Advisory Committee Chair
Ryoichi Kawai
Advisory Committee Members
Renatto P Camata
Nikolai Chernov
Perry A Gerakines
Gunter Stolz
Document Type
Dissertation
Date of Award
2008
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
We investigated the energetics of a Brownian motor driven by position dependent temperature, commonly known as the B¨uttiker-Landauer motor. Overdamped models (M = 0) predict that the motor can attain Carnot efficiency. However, the overdamped limit (M → 0), contradicts the previous prediction due to the kinetic energy contribution to the heat transfer. Using molecular dynamics simulation and numerical solution of the inertial Langevin equation, we confirmed that the motor can never achieve Carnot efficiency and verified that the heat flow via kinetic energy diverges asM−1/2 in the overdamped limit. The reciprocal process of the motor, namely the B¨uttiker-Landauer refrigerator was also examined. In this case, the overdamped approach succeeds in predicting the heat transfer only when temperature is homogeneous. It was found that the Onsager symmetry between the motor and refrigerator does not suffer from the singular behavior of the kinetic energy contribution. Having established that the kinetic energy contribution greatly reduces the efficiency of the motor we examine the role of different potential and temperature profiles in order to minimize this heat transfer and enhance the motor efficiency. It was found that optimizing the potential shape in order to reduce the kinetic energy contribution reduces the motor velocity as well leading only to a limited gain in efficiency. We also studied the efficiency at maximum power of the motor and found that it can never reach the efficiency of an endoreversible engine working at maximum power, namely the Curzon-Ahlborn efficiency. The performance of the B¨uttiker-Landauer refrigerator was also investigated. Cooling is possible only for small temperature gradients as the kinetic energy contribution reduces the cooling effect. The behavior of the reiii frigerator as a function of different parameters of the system was studied in presence of uniform temperature. Modifying the potential shape neither enhances the cooling rate nor the coefficient of performance of the refrigerator.
Recommended Citation
Benjamin, Ronald, "Stochastic Energetics Of The Buttiker-Landauer Motor And Refrigerator" (2008). All ETDs from UAB. 3664.
https://digitalcommons.library.uab.edu/etd-collection/3664