Western Australian Geothermal Centre of Excellence, University of Western Australia, Western Australia 6009, Australia.
Philos Trans A Math Phys Eng Sci. 2010 Jan 13;368(1910):285-300. doi: 10.1098/rsta.2009.0204.
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,(1) 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.
我们提出了熵产生作为地球动力学复杂过程的抽象工具的应用。地球动力学理论通常基于最大耗散原理等同于最大熵产生。这代表了热力学第二定律对其上限的限制。在本文中，我们从运动方程、热力学第一定律和熵的可逆和不可逆项的分解出发，（1）得出了一个积分形式的熵平衡方程。我们提出，这个方程的极值可以给出上下限，可以用来约束地球动力学的解。这个过程代表了对经典连续力学极限分析理论的扩展，该理论只考虑了应力和应变率。然而，新方法将分析扩展到了依赖温度的问题，其中热反馈可能起着重要作用。我们将所提出的方法应用于一个简单的对流/传导传热问题，例如在行星系统中。结果表明，对于自驱动传热过程，没有必要深入了解行星内部的材料参数来推导出上下限。通过考虑塑性和粘性蠕动等精确耗散过程，可以对分析进行细化。
