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非平衡热力学中传热过程熵产表达式的修正

董源 过增元

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非平衡热力学中传热过程熵产表达式的修正

董源, 过增元

The modification of entropy production by heat condution in non-equilibrium thermodynamics

Dong Yuan, Guo Zeng-Yuan
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  • 熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.
    The entropy production is expressed as the product of the generalized force (driving force) and generalized flux, which plays a central role in classical non-equilibrium thermodynamics. This expression has shortcomings in two aspects: first, the decomposition into generalized fluxes and forces is arbitrary to some extent; more importantly, the entropy production is negative value calculated in heat wave propagation, which breaks the second law. In this paper, we carry out analyses based on the thermomass theory and show that the entropy production is induced by the dissipation of thermomass energy during heat condution. The generalized force of entropy production is not driving force but resistive force, having a unit of force in Newton’s mechanics. The modified expression for entropy production not only guarantees its positiveness in propagation of heat waves consistent with the extended irreversible thermodynamics, but also avoids the arbitrariness of decomposition.
    • 基金项目: 国家自然科学基金(批准号: 51076080, 51136001)和清华大学自主科研计划资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51076080, 51136001) and the Tsinghua University Initiative Scientific Research Program of China.
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    [2]

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    [3]

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    [4]

    Zeng D L 1991 Engineering Non-Equilibrium Thermodynamics (Beijing: Science Press) (in Chinese) [曾丹苓 1991 工程非平衡热动力学 (北京: 科学出版社)]

    [5]

    Grandy Jr W T 2008 Entropy and the Time Evolution of Macroscopic Systems (New York: Oxford University Press)

    [6]

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    [7]

    Casimir H B G 1945 Rev. Mod. Phys. 17 343

    [8]

    Glansdorf P, Prigogine I 1971 Thermodynamic Theory of Structure, Stability and Fluctuations (New York: Wiley)

    [9]

    Lebon G, Casas-Vazquez J, Jou D 2008 Understanding Non- Equilibrium Thermodynamics: Foundations, Applications, Frontiers (Berlin: Springer-Verlag)

    [10]

    Stritzker B, Pospieszczyk A, Tagle J A 1981 Phys. Rev. Lett. 47 356

    [11]

    Torii S, Yang W J 2005 Int. J. Heat Mass Trans. 48 537

    [12]

    Guo Z Y, Xu Y S 1995 J. Electron. Packaging 117 174

    [13]

    Cattaneo C 1948 Atti. Sem. Mat. Fis. Univ. Modena 3 83

    [14]

    Vernotte P 1958 C. R. Acad. Sci 246 3154

    [15]

    Morse P M, Feshbach H 1953 Methods of Theoretical Physics (New York: McGraw-Hill)

    [16]

    Tzou D Y 1989 J. Heat Trans. 111 232

    [17]

    Tzou D Y 1992 Thermal shock phenomena under high-rate response in solids in: Tien C L (Ed) Annual Review of Heat Transfer IV (Whashington DC: Hemisphere) Chapter 3 pp 111–185

    [18]

    Tzou D Y 1997 Macro- to Microscale Heat Transfer: The Lagging Behavior (Whashington DC: Taylor & Francis)

    [19]

    Criado-Sancho M, Llebot J E 1993 Phys. Rev. E 47 4104

    [20]

    Al-Nimr M A, Naji M, Arbaci V S 2000 J. Heat Trans. 122 217

    [21]

    Jou D, Casas-Vazquez J, Lebon G 1999 Rep. Pro. Phys. 62 1035

    [22]

    Müller I 1985 Thermodynamics (London: Pitman)

    [23]

    Sieniutycz S, Salamon P 1992 Extended Thermodynamic System (New York: Taylor and Francis)

    [24]

    Barletta A, Zanchini E 1997 Int. J. Heat Mass Trans. 40 1007

    [25]

    Jou D, Casas-Vazquez J, Lebon G 2008 Proceedings of the Estonian Academy of Sciences 57 118

    [26]

    Cao B Y, Guo Z Y 2007 J. Appl. Phys. 102 53503

    [27]

    Guo Z Y, Hou Q W 2010 ASME J. Heat Trans. 132 072403

    [28]

    Wang H D, Cao B Y, Guo Z Y 2010 Int. J. Heat Mass Trans. 53 1796

    [29]

    Song B,Wu J, Guo Z Y 2010 Acta Phys. Sin. 59 7129 (in Chinese) [宋柏,吴晶,过增元 2010 物理学报 59 7129]

    [30]

    Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273 (in Chinese) [过增元,曹炳阳 2008 物理学报 57 4273]

    [31]

    Hou Q W, Cao B Y, Guo Z Y 2009 Acta Phys. Sin. 58 7809 (in Chinese) [侯泉文,曹炳阳,过增元 2009 物理学报 58 7809]

    [32]

    Guo Z Y, Cao B Y, Zhu H Y, Zhang Q G 2007 Acta Phys. Sin. 56 3306 (in Chinese) [过增元,曹炳阳,朱宏晔,张清光 2007 物理学报 56 3306]

  • [1]

    Kreuzer H J 1981 Nonequilibrium Thermodynamics and Its Statistical Foundations (New York: Oxford University Press)

    [2]

    Jou D, Casas-Vazquez J, Lebon G 2010 Extended Irreversible Thermodynamics (4th Ed) (New York: Springer)

    [3]

    Groot S R, Mazur P 1984 Non-Equilibrium Thermodynamics (New York: Dover Publications)

    [4]

    Zeng D L 1991 Engineering Non-Equilibrium Thermodynamics (Beijing: Science Press) (in Chinese) [曾丹苓 1991 工程非平衡热动力学 (北京: 科学出版社)]

    [5]

    Grandy Jr W T 2008 Entropy and the Time Evolution of Macroscopic Systems (New York: Oxford University Press)

    [6]

    Onsager L 1931 Phys. Rev. 37 405

    [7]

    Casimir H B G 1945 Rev. Mod. Phys. 17 343

    [8]

    Glansdorf P, Prigogine I 1971 Thermodynamic Theory of Structure, Stability and Fluctuations (New York: Wiley)

    [9]

    Lebon G, Casas-Vazquez J, Jou D 2008 Understanding Non- Equilibrium Thermodynamics: Foundations, Applications, Frontiers (Berlin: Springer-Verlag)

    [10]

    Stritzker B, Pospieszczyk A, Tagle J A 1981 Phys. Rev. Lett. 47 356

    [11]

    Torii S, Yang W J 2005 Int. J. Heat Mass Trans. 48 537

    [12]

    Guo Z Y, Xu Y S 1995 J. Electron. Packaging 117 174

    [13]

    Cattaneo C 1948 Atti. Sem. Mat. Fis. Univ. Modena 3 83

    [14]

    Vernotte P 1958 C. R. Acad. Sci 246 3154

    [15]

    Morse P M, Feshbach H 1953 Methods of Theoretical Physics (New York: McGraw-Hill)

    [16]

    Tzou D Y 1989 J. Heat Trans. 111 232

    [17]

    Tzou D Y 1992 Thermal shock phenomena under high-rate response in solids in: Tien C L (Ed) Annual Review of Heat Transfer IV (Whashington DC: Hemisphere) Chapter 3 pp 111–185

    [18]

    Tzou D Y 1997 Macro- to Microscale Heat Transfer: The Lagging Behavior (Whashington DC: Taylor & Francis)

    [19]

    Criado-Sancho M, Llebot J E 1993 Phys. Rev. E 47 4104

    [20]

    Al-Nimr M A, Naji M, Arbaci V S 2000 J. Heat Trans. 122 217

    [21]

    Jou D, Casas-Vazquez J, Lebon G 1999 Rep. Pro. Phys. 62 1035

    [22]

    Müller I 1985 Thermodynamics (London: Pitman)

    [23]

    Sieniutycz S, Salamon P 1992 Extended Thermodynamic System (New York: Taylor and Francis)

    [24]

    Barletta A, Zanchini E 1997 Int. J. Heat Mass Trans. 40 1007

    [25]

    Jou D, Casas-Vazquez J, Lebon G 2008 Proceedings of the Estonian Academy of Sciences 57 118

    [26]

    Cao B Y, Guo Z Y 2007 J. Appl. Phys. 102 53503

    [27]

    Guo Z Y, Hou Q W 2010 ASME J. Heat Trans. 132 072403

    [28]

    Wang H D, Cao B Y, Guo Z Y 2010 Int. J. Heat Mass Trans. 53 1796

    [29]

    Song B,Wu J, Guo Z Y 2010 Acta Phys. Sin. 59 7129 (in Chinese) [宋柏,吴晶,过增元 2010 物理学报 59 7129]

    [30]

    Guo Z Y, Cao B Y 2008 Acta Phys. Sin. 57 4273 (in Chinese) [过增元,曹炳阳 2008 物理学报 57 4273]

    [31]

    Hou Q W, Cao B Y, Guo Z Y 2009 Acta Phys. Sin. 58 7809 (in Chinese) [侯泉文,曹炳阳,过增元 2009 物理学报 58 7809]

    [32]

    Guo Z Y, Cao B Y, Zhu H Y, Zhang Q G 2007 Acta Phys. Sin. 56 3306 (in Chinese) [过增元,曹炳阳,朱宏晔,张清光 2007 物理学报 56 3306]

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出版历程
  • 收稿日期:  2011-03-09
  • 修回日期:  2011-05-18
  • 刊出日期:  2012-03-15

非平衡热力学中传热过程熵产表达式的修正

  • 1. 清华大学航天航空学院热科学与动力工程教育部重点实验室, 北京 100084
    基金项目: 国家自然科学基金(批准号: 51076080, 51136001)和清华大学自主科研计划资助的课题.

摘要: 熵产是非平衡热力学中的核心物理量,传统上表示为广义力(驱动力)与广义流的乘积.这种表达存在两方面缺陷:一是广义力与广义流的拆分具有任意性;更重要的是,以其计算热波传递时熵产可以为负值,从而违反热力学第二定律.本文基于热质理论分析表明,传热过程的熵产实质上是由热质流体的热质能耗散引起的,所以熵产中的力不是驱动力而是阻力,并且具有力的量纲.由此提出的熵产修正表达式,不仅在计算热波传递过程中熵产恒为正值,与扩展不可逆热力学中的熵产表达式一致,而且不存在力和流拆分的任意性.

English Abstract

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