本文選題：布朗熱機(或制冷機) + 福克—普朗克方程�。� 參考：《南昌大學》2016年博士論文

【摘要】：布朗熱機(馬達),是一種利用非平衡的熱漲落來引起布朗粒子產生定向的粒子流,從而實現(xiàn)有用功輸出的裝置。由于它強烈地依賴著熱漲落,使得其只能在微觀納米尺度下才可能實現(xiàn)。因此,在當今對小尺度能源的需求和裝置微型化趨勢的形勢下,其引起了人們廣泛的關注。本文基于隨機動力學和熱力學理論主要研究了兩類連續(xù)型和分立型布朗熱機(制冷機)的熱力學性能特征及其優(yōu)化理論,具體內容如下:第一章,簡單介紹了布朗熱機的發(fā)展及熱驅動的布朗熱機模型的理論基礎,同時介紹了本文研究的主要內容。第二章,利用Fokker-Planck方程研究了布朗粒子在周期性連續(xù)棘齒勢和線性變化溫度場中運動所構建的一類布朗熱機及制冷機模型,分析了此類布朗熱機及制冷機的熱力學性能。在最大功率和最大品質因子的條件下,分別對熱機和制冷機性能參數(shù)進行優(yōu)化。將所得結論與分段均勻溫度場分布的模型進行比較,發(fā)現(xiàn)后者的制冷系數(shù)低于前者。進一步,討論了溫度場的邊界與棘齒勢不重合時,布朗熱機的性能參數(shù)與偏移量的關系。第三章,利用主方程研究了與兩個溫源同時接觸的分立型費曼棘齒-棘爪制冷機模型,分析了制冷機的熱力學性能特征。發(fā)現(xiàn)制冷系數(shù)和制冷率曲線為一閉合曲線,說明此制冷機是不可逆的。通過采用三個優(yōu)化目標函數(shù)對制冷機進行優(yōu)化,得到可通過恰當?shù)剡x擇參數(shù)使得制冷機工作在最優(yōu)狀態(tài)。最后,簡單討論了此模型作為熱機的熱力學性能特征。第四章,利用主方程研究了一類由簡單的三態(tài)模型構造的布朗熱機和制冷機模型,在非穩(wěn)態(tài)情況下,分析了此模型的熱力學性能,得到了性能參數(shù)隨時間和系統(tǒng)各參量的演化規(guī)律。發(fā)現(xiàn)當時間趨于無窮大時,系統(tǒng)各性能參數(shù)趨于穩(wěn)態(tài)時的值。第五章,研究了由兩個多方過程和兩個絕熱過程構成的非卡諾制冷機模型。假設傳熱過程服從牛頓熱傳遞規(guī)律,推導出制冷機的制冷系數(shù)與制冷率的表達式,畫出了制冷率與制冷系數(shù)之間的特征曲線。并且通過數(shù)值模擬研究了在最大品質因子下制冷機的制冷系數(shù)。分析了在長時間和短時間的熱接觸條件下制冷系數(shù)的優(yōu)化值,并與經(jīng)典的Curzon-Ahlborn(CA)制冷系數(shù)進行比較。
[Abstract]:Brownian heat engine (motor) is a device which uses unbalanced heat fluctuations to cause Brownian particles to produce directional particle flow and thus realize the output of hard work. Because of its strong dependence on thermal fluctuations, it can only be realized at micro-nano-scale. Therefore, with the demand for small scale energy and the trend of miniaturization of devices, people pay more attention to it. Based on the theory of stochastic dynamics and thermodynamics, the thermodynamic characteristics and optimization theory of two kinds of continuous and discrete Brownian heat engines (refrigerators) are studied in this paper. The main contents are as follows: chapter 1, This paper briefly introduces the development of Brownian heat engine and the theoretical basis of Brownian heat engine model driven by heat, and introduces the main contents of this paper. In chapter 2, we study a kind of Brownian heat engine and refrigerator model based on the Fokker-Planck equation, and analyze the thermodynamic properties of the Brownian heat engine and refrigerator. Under the condition of maximum power and maximum quality factor, the performance parameters of heat engine and refrigerating machine are optimized respectively. The results are compared with the model of uniform temperature field, and the refrigeration coefficient of the latter is lower than that of the former. Furthermore, when the boundary of the temperature field is not coincident with the ratchet potential, the relationship between the performance parameters and the deviation of the Brownian heat engine is discussed. In chapter 3, the main equation is used to study the model of a separate Feynman ratchet chiller in contact with two temperature sources at the same time, and the thermodynamic characteristics of the refrigerator are analyzed. It is found that the refrigeration coefficient and the refrigeration rate curve are a closed curve, which indicates that the refrigerator is irreversible. By using three optimization objective functions to optimize the refrigerator, it is obtained that the refrigerating machine can work in the optimal state by selecting the appropriate parameters. Finally, the thermodynamic properties of the model as a heat engine are briefly discussed. In chapter 4, we study a kind of Brownian heat engine and refrigerating machine model constructed from simple three-state model by using master equation. In the case of unsteady state, we analyze the thermodynamic performance of this model. The evolution laws of performance parameters with time and system parameters are obtained. It is found that when the time tends to infinity, the performance parameters of the system tend to steady state. In chapter 5, a non-Carnot refrigerator model is studied, which consists of two multiparty processes and two adiabatic processes. Assuming that the heat transfer process is based on Newtonian heat transfer law, the expressions of refrigeration coefficient and refrigeration rate of the refrigerator are derived, and the characteristic curves between the refrigeration rate and the refrigeration coefficient are drawn. The refrigeration coefficient of the refrigerator under the maximum quality factor is studied by numerical simulation. The optimal refrigeration coefficient under long and short time thermal contact is analyzed and compared with the classical Curzon-Ahlborn (CA) refrigeration coefficient.
【學位授予單位】：南昌大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：O55

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