electrons are transmitted according to the momentum in the direction of transport only are derived, respectively. The optimal performance of the k r -filtered ESE heat pump is analyzed by using the theory of finite time thermodynamics (FTT). The optimal regions of COP and heating load for the k r -filtered heat pump are obtained. By comparing the performance of the k r -filtered device with that of the k x -filtered device, it is found that the heating load performance and the COP versus heating load characteristic curves of the k r -filtered heat pump are totally different from those of the k x -filtered device; and the maximum COP and maximum heating load of the k r -filtered device are generally higher than those of the k x -filtered device. The influences of heat leakage, resonance width, hot reservoir temperature and chemical potential on the performance of the total momentum filtered ESE heat pump are further analyzed by numerical calculations. The obtained results can provide some theoretical guidelines for the design of practical electron systems such as solid-state thermionic heat pump devices.

Performance optimization of a total momentum filtered energy selective electron (ESE) heat engine with double resonances

A model of an energy selective electron (ESE) heat engine with double resonances which filter electrons according to their total momentum is established in this paper. The optimal performance of the double resonance ESE heat engine is analyzed by using the theory of finite time thermodynamics (FTT). The performance of the double resonance ESE heat engine is compared with that of the single resonance device. It is shown that the double resonance device can generate more power but at the same time becomes less efficient. Performance comparisons are also performed between the total momentum filtered ESE heat engine in which the electrons are transmitted according to the total electron momentum in all the three dimensions and the conventional ESE heat engine where the electrons are filtered according to the momentum in the direction of transport only. It is found that the total momentum filtered ESE heat engine outperforms the conventionally filtered ESE heat engine on both power output and efficiency performance. Moreover, the effects of resonance width, energy spacing of two resonances and cold reservoir temperature on the performance of the total momentum filtered double resonance heat engine are analyzed in detail by numerical calculations. In practical operation of the double resonance ESE heat engine, the values of resonance width, energy spacing and cold reservoir temperature should be small in order for the device to obtain higher efficiency.

Ecological optimization of energy selective electron (ESE) heat engine

The ecological performance optimization of an energy selective electron (ESE) heat engine operated at maximum power regime and the intermediate regime (i.e. between maximum power operation and reversible operation) is carried out in this paper by using finite time thermodynamics. In the analyses, the analytical formulae for the entropy generation rate and the ecological function of the ESE heat engine are derived for the two operation regimes, respectively. The performance characteristic curves are obtained by numerical examples. The influence of the resonance widths on the ecological performance of the ESE heat engine at intermediate regime is discussed. The ecological performances are analyzed and compared with the power and efficiency characteristic. It is shown that, when the working point is changed from the maximum power point to the maximum ecological function point, the efficiency increases and the entropy generation rate decreases mostly with only a small power output drop. The results obtained herein have theoretical significance for the understanding of thermodynamic performance of the micro-nano devices.

Energy selective electron heat pump with transmission probability

The electron transport through an energy transmission spectrum between two reservoirs with different temperatures and chemical potentials is studied. The heat flow carried by the electrons is obtained. Taking into account the radiative heat leaks between the two electron reservoirs, the performance parameters of the heat pump are derived by numerical calculation. The performance characteristic curves of the heat pump are plotted. The influence of the heat leaks, the position of resonance energy level and the width of the level on the operation performance of the heat pump is analyzed. When the width of resonance energy level is infinitely small, the coefficient of performance may reach the value of Carnot heat pump.