Flow of a new class of non-Newtonian fluids in tubes of non-circular cross-sections
Juan P Gomez-Constante,Kumbakonam R. Rajagopal +1 more
TLDR
The flow of a fluid obeying a constitutive relation of the symmetric part of the velocity gradient in a tube of elliptic and other non-circular cross-sections is considered with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube.Abstract:
Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section. After first proving that purely axial flows are possible, that is, there are no secondary flows as in the case of many viscoelastic fluids, we determine the velocity profile and the shear stresses at the boundaries. We find that the maximum shear stress is attained at the co-vertex of the ellipse. In general tubes of non-circular cross-section, the maximum shear stress occurs at the point on the boundary that is closest to the centroid of the cross-section. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.read more
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Rivlin's legacy in continuum mechanics and applied mathematics
Michel Destrade,Jeremiah G. Murphy,Jeremiah G. Murphy,Giuseppe Saccomandi,Giuseppe Saccomandi +4 more
TL;DR: Ronald Rivlin was one of the last savants, equally proficient in solid and fluid mechanics and in the mathematical methods needed to advance these disciplines, who made seminal contributions in all areas of continuum mechanics.
Journal ArticleDOI
Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids
TL;DR: In this paper, the authors propose a new model for non-Newtonian viscoelastic fluids based on implicit constitutive relations, where the left Cauchy-Green tensor is expressed as a function of stress.
Journal ArticleDOI
Implicit type constitutive relations for elastic solids and their use in the development of mathematical models for viscoelastic fluids
TL;DR: In this article, the Gibbs free energy instead of the Helmholtz free energy is used to model the left Cauchy-Green tensor as a function of stress in the context of viscoelastic fluids.
Book ChapterDOI
The Mechanics and Mathematics of Bodies Described by Implicit Constitutive Equations
TL;DR: In this paper, the authors provide a brief discussion of the rationale and need for implicit constitutive relations for describing the response of many real materials such as the Cauchy theory of elasticity and the Navier-Stokes equations.
References
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