On energy and entropy inflows in the theory of heat conduction

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• 作者：Paolo Podio-Guidugli (1) (2)
  
  1. Accademia Nazionale dei Lincei ; Rome ; Italy
  2. Department of Mathematics ; Universit脿 di Roma TorVergata ; Via della Ricerca Scientifica 1 ; 00133 ; Rome ; Italy
  
• 关键词：Energy inflow ; Entropy inflow ; M眉ller鈥揕iu entropy principle
• 刊名：Archive of Applied Mechanics (Ingenieur Archiv)
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：85
• 期：3
• 页码：347-353
• 全文大小：157 KB
• 参考文献：1. Bargmann, S., Favata, A., Podio-Guidugli, P.: On energy and entropy influxes in the Green鈥揘aghdi Type III theory of heat conduction. Proc. R. Soc. Lond. A, 2013 469, 20120705 (published on line 13 Feb 2013)
  2. Bargmann, S., Steinmann, P.: Classical results for a non-classical theory: remarks on thermodynamic relations in Green鈥揘aghdi thermo-hyperelasticity. Contin. Mech. Thermodyn. 19(1-2), 59鈥?6 (2007) CrossRef
  3. M眉ller, I.: Die K盲ltefunktion, eine universelle Funktion in der Thermodynamik viskoser w盲rmeleitender Fl眉ssigkeiten. Arch. Ration. Mech. Anal. 30, 1鈥?6 (1971) CrossRef
  4. M眉ller, I.: The coldness, a universal function in thermoelastic bodies. Arch. Ration. Mech. Anal. 41, 319鈥?32 (1971) CrossRef
  5. Liu, I.S.: Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Ration. Mech. Anal. 46, 131鈥?48 (1972)
  6. Liu, I.S.: On the entropy supply in a classical and a relativistic fluid. Arch. Ration. Mech. Anal. 50, 111鈥?17 (1973)
  7. Coleman, B., Noll, W.: The thermodynamics of elastic materials with heat conduction and viscosity. Arch. Ration. Mech. Anal. 13, 167鈥?78 (1963) CrossRef
  8. Liu, I.S.: Entropy flux relation for viscoelastic bodies. J. Elast. 90, 259鈥?70 (2008) CrossRef
  9. M眉ller, I., Weiss, W.: Entropy and Energy. Springer, New York (2005)
  10. Serrin, J.B.: An outline of thermodynamic structure. In: Serrin, J.B. (ed.) New Perspectives in Thermodynamics, pp. 3鈥?2. Springer, New York (1986)
  11. Antman, S.S.: Nonlinear Problems of Elasticity, 2nd edn. Springer, New York (2005)
  12. M眉ller, I.: Thermodynamics. Pitman, London (1985)
  13. Liu, I.S.: On the entropy flux/heat flux relation in thermodynamics with Lagrange multipliers. Contin. Mech. Thermodyn. 8, 247鈥?56 (1996) CrossRef
  14. Liu, I.S.: Continuum Mechanics. Springer, New York (2002) CrossRef
  15. 艩ilhav媒, M.: The Mechanics and Thermodynamics of Continuous Media. Springer, New York (1997)
  16. Liu, I.S.: On entropy flux of transversely isotropic elastic bodies. J. Elast. 96, 97鈥?04 (2009) CrossRef
  17. Liu, I.S.: On representations of anisotropic invariants. Int. J. Eng. Sci. 30, 1099鈥?109 (1982)
  
• 刊物类别：Engineering
• 刊物主题：Theoretical and Applied Mechanics
  Mechanics
  Complexity
  Fluids
  Thermodynamics
  Systems and Information Theory in Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1432-0681

文摘

In continuum mechanics, both energy and entropy inflows consist of a scalar source term and a vectorial influx term; customarily, the energy inflow is assumed equal to the entropy inflow multiplied by the absolute temperature. Here, working for simplicity within the framework of the standard theory of heat conduction, an argument is given in support of taking the source terms proportional; moreover, it is proved that the same must be done for influx terms in case conduction is isotropic, but generally not in case of inferior symmetry.