- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Energy harvesting through gas dynamics in the free molecular flow regime between structured surfaces at different temperatures

Tobias Baier1,*, Julia Dölger2, and Steffen Hardt1,†

  • 1Center of Smart Interfaces, TU Darmstadt, Darmstadt, Germany
  • 2Department of Physics, Technical University of Denmark, Denmark

  • *baier@csi.tu-darmstadt.de
  • †hardt@csi.tu-darmstadt.de
PDF

Phys. Rev. E 89, 053003 – Published 6 May, 2014

DOI: https://doi.org/10.1103/PhysRevE.89.053003

Abstract

For a gas confined between surfaces held at different temperatures the velocity distribution shows a significant deviation from the Maxwell distribution when the mean free path of the molecules is comparable to or larger than the channel dimensions. If one of the surfaces is suitably structured, this nonequilibrium distribution can be exploited for momentum transfer in a tangential direction between the two surfaces. This opens up the possibility to extract work from the system which operates as a heat engine. Since both surfaces are held at constant temperatures, the mode of momentum transfer is different from the thermal creep flow that has gained more attention so far. This situation is studied in the limit of free-molecular flow for the case that an unstructured surface is allowed to move tangentially with respect to a structured surface. Parameter studies are conducted, and configurations with maximum thermodynamic efficiency are identified. Overall, it is shown that significant efficiencies can be obtained by tangential momentum transfer between structured surfaces.

View figure in article

Article Text

References (29)

  1. Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications (Birkhäuser, Boston, 2007).
  2. W. Crookes, U.S. Patent No. 182172 (1876).
  3. M. Knudsen, Ann. Phys. 338, 1435 (1910).
  4. J. C. Maxwell, Philos. Mag. 19, 19 (1860).
  5. L. Boltzmann, Vorlesungen über Gastheorie (J. A. Barth, Leipzig, 1896).
  6. S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, England, 1970).
  7. N. K. Gupta, S. An, and Y. B. Gianchandani, J. Micromech. Microeng. 22, 105026 (2012).
  8. A. A. Donkov, S. Tiwari, T. Liang, S. Hardt, A. Klar, and W. Ye, Phys. Rev. E 84, 016304 (2011).
  9. S. Taguchi, Phys. Fluids 22, 102001 (2010).
  10. S. McNamara and Y. Gianchandani, J. Microelectromech. Syst. 14, 741 (2005).
  11. E. P. Muntz, Y. Sone, K. Aoki, S. Vargo, and M. Young, J. Vac. Sci. Technol.  A 20, 214 (2002).
  12. Y. Sone, Y. Waniguchi, and K. Aoki, Phys. Fluids 8, 2227 (1996).
  13. J. P. Heremans, V. Jovovic, E. S. Toberer, A. Saramat, K. Kurosaki, A. Charoenphakdee, S. Yamanaka, and G. J. Snyder, Science 321, 554 (2008).
  14. A. I. Boukai, Y. Bunimovich, J. Tahir-Kheli, J. K. Yu, W. A. Goddard, III, and J. R. Heath, Nature (London) 451, 168 (2008).
  15. A. I. Hochbaum, R. Chen, R. D. Delgado, W. Liang, E. C. Garnett, M. Najarian, A. Majumdar, and P. Yang, Nature (London) 451, 163 (2008).
  16. B. Poudel, Q. Hao, Y. Ma, Y. Lan, A. Minnich, B. Yu, X. Yan, D. Wang, A. Muto, D. Vashaee, X. Chen, J. Liu, M. S. Dresselhaus, G. Chen, and Z. Ren, Science 320, 634 (2008).
  17. K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. Hogan, E. K. Polychroniadis, and M. G. Kanatzidis, Science 303, 818 (2004).
  18. R. Venkatasubramanian, E. Siivola, T. Colpitts, and B. O'Quinn, Nature (London) 413, 597 (2001).
  19. S. Kosuge, K. Aoki, S. Takata, R. Hattori, and D. Sakai, Phys. Fluids 23, 030603 (2011).
  20. J. J. Duderstadt and W. R. Martin, Transport Theory, Vol. 1 (John Wiley & Sons, Chichester, England, 1979).
  21. G. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, New York, 1994).
  22. R. Kersevan, in Proceedings of CAS-CERN Accelerator School and ALBA Synchrotron Light Facility, CERN Accelerator School, edited by D. Brandt (CERN, Meyrin, Switzerland, 2007), pp. 285–312.
  23. H. J. Korsch and F. Zimmer, in Computational Statistical Physics (Springer, New York, 2002), pp. 15–36.
  24. T. Chumley, S. Cook, and R. Feres, Comput. Math. Appl. 65, 1596 (2013).
  25. S. Hardt, S. Tiwari, and A. Klar, Microfluid. Nanofluid. 6, 489 (2009).
  26. X. Shan and M. Wang, Adv. Mech. Eng. 2013, 692842 (2013).
  27. M. Abramowitz and I. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970).
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes (Cambridge University Press, Cambridge, England, 1992).
  29. C. Shen, Rarefied Gas Dynamics (Springer, New York, 2006).

Outline

Information

Phys. Rev. E 89, 053003– Published 6 May, 2014
  • Received 14 January 2014

©2014 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation