A thermodynamic Approach to Rate Equations in Continuum Physics  

作　　者：Angelo Morro 

机构地区：[1]DIBRIS, University of Genoa, Genova 16145, Italy

出　　处：《Journal of Physical Science and Application》2017年第6期15-23,共9页物理科学与应用（英文版）

摘　　要：The paper addresses the formulation of rate equations, via objective time derivatives, within continuum physics. The concept of objectivity is reviewed and distinction is made with material frame-indifference whose meaning is restricted to the invariance of the balance equations relative to Galilean frames. Objective time derivatives are defined to leave the tensor character of the appropriate field invariant within the set of Euclidean frames. Rate equations are required to involve objective time derivatives and to be consistent with the second law of thermodynamics. Here the general structure of objective time derivatives is established and the known derivatives of the physical literature are shown to be particular cases. Next, to fix ideas, a rate equation is considered for the model of heat conduction via a generalization of the Maxwell-Cattaneo equation with higher-order gradients as in the Guyer-Krumhansl equation. The thermodynamic restrictions are investigated and the expected effects, of the selected derivative of the heat flux, on the stress tensor are derived.纸探讨率方程的明确的表达，经由客观时间衍生物，在连续统物理以内。客观性的概念被考察，区别与其意思相对 Galilee 的框架被限制为平衡方程的不变性的材料框架不在乎被做。客观时间衍生物被定义离开在欧几里德几何学的框架的集合以内不变的适当的地的张肌特性。率方程被要求包含客观时间衍生物并且与热力学的第二条法律一致。这里，客观时间衍生物的一般结构被建立，物理文学的已知的衍生物被显示是特别盒子。到改正想法，下次，一个率方程与高顺序的坡度经由 Maxwell-Cattaneo 方程的归纳为热传导的模型被考虑作为在 Guyer-Krumhansl 方程。热力学的限制被调查，热流动的选择衍生物，期望的效果在压力张肌上被导出。

关 键 词：Objective derivatives rate equations thermodynamic consistency 

分 类 号：O312.2[理学—一般力学与力学基础] O414.1[理学—力学]