Author(s): Cruz, Daniel Onofre de Almeida ; Pinho, Fernando Manuel Coutinho Tavares de
Date: 2019
Persistent ID: http://hdl.handle.net/11422/8446
Origin: Oasisbr
Subject(s): CNPQ::CIENCIAS EXATAS E DA TERRA::FISICA::AREAS CLASSICAS DE FENOMENOLOGIA E SUAS APLICACOES::DINAMICA DOS FLUIDOS; Upper Convected Maxwell model; Wall-free steady planar stagnation point flow; Analytical solution; Stress and pressure fields
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Indisponível.
The general analytical solution for the two-dimensional steady planar extensional flow with wall-free stagnation point is obtained for viscoelastic fluids described by the upper convected Maxwell model providing the stress and pressure fields. The two normal stress fields contain terms that are unbounded for |a|De < ½, |a|De > ½ and even for any |a|De, where De denotes the Deborah number and |a|De denotes the Weissenberg number, but the pressure field is only unbounded for |a|De < ½. Properties of the first invariant of the stress tensor impose relations between the various stress and pressure coefficients and also require that they are odd functions of |a|De. The solution is such that no stress singularities exist if the stress boundary conditions are equal to the stress particular solutions. For |a|De < ½ the only way for the pressure to be bounded is for the stresses to be constant in the whole extensional flow domain and equal to those particular stresses, in which case the loss of stress smoothness, reported previously in the literature, does not exist. For |a|De > ½, however, the pressure remains bounded even in the presence of stress singularities. In all flow cases studied, the stress and pressure fields are contained by the general solution, but may require some coefficients to be null.
