Performance Characteristics and Optimal Analysis of an Energy Selective Electron Refrigerator

Abstract

In this paper, the energy selective electron (ESE) refrigerator with an ideal energy filter based on resonant tunneling is established. It consists of two infinitely large electron reservoirs with different temperatures and chemical potentials, and electrons can be exchanged between the two reservoirs through the ideal energy filter. According to Landauer formula and the assumption of being coupled tightly with the electron current, the expressions for the heat flux, the cooling rate and the coefficient of performance (COP) are derived analytically. The performance characteristic curves such as the cooling rate versus coefficient of performance, the cooling rate and coefficient of performance versus the position of energy level are plotted by numerical calculation. The optimal regions of the cooling rate and the COP are determined. Moreover, we optimize the cooling rate and the COP respectively with respect to the position of energy level. The influence of the width of energy level on performance of the ESE refrigerator is discussed. Finally, based on the optimization criterion for refrigerator, i.e. the product of the COP times the cooling rate, the optimal performance of the ESE refrigerator is discussed in detail.

Keywords

• Electron transport; thermoelectric ESE refrigerator; irreversible thermodynamics.

References

1. G. J. Snyder, E. S. Toberer, Complex thermoelectric materials, Nature Mater., 7, 105-114, 2008.
2. P. Pichanusakorn, P. Bandaru, Nanostructured thermoelectrics, Mater. Sci. Eng. R, 67, 19-63, 2010.
3. R. Ventkatasubramanian, E. Siivola, T. Colpitts, B. O’Quinn, Thin-film thermoelectric devices with high room-temperature figures of merit, Nature, 413, 597602, 2001.
4. T. C. Harman, P. J. Taylor, M. P. Walsh, B. E. Laforge, Quantum Dot Superlattice Thermoelectric Materials and Devices, Science, 297, 2229-2232, 2002.
5. K. F. Hsu, S. Loo, F. Guo, W. Chen, J. S. Dyck, C. Uher, T. K. E. Hogan, Cubic AgPbmSbTe2+m: Bulk thermoelectric Materials with High Figure of Merit, Science, 303, 818-21, 2004.
6. N. Nakpathomkun, H. Q. Xu, H. Linke, Thermoelectric efficiency at maximum power in low-dimensional systems, Phys. Rev. B, 82, 235428, 2010.
7. G. Min, D. M. Rowe, Experimental evaluation of prototype thermoelectric domestic-refrigerators, Appl. Energy, 83, 133-152, 2006.
8. M. D. Ulrich, P. A. Barnes, C. B. Vining, Comparision of solid-state thermionic refrigeration with thermoelectric refrigeration, J. Appl. Phys., 90, 16251631, 2001.

9. D. Vashaee, A. Shakouri, Improved thermoelectric Power Factor in Metal-Based Superlattices, Phys. Rev. Lett., 92, 106103, 2004.
10. T. E. Humphrey, R. Newbury, R. P. Taylor, H. Linke, Reversible quantum Brownian heat engine, Phys. Rev. Lett., 89, 116801, 2002.
11. T. E. Humphrey, Mesoscopic quantum ratchets and the thermodynamics of energy selective electron heat engines, Ph.D. Thesis , Sydney, Australia: University of New South Wales, 2003.
12. T. E. Humphrey, H. Linke, Reversible thermoelectric nanomaterials, Phys. Rev. Lett., 94, 096601, 2005.
13. M. F. O’Dwyer, T. E. Humphrey, H. Linke, Concept study for a high-efficiency nanowire based thermoelectric, Nanotechnology, 17, S1-6, 2006.
14. M. F. O’Dwyer, R. A. Lewis, C. Zhang, Electronic efficiency in nanostructured thermionic and thermoelectric devices, Phys. Rev. B, 72, 205330, 2005.
15. B. X. He, J. Z. He, Thermoelectric refrigerator of a double-barrier InAs/InP nanowire heterostructure, Acta Phys. Sinica, 59, 3846-3850, 2010. ( in Chinese)
16. B. X. He, J. Z. He, G. L. Miao, Influence of nanowire heterotructure on performance of electron refrigerator, Acta Phys. Sinica, 60, 040509, 2011. ( in chinese)
17. Z. Ding, L. Chen, F. Sun, Performance characteristic of energy selective electron (ESE) refrigerator with filter heat conduction, Rev. Mex. Fis., 56, 125-131, 20 Z. Ding, L. G. Chen, F. Sun, Performance characteristic of energy selective electron (ESE) heat engine with filter heat conduction, I. J. Energy Eng., 2, 627-640, 2011.
18. Z. Ding, L. Chen, F. Sun, Ecological optimization of a total momentum filtered energy selective electron (ESE) heat engine, Appl. Math. Modelling, 35, 276284, 2011.
19. Z. Ding, L. Chen, F. Sun, Performance optimization of a total momentum filtered energy selective electron (ESE) heat engine with double resonance, Math. Comp. Model. Dyn. Syst., 54, 2064-2076, 2011.
20. Z. Ding, L. Chen, F. Sun, Modeling and performance analysis of energy selective electron (ESE) engine with heat leakage and transmission probability, Sci. China; Phys. Mech. Astron., 54, 1925-1936, 2011.
21. Z. Ding, L. Chen, F. Sun, Performance analysis of an irreversible energy selective electron (ESE) heat pump with heat leakage, J. Energy Inst., 85, 227-235, 2012.
22. H. Wang, G. X. Wu, H. Lu, Performance of an energy selective electron refrigerator at maximum cooling rate, Phys. Scri., 83, 055801, 2011.
23. H. Wang, G. X. Wu, Y. M. Fu, D. J. Chen, Performance analysis and parametric optimum criteria of the nanothermoeletric engine with a single-level quantum dot at maximum power, J. Appl. Phys., 111, 094318, 2012.
24. J. Z. He, X. M. Wang, H. N. Liang, Optimum performance analysis of an energy selective electron refrigerator affected by heat leaks, Phys. Scri., 80, 035701, 2009.
25. J. Z. He, B. X. He, Energy selective electron heat pump with transmission probability, Acta Phys. Sin., 59, 2345-2349, 2010.
26. X. M. Wang, J. Z. He, J. Wang, Analysis of performance characteristics of the energy selective electron heat engine and refrigerator, Acta Electronica Sinica, 36, 2178-2182, 2008. (in Chinese)
27. X. M. Wang, J. Z. He, W. Tang, Performance characteristics of an energy selective electron refrigerator with double resonances, Chin. Phys. B, 18, 984-990, 2009.
28. X. M. Wang, J. Z. He, H. N. Liang, Performance characteristics and optimal analysis of a nonlinear diode refrigerator, Chin. Phys. B, 20, 020503, 2011.
29. J. Z. He, X. M. Wang, Y. C. Zhang, Performance characteristics of a quantum dot thermoelectric refrigerator, I. J. Mod. Phys. B, 26, 1250134, 2012.
30. X. G. Luo, C. Li, N. Liu, R. W. Li, J. Z. He, T. Qiu, The impact of energy spectrum width in the energy selective electron low-temperature thermionic heat engine at maximum power, Phys. Lett. A, 377, 15661570, 2013.
31. L. Chen, Z. Ding, F. Sun, Model of a total momentum filtered energy selective electron heat pump affected by heat leakage and its performance characteristics, Energy, 36, 4011-4018, 2011.
32. S. Su, J. Guo, G. Su, J. Chen, Performance optimum analysis and load matching of an energy selective electron heat engine, Energy, 44, 570-575, 2012.
33. Z. Yan, J. Chen, A class of irreversible Carnot refrigeration cycles with a general eat transfer law, J. Phys. D: Appl. Phys., 23, 136-141, 1990.
34. A. C. Hernandez, A. Medina, J. M. M. Roco, J. A. White, S. Velasco, Unified optimization criterion for energy converters, Phys. Rev. E, 63, 037102, 2001.
35. C. D. Tomas, A. C. Hernandez, J. M. M. Roco, Optimal low symmetric dissipation Carnot engines and refrigerators, Phys. Rev. E, 85, 010104, 2012.
36. Y. Wang, M. X. Li, Z. C. Tu, A. C. Hernandez, J. M. M. Roco, Cofficient of performance at maximum figure of merit and its bounds for low-dissipation Carnot-like refrigerators, Phys. Rev. E, 86, 011127, 20