We study a class of cyclic Brownian heat engines in the framework of finite-time thermodynamics. For infinitely long cycle times, the engine works at the Carnot efficiency limit producing, however, zero power. For the efficiency at maximum power, we find a universal expression, different from the endoreversible Curzon-Ahlborn efficiency. Our results are illustrated with a simple one-dimensional engine working in and with a time-dependent harmonic potential.

Efficiency at maximum power: An analytically solvable model for stochastic heat engines

This Perspective reviews the fundamental physics of space–charge interactions that are important in various media: vacuum gap, air gap, liquids, and solids including quantum materials. It outlines the critical and recent developments since a previous review paper on diode physics [Zhang et al. Appl. Phys. Rev. 4, 011304 (2017)] with particular emphasis on various theoretical aspects of the space–charge limited current (SCLC) model: physics at the nano-scale, time-dependent, and transient behaviors; higher-dimensional models; and transitions between electron emission mechanisms and material properties. While many studies focus on steady-state SCLC, the increasing importance of fast-rise time electric pulses, high frequency microwave and terahertz sources, and ultrafast lasers has motivated theoretical investigations in time-dependent SCLC. We particularly focus on recent studies in discrete particle effects, temporal phenomena, time-dependent photoemission to SCLC, and AC beam loading. Due to the reduction in the physical size and complicated geometries, we report recent studies in multi-dimensional SCLC, including finite particle effects, protrusive SCLC, novel techniques for exotic geometries, and fractional models. Due to the importance of using SCLC models in determining the mobility of organic materials, this paper shows the transition of the SCLC model between classical bulk solids and recent two-dimensional (2D) Dirac materials. Next, we describe some selected applications of SCLC in nanodiodes, including nanoscale vacuum-channel transistors, microplasma transistors, thermionic energy converters, and multipactor. Finally, we conclude by highlighting future directions in theoretical modeling and applications of SCLC.

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Space–charge limited current in nanodiodes: Ballistic, collisional, and dynamical effects

Opportunities and strategies for multigrade waste heat utilization in various industries: A recent review

In this paper, an irreversible thermionic refrigerator model based on van der Waals heterostructure with various irreversibilities is established by utilizing combination of non-equilibrium thermodynamics and finite time thermodynamics. The basic performance characteristics of the refrigerator are obtained. The effects of key factors, such as bias voltages, Schottky barrier heights and heat leakages, on the performance are studied. Results show that cooling rates and coefficients of performances (COPs) can attain the double maximum with proper modulation of barrier heights and bias voltages. Increasing cross-plane thermal resistance as well as decreasing electrode-reservoir thermal resistance and reservoir-reservoir thermal resistance can enhance the performance of the device. The optimal performance region is the interval between the maximum cooling rate point and the maximum COP point. By modulating the bias voltage, the working state of the device can fall into the optimal performance region. The optimal performance of the refrigerator when using single layer graphene and a few layers graphene as electrode material is also compared.

Performance optimization of thermionic refrigerators based on van der Waals heterostructures

Thermionic energy converters are solid-state heat engines that have the potential to produce electricity with efficiencies of over 30% and area-specific power densities of 100 Wcm-2. Despite this prospect, no prototypes reported in the literature have achieved true efficiencies close to this target, and many of the most recent investigations report power densities on the order of mWcm-2 or less. These discrepancies stem in part from the low-temperature ( 1 Wcm-2 and employing emitter temperatures of 1300 K or higher. With this result in mind, this review provides an overview of historical and current design architectures and comments on their capacity to realize the efficiency and power potential of thermionic energy converters. Also emphasized is the importance of using standardized efficiency metrics to report thermionic energy converter performance data.

https://onlinelibrary.wiley.com/doi/pdf/10.1002/advs.202003812

Progress Toward High Power Output in Thermionic Energy Converters

A self-reliant quantum cooler without an external control is proposed. To understand the thermal transport properties of the quantum system interacting with the baths described by the grand canonical ensemble, a two-level system with a single energy transport channel and a two-level coupled system with multi-channels are established. By considering the temperature dependence of the chemical potentials of the ultracold atom baths, the steady-state heat flows, particle currents, and entropy productions of these systems are derived. Results show that a steady heat current flows against the thermal bias for a nonequilibrium system coupled with ultracold quantum gases and the cooling rate can be enhanced by quantum coherence.

Jianying Du

Papers

Self-reliant cooling of ultracold atoms