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2011 | 119 | 6 | 747-760
Article title

Endoreversible Modeling and Optimization of a Multistage Heat Engine System with a Generalized Heat Transfer Law via Hamilton-Jacobi-Bellman Equations and Dynamic Programming

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EN
Abstracts
EN
A multistage endoreversible Carnot heat engine system operating between a finite thermal capacity high-temperature fluid reservoir and an infinite thermal capacity low-temperature environment with a generalized heat transfer law [q ∝ ( Δ (T^{n}))^{m}] is investigated in this paper. Optimal control theory is applied to derive the continuous Hamilton-Jacobi-Bellman equations, which determine the optimal fluid temperature configurations for maximum power output under the conditions of fixed initial time and fixed initial temperature of the driving fluid. Based on the general optimization results, the analytical solution for the case with Newtonian heat transfer law [q ∝ Δ(T)] is further obtained. Since there are no analytical solutions for the other heat transfer laws, the continuous Hamilton-Jacobi-Bellman equations are discretized and the dynamic programming algorithm is adopted to obtain the complete numerical solutions of the optimization problem, and the relationships among the maximum power output of the system, the process period and the fluid temperature are discussed in detail. The results show that the optimal high-temperature fluid reservoir temperature for the maximum power output of the multistage heat engine system with Newtonian and linear phenomenological [q ∝ Δ (T^{-1})] heat transfer laws decrease exponentially and linearly with time, respectively, while those with the Dulong-Petit [q∝(Δ T)^{1.25}], radiative [q∝ Δ (T^4)] and [q∝(Δ(T^4))^{1.25}] heat transfer laws are different from the former two cases significantly.
Keywords
EN
Year
Volume
119
Issue
6
Pages
747-760
Physical description
Dates
published
2011-06
received
2011-02-11
References
  • 1. B. Andresen, R.S. Berry, M.J. Ondrechen, P. Salamon, Acc. Chem. Res. 17, 266 (1984)
  • 2. A. Bejan, J. Appl. Phys. 79, 1191 (1996)
  • 3. R.S. Berry, V.A. Kazakov, S. Sieniutycz, Z. Szwast, A.M. Tsirlin, Thermodynamic Optimization of Finite Time Processes, Wiley, Chichester 1999
  • 4. L. Chen, C. Wu, F. Sun, J. Non-Equilib. Thermodyn. 24, 327 (1999)
  • 5. S. Sieniutycz, Phys. Rep. 326, 165 (2000)
  • 6. K.H. Hoffman, J. Burzler, A. Fischer, M. Schaller, S. Schubert, J. Non-Equilib. Thermodyn. 28, 233 (2003)
  • 7. S. Sieniutycz, Prog. Energy Combus. Sci. 29, 193 (2003)
  • 8. L. Chen, F. Sun, Advances in Finite Time Thermodynamics: Analysis and Optimization, Nova Sci. Publ., New York 2004
  • 9. L. Chen, Finite-Time Thermodynamic Analysis of Irreversible Processes and Cycles, High Education Press, Beijing 2005 (in Chinese)
  • 10. B. Andresen, in: Meeting the Entropy Challenge: An Int. Thermodynamics Symp. in Honor and Memory of Professor Joseph H. Keenan, AIP Conf. Proc., Vol. 1033, 2008, p. 213
  • 11. S. Sieniutycz, J. Jezowski, Energy Optimization in Process Systems, Elsevier, Oxford, UK 2009
  • 12. F.L. Curzon, B. Ahlborn, Am. J. Phys. 43, 22 (1975)
  • 13. Z. Yan, Chin. J. Eng. Thermophys. 6, 1 (1985) (in Chinese)
  • 14. F. Sun, X. Lai, in: Proc. Sect. Conf. Univers. Res. Assoc. Eng. Thermophys., 1986, Science Press, Beijing 1988, p. 91 (in Chinese)
  • 15. F. Sun, X. Lai, J. Eng. Thermal Energy Pow. 3, 1 (1988) (in Chinese)
  • 16. W. Chen, F. Sun, L. Chen, Chin. Sci. Bull. 36, 763 (1991)
  • 17. D. Gutowicz-Krusin, J. Procaccia, J. Ross, J. Chem. Phys. 69, 3898 (1978)
  • 18. A. Bejan, Advanced Engineering Thermodynamics, Wiley, New York 1988
  • 19. Z. Yan, L. Chen, Chin. Sci. Bull. 30, 1543 (1988) (in Chinese)
  • 20. C. Wu, Int. J. Ambient Energy 10, 145 (1989)
  • 21. C. Wu, Energy Convers. Management 33, 279 (1992)
  • 22. S. Goktun, S. Ozkaynak, H. Yavuz, Energy Int. J. 18, 651 (1993)
  • 23. L. Chen, F. Sun, C. Wu, Appl. Thermal Eng. 17, 277 (1997)
  • 24. L. Chen, X. Zhu, F. Sun, C. Wu, Appl. Energy 78, 305 (2004)
  • 25. L. Chen, X. Zhu, F. Sun, C. Wu, Appl. Energy 83, 537 (2006)
  • 26. F. Angulo-Brown, R. Paez-Hernandez, J. Appl. Phys. 74, 2216 (1993)
  • 27. M. Huleihil, B. Andresen, J. Appl. Phys. 100, 014911 (2006)
  • 28. A. de Vos, Am. J. Phys. 53, 570 (1985)
  • 29. A. de Vos, J. Phys. D, Appl. Phys. 20, 232 (1987)
  • 30. L. Chen, Z. Yan, J. Chem. Phys. 90, 3740 (1989)
  • 31. J.M. Gordon, Am. J. Phys. 58, 370 (1990)
  • 32. S. Sieniutycz, Phys. Rev. E 56, 5051 (1997)
  • 33. S. Sieniutycz, J. Non-Equilib. Thermodyn. 22, 260 (1997)
  • 34. S. Sieniutycz, Int. J. Heat Mass Transfer 41, 183 (1998)
  • 35. S. Sieniutycz, Energy Convers. Management 39, 1735 (1998)
  • 36. S. Sieniutycz, Open Sys. Information Dyn. 5, 369 (1998)
  • 37. S. Sieniutycz, Int. J. Eng. Sci. 36, 577 (1998)
  • 38. S. Sieniutycz, in: Recent Advances in Finite Time Thermodynamics, Eds. C. Wu, L. Chen, J. Chen, Nova Science Publ., New York 1999, p. 189
  • 39. S. Sieniutycz, M.R. von Spakovsky, Energy Convers. Management 39, 1423 (1998)
  • 40. Z. Szwast, S. Sieniutycz, in Ref. [38], p. 221
  • 41. S. Sieniutycz, Z. Szwast, J. Non-Equilib. Thermodyn. 28, 85 (2003)
  • 42. S. Sieniutycz, Int. J. Heat Mass Transfer 49, 789 (2006)
  • 43. J. Li, L. Chen, F. Sun, J. Energy Inst. 82, 53 (2009)
  • 44. J. Li, L. Chen, F. Sun, Math. Compt. Modell. 49, 542 (2009)
  • 45. S. Sieniutycz, P. Kuran, Int. J. Heat Mass Transfer 48, 719 (2005)
  • 46. S. Sieniutycz, P. Kuran, Int. J. Heat Mass Transfer 49, 3264 (2006)
  • 47. P. Kuran, Ph.D. Thesis, Supervised by Prof. Sieniutycz, Warsaw University of Technology, Warsaw (Poland) 2006
  • 48. S. Sieniutycz, Int. J. Heat Mass Transfer 50, 2714 (2007)
  • 49. S. Sieniutycz, Int. J. Thermal Sci. 47, 495 (2008)
  • 50. S. Sieniutycz, Appl. Math. Modell. 33, 1457 (2009)
  • 51. S. Sieniutycz, Int. J. Heat Mass Transfer 53, 2864 (2010)
  • 52. J. Li, L. Chen, F. Sun, Thermal Sci. 14, 1 (2010)
  • 53. S. Sieniutycz, Energy, 34, 334 (2009)
  • 54. S. Xia, L. Chen, F. Sun, Chin. Sci. Bull. 56, 1147 (2011)
  • 55. S. Xia, L. Chen, F. Sun, Energy 36, 633 (2011)
  • 56. L. Chen, J. Li, F. Sun, Appl. Energy 85, 52 (2008)
  • 57. J. Li, L. Chen, F. Sun, C. Wu, Int. J. Ambient Energy 29, 149 (2008)
  • 58. J. Li, L. Chen, F. Sun, J. Energy Inst. 81, 168 (2008)
  • 59. J. Li, L. Chen, F. Sun, Proc. IMechE, Part E: J. Proc. Mech. Eng. 222, 55 (2008)
  • 60. J. Li, L. Chen, F. Sun, Appl. Energy 85, 96 (2008)
  • 61. J. Li, L. Chen, F. Sun, Pramana J. Phys. 74, 219 (2010)
  • 62. C.T. O'Sullivan, Am. J. Phys. 58, 956 (1990)
  • 63. L. Chen, S. Xia, F. Sun, J. Appl. Phys. 105, 044907 (2009)
  • 64. S. Xia, L. Chen, F. Sun, Braz. J. Phys. 39, 98 (2009)
  • 65. J. Li, L. Chen, F. Sun, Sci. China Ser. G: Phys., Mech. Astron. 52, 587 (2009)
  • 66. S. Sieniutycz, Int. J. Thermodyn. 6, 1 (2003)
  • 67. R.E. Bellman, Adaptive Control Processes: a Guided Tour, Princeton University Press, Princeton 1961
  • 68. S. Hu, Z. Wang, W. Hu, Optimal Control Theory and System, Science Press, Beijing 2005 (in Chinese)
  • 69. Z. Yan, J. Chen, J. Chem. Phys. 92, 1994 (1990)
  • 70. L. Chen, F. Sun, C. Wu, Appl. Energy 83, 71 (2006)
  • 71. G. Xiong, J. Chen, Z. Yan, J. Xiamen University (Nature Science) 28, 489 (1989) (in Chinese)
  • 72. B. Andresen, J.M. Gordon, Int. J. Heat Fluid Flow 13, 294 (1992)
  • 73. V. Badescu, J. Non-Equilib. Thermodyn. 29, 53 (2004)
  • 74. S. Xia, L. Chen, F. Sun, Appl. Math. Modell. 34, 2242 (2010)
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Publication order reference
YADDA identifier
bwmeta1.element.bwnjournal-article-appv119n603kz
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