Access

You are not currently logged in.

Access your personal account or get JSTOR access through your library or other institution:

login

Log in to your personal account or through your institution.

If You Use a Screen Reader

This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.

Time-dependent, irreversible entropy production and geodynamics

Klaus Regenauer-Lieb, Ali Karrech, Hui Tong Chua, Franklin G. Horowitz and Dave Yuen
Philosophical Transactions: Mathematical, Physical and Engineering Sciences
Vol. 368, No. 1910, Patterns in our planet: applications of multi-scale non-equilibrium thermodynamics to Earth-system science (13 January 2010), pp. 285-300
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/25663249
Page Count: 16
  • Read Online (Free)
  • Cite this Item
Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Time-dependent, irreversible entropy production and geodynamics
Preview not available

Abstract

We present an application of entropy production as an abstraction tool for complex processes in geodynamics. Geodynamic theories are generally based on the principle of maximum dissipation being equivalent to the maximum entropy production. This represents a restriction of the second law of thermodynamics to its upper bound. In this paper, starting from the equation of motion, the first law of thermodynamics and decomposition of the entropy into reversible and irreversible terms, we come up with an entropy balance equation in an integral form. We propose that the extrema of this equation give upper and lower bounds that can be used to constrain geodynamics solutions. This procedure represents an extension of the classical limit analysis theory of continuum mechanics, which considers only stress and strain rates. The new approach, however, extends the analysis to temperature-dependent problems where thermal feedbacks can play a significant role. We apply the proposed procedure to a simple convective/conductive heat transfer problem such as in a planetary system. The results show that it is not necessary to have a detailed knowledge of the material parameters inside the planet to derive upper and lower bounds for self-driven heat transfer processes. The analysis can be refined by considering precise dissipation processes such as plasticity and viscous creep.

Page Thumbnails

  • Thumbnail: Page 
285
    285
  • Thumbnail: Page 
286
    286
  • Thumbnail: Page 
287
    287
  • Thumbnail: Page 
288
    288
  • Thumbnail: Page 
289
    289
  • Thumbnail: Page 
290
    290
  • Thumbnail: Page 
291
    291
  • Thumbnail: Page 
292
    292
  • Thumbnail: Page 
293
    293
  • Thumbnail: Page 
294
    294
  • Thumbnail: Page 
295
    295
  • Thumbnail: Page 
296
    296
  • Thumbnail: Page 
297
    297
  • Thumbnail: Page 
298
    298
  • Thumbnail: Page 
299
    299
  • Thumbnail: Page 
300
    300