非均匀线性温度场中布朗制冷机性能优化  

The performance optimization for a Brownian refrigerator in an inhomogeneous linear thermal field

作　　者：肖宇玲[1] 缪贵玲 何济洲[1] 

机构地区：[1]南昌大学物理系,南昌330031 [2]江西师范高等专科学校,数学与计算机学院,鹰潭335000

出　　处：《中国科学：物理学、力学、天文学》2016年第7期91-99,共9页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金自助资助项目(编号:11365015)

摘　　要：本文研究了一种由周期性非均匀线性温场所驱动的布朗制冷机性能特征.利用布朗粒子的动力学方程——Langevin equation,获得了稳态时布朗制冷机的粒子流、制冷率和制冷系数的解析表达式.通过数值计算分析了势垒高度、非对称性、外力和温比等参数对制冷机性能的影响.在最大品质因子条件下,对制冷机性能参数进行优化,画出了优化的制冷系数和制冷率随温比的演化曲线.研究表明:在准静态极限下,制冷系数趋于用等效温度给出的卡诺制冷系数,制冷率趋于零;制冷系数随制冷率增加而减少;优化的制冷系数随温比减小而下降,而对应的制冷率却相反;相比于在分段均匀温度场中,非均匀线性温度场将导致制冷系数的提高.The performance characteristic of a Brownian refrigerator which is driven by the cyclic and inhomogeneous linear thermal field is studied. Based on the dynamic equation of the Brownian particle （Langevin equation） the analytical expressions of the particle current, the cooling rate and the coefficient of performance are derived at steady state. Through numerical calculation, the effect of the model parameters, such as the height of potential barrier, the asymmetry, the external force and the temperature ratio on the performance of the refrigerator is analyzed. The performance parameters of the refrigerator are optimized at the maximum figure of merit. The curves of the optimized cooling rate and the coefficient of performance are plotted. It is shown that the coefficient of performance tends to the Carnot value expressed by the effective temperatures and the cooling rate tends to zero in the quasistatic limit; the coefficient of performance decreases as the cooling rate increases. The optimized coefficient of performance decreases as the temperature ratio decreases, but the corresponding cooling rate is opposite; comparing with one at the piecewise constant temperature reservoir, the coefficient of performance will increase at the inhomogeneous linear thermal reservoir.

关 键 词：布朗制冷机 非均匀温场 制冷系数 制冷率 品质因子 

分 类 号：TB651[一般工业技术—制冷工程]