Continuum Mechanics and Thermodynamics

, Volume 2, Issue 4, pp 301–305 | Cite as

On Fourier's law of heat conduction

  • I-Shih Liu


A linear theory of fluid is considered in which the gradients of density, internal energy and velocity are among the constitutive variables. Thus the heat flux may be a linear combination of the gradients of density and internal energy. It is proved that this linear combination may be written as the gradient of temperature so that Fourier's law of heat conduction holds.


Heat Flux Linear Combination Heat Conduction Internal Energy Linear Theory 
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  1. 1.
    Liu, I-Shih: Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rational Mech. Anal. 46 (1972) 131Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • I-Shih Liu
    • 1
  1. 1.Instituto de MatemáticaUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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