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Numerical modeling of a non‐linear viscous flow in order to determine how parameters in constitutive relations influence the entropy production
Author(s) -
Müller Wolfgang H.,
Abali B. Emek
Publication year - 2012
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201210162
Subject(s) - constitutive equation , entropy production , rheology , newtonian fluid , mechanics , dissipation , compressibility , thermodynamics , viscometer , non newtonian fluid , entropy (arrow of time) , viscosity , materials science , physics , finite element method
Some rheological materials, such as melting polymers, cosmetic creams, ketchup, toothpaste, can be modeled as non‐NEWTONian fluids by using a non‐linear constitutive relation. An incompressible flow of this kind of amorphous matter can be considered as a thermodynamic process, and a solution for the pressure, velocity and temperature fields describe it fully. Since such flow processes are generally irreversible, entropy is produced leading to dissipation in the system. This energy loss can be measured indirectly in a cone/plate viscometer which is used to determine viscosity of a BINGHAM fluid. While dissipation is an observable quantity we also want to be able to calculate it. Thus the goal of this work is to explain briefly how to compute a transient flow of a viscous fluid in two‐dimensional channel under a sinusoidal traction and calculate the dissipated energy for non‐NEWTONian fluids. (© 2012 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)