連続体におけるエントロピー増大の非瞬時性と非局所性 : 時間極性物質と熱極性物質

概要

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Though it is adequate to describe the macroscopic behavior of materials from the viewpoint of the continuum theory, the existence of microstructures of materials has been ignored on these theories. The concept of polar materials has been introduced in order to modify the classical continuum approach. In this paper, the entropy inequality is described by the integral form in order to express the noninstantaneity and nonlocality. Second order terms of the fluctuation from the average value in a small region (mesodomain) are considered. Theses terms may express the additional entropy production rates caused by the noninstantaneity and nonlocality. Materials with these effects can be called chronopolar materials and thermopolar materials. It is shown that the temperature gradient, curvature and velocity should not be omitted from the arguments of the thermodynamic potential or stress constitutive equations. The hyperbolic differential equation of heat conduction is derived, which gives finite speeds of temperature propagation.
日本応用数理学会の論文
1995-06-15