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Nonequilibrium temperatures, heat waves, and nonlinear heat transport equations

机译：非平衡温度，热波和非线性热传递方程

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摘要

A dynamical nonequilibrium temperature has been proposed to describe relaxational equations for the heat flux. This temperature provides an alternative description to the Maxwell-Cattaneo equation. In the linear regime and in bulk systems both descriptions are equivalent but this is not so when nonlinear effects are included. Here we explore the influence of nonlinear terms on the phase speed of heat waves in nonequilibrium steady states in both theoretical models and we show that their predictions are different. This could allow to explore which description is more suitable, when experiments on these situations will become available. Furthermore, we have analyzed a nonlinear and nonlocal constitutive equation for the heat flux and we have shown its analogy with the Navier-Stokes equation in the regime of phonon hydrodynamics in nanosystems. This analogy allows one to define a dimensionless number for heat flow, analogous to the Reynolds number, and to predict a critical heat flux where nonlinear effects could become dominant.
机译：已经提出了动态非平衡温度来描述热通量的松弛方程。该温度为麦克斯韦-卡塔尼方程提供了另一种描述。在线性状态和整体系统中，这两种描述是等效的，但是当包括非线性效应时，情况并非如此。在这里，我们在两种理论模型中都探讨了非线性项对热波在非平衡稳态下的相速度的影响，并表明它们的预测是不同的。当针对这些情况的实验将可用时，这可以允许探索哪种描述更合适。此外，我们分析了热通量的非线性和非局部本构方程，并在纳米系统中的声子流体动力学范围内将其与Navier-Stokes方程进行了类比。这种类比允许人们为热流定义一个无量纲的数，类似于雷诺数，并预测一个临界热通量，在该通量中非线性效应可能成为主导。

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  • 来源
    《Physical review》 |2010年第5期|p.054301.1-054301.9|共9页
  • 作者

    V. A. Cimmelli; A. Sellitto; D. Jou;

  • 作者单位

    Department of Mathematics and Computer Science, University of Basilicata, Campus Macchia Romana, 85100 Potenza, Italy;

    Department of Mathematics and Computer Science, University of Basilicata, Campus Macchia Romana, 85100 Potenza, Italy;

    Departament de Fisica, Universitaet Autbnoma de Barcelona, 08193 Bellaterra, Catalonia, Spain and Institut d'Estudis Catalans, Carme 47, 08001 Barcelona, Catalonia, Spain;

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