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Power and efficiency performances of a thermal Brownian heat engine, which consists of Brownian particles moving in a periodic sawtooth potential with and without external forces and contacting with alternating hot and cold reservoirs along the space coordinate, are studied in this paper. The performance characteristics are obtained by numerical calculations. It is shown that due to the heat flow via the change of kinetic energy of the particles, the Brownian heat engine is always irreversible and the efficiency can never approach the Carnot efficiency. The influences of the operation parameters, i.e. barrier height of the potential, asymmetry of the potential and temperature ratio of the heat reservoirs on the power output, the efficiency and the current performances of the Brownian heat engine are investigated in detail by numerical analysis. When there is no external force, the power output versus efficiency characteristic curves are closed loop-shaped ones, which are similar to those of real conventional irreversible heat engines; whereas when the external force is considered, the power output versus efficiency characteristic curves of the heat engine changed into open loop-shaped ones. Furthermore, the limited regions of the external force and barrier height of the potential are explored by analyzing the current property of the model. It is shown that by reasonable choice of the parameters, the Brownian heat engine can be controlled to operate in the optimal regimes.

a b s t r a c tThe operation of a universal steady flow endoreversible heat engine cycle model consisting of two constant thermal-capacity heating branches, a constant thermal-capacity cooling branch and two adiabatic branches is viewed as a production process with exergy as its output. The finite time exergoeconomic performance optimization of the universal endoreversible heat engine cycle is investigated by taking profit optimization criterion as the objective. The analytical formulae for power, efficiency and profit rate function of the universal endoreversible heat engine cycle with heat resistance loss are derived. The focus of this paper is to search the compromised optimization between economics (profit) and the utilization factor (efficiency) for endoreversible cycles. Moreover, analysis and optimization of the model are carried out in order to investigate the effect of cycle process on the performance of the universal endoreversible heat engine cycle using numerical examples. The results obtained herein include the performance characteristics of six endoreversible heat engines, including Carnot, Diesel, Otto, Atkinson, Brayton and Dual cycles.

a b s t r a c tA generalized model of an irreversible thermal Brownian refrigerator, which consists of Brownian particles moving in a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate, is established in this paper. The heat flows driven by both potential and kinetic energies of the particles as well as the heat leakage between the hot and cold reservoirs are taken into account. The optimum performance of the generalized model is analyzed using the theory and method of finite time thermodynamics. The analytical expressions for cooling load, coefficient of performance (COP) and power input of the Brownian refrigerator are derived. It is shown by numerical examples that due to the heat leakage between the heat reservoirs and heat flow via the change of kinetic energy of the particles, the Brownian refrigerator is always irreversible and the COP can never attain the Carnot COP. The influences of the heat leakage, the external force, barrier height of the potential, asymmetry of the sawtooth potential and temperature ratio of the heat reservoirs on the performance of the Brownian refrigerator are also investigated in detail. The effective regions of external force and barrier height of the potential in which the Brownian motor can operate as a refrigerator are determined. It is found that the performance of the Brownian refrigerator depends strictly on the design parameters. If these design parameters are properly chosen, the Brownian refrigerator can be controlled to operate in the optimal regimes. The results obtained herein about the general Brownian refrigerator model include those obtained in many previous literatures.

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