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Quantification of the degree of irreversibility in terms of material parameters by using Ziegler's non‐linear constitutive relation for the stress‐velocity gradient relationship
Author(s) -
Müller Wolfgang H.,
Emek Abali B.
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110195
Subject(s) - constitutive equation , entropy production , nonlinear system , cauchy stress tensor , entropy (arrow of time) , velocity gradient , statistical physics , mathematics , thermodynamics , mathematical analysis , mechanics , physics , quantum mechanics , finite element method
The non‐trivial task of an engineer is to derive or at least to use a constitutive relation which leads to a solvable equation but still expresses the system behavior adequately, so that the solution for the motion is accurate. Often the system has solid‐like or fluid‐like behavior, and an appropriate relation is chosen. In the so‐called Bingham‐Ilyushin matter both regimes occur simultaneously. This can be expressed by using a tensor‐linear constitutive relation with a nonlinear (viscosity) term and even be solved in a specific case of material parameters ( b = 0 ). The analytical solution for the velocity distribution in a channel with moving walls is presented here. The velocity gradients lead to an increase in temperature. The internal friction due to the (nonlinear) viscosity contributes to the entropy production and accounts for the irreversibility of the process. The aim is to analyze the role of each material parameter in the entropy production which might be used as a measure of irreversibility of the process. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)