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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
You can always find the topics here!Topics: Entropy, Thermodynamics, Geodynamics, Convection, Surface temperature, Heat transfer, Heat engines, Heat, Continuum mechanics, Engines
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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.
Philosophical Transactions: Mathematical, Physical and Engineering Sciences © 2010 Royal Society