Title
Do General Viscoelastic Stresses For The Flow Of An Upper Convected Maxwell Fluid Satisfy The Momentum Equation
Keywords
Method of characteristics; Stagnation point flow; Stress singularities; Upper convected Maxwell fluid
Abstract
Given a general velocity field consistent with the stagnation point flow, can the viscoelastic stresses arising in the flow of an upper convected Maxwell fluid found by solving the constitutive equation also satisfy the momentum equation? Consideration is given to the study of the stress tensor arising in the steady flow of an upper convected Maxwell (UCM) fluid with a velocity field consistent with the stagnation point flow. By the method of characteristics, exact solutions to the partial differential equations arising in the approximating model of the viscoelastic stresses in the flow of an upper convected Maxwell (UCM) fluid are obtained for the three components of the stress tensor, for reasonably general velocity fields.We are able to account for the effects of variable boundary data at the inflow by considering the viscoelastic stresses over two spatial variables. Furthermore, we assume a relatively general velocity field. As a special case, some results present in the recent literature are obtained; it is known that these special case solutions do not satisfy the momentum equation. In the general case we consider, we find that the general solution will not satisfy the momentum equation except in a limited restricted case.We discuss how this shortcoming might be rectified by use of a more general velocity field. © Springer Science+Business Media B.V. 2012.
Publication Date
11-1-2012
Publication Title
Meccanica
Volume
47
Issue
8
Number of Pages
1977-1985
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1007/s11012-012-9568-8
Copyright Status
Unknown
Socpus ID
84869870931 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/84869870931
STARS Citation
Van Gorder, Robert A., "Do General Viscoelastic Stresses For The Flow Of An Upper Convected Maxwell Fluid Satisfy The Momentum Equation" (2012). Scopus Export 2010-2014. 4722.
https://stars.library.ucf.edu/scopus2010/4722