The Thermodynamic Performance Analysis On Two Kinds Of Brownian Heat Engines And Refrigerators

Brownian heat engines(motors) are the devices that can achieve some useful work in which transport of Brownian particles is induced by the nonequilibrium thermal fluctuations. Because it strongly depends on the thermal fluctuations, it only can be realized in nanometer scale. Therefore, under the tendency of the energy demand in small scale and device miniaturization, Brownian heat engines have recently attracted considerable attention. In this thesis, based on stochastic dynamics and thermodynamics, thermodynamic performance characteristics and optimal theory of two kind of continuous and discrete Brownian heat engines(refrigerators) are mainly researched. The concrete contents are as follow:In chapter I, the development of Brownian engines and the basis theory about the thermally-driven Brownian heat engine models are briefly introduced. Meanwhile, the main research contents of this thesis are listed.In chapter II, based on Fokker-Planck equation a class of Brownian heat engine and refrigerator models are studied in which the Brownian particles move in a cyclic and continuous ratchet potential and inhomogeneous linear thermal field. The thermodynamic performance of the Brownian heat engines and refrigerators is analyzed. The performance parameters of the heat engine and refrigerator are optimized at the maximum power and the maximum figure of merit, respectively. Then, the results obtained above are compared with those of the models in the piecewise uniform temperature field, it is found that the coefficient of performance of the latter is lower than that of the former. Further, when the boundaries of the thermal field and the ratchet potential are inconsistent, the relationship between the performance parameters of Brownian heat engines and the offset value is discussed.In chapter III, based on master equation the model of a discrete Feynman ratchet- pawl refrigerator simultaneously contact with two heat reservoirs is studied. The thermodynamic performance characteristics of the refrigerator are analyzed. It is found that the characteristic curve between the cooling rate and the coefficient of performance is a closed one and it is indicated that the refrigerator is irreversible. By using three optimization objective functions, the performance of the refrigerator is optimized. The refrigerator can work in the optimal state through choosing the appropriate parameters. Lastly, the thermodynamic performance characteristics of the model working as Feynman heat engine are simply discussed.In chapter IV, based on master equation, a class of Brownian heat engine and refrigerator models which consist of simple three states are constructed. The thermodynamic performance is analyzed at the non-steady state conditions. The evolution law of the performance parameters, which is dependent on time and system parameters, is obtained. It is found that when time tends to infinity the values of these performance parameters tend to ones of the steady-state cases.In chapter V, the non-Carnot refrigerator is composed of two polytrophic and two adiabatic processes. It is assumed that Newton’s heat transfer law is obeyed during heat transfer processes, the expressions for the coefficient of performance(COP) and cooling rate of the refrigerator are derived. The characteristic curves between the cooling rate and the COP are plotted. Moreover, the optimal COP of the refrigerator at maximum figure of merit is studied by the numerical calculation. The optimal COP is analyzed at two special limit cases of long and short contact times, and compared with that of the classical Curzon-Ahlborn COP.