A general transformation procedure for differential viscoelastic models

A general transformation procedure (GTP) for viscoelastic differential constitutive equations is proposed. This procedure is devised to transform a differential model (e.g. Oldroyd-B, White–Metzner (WM) and Phan-Thien–Tanner (PTT)) into another model which has just one differential equation to be so...

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Bibliographic Details
Published in:Journal of non-Newtonian fluid mechanics 2003, Vol.111 (2), p.151-174
Main Authors: Mompean, G., Thompson, R.L., Souza Mendes, P.R.
Format: Article
Language:English
Subjects:
Differential
Exact sciences and technology
Flows in ducts, channels, nozzles, and conduits
Fluid dynamics
Fundamental areas of phenomenology (including applications)
Non-newtonian fluid flows
Physics
Transformation
Viscoelastic
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Summary:A general transformation procedure (GTP) for viscoelastic differential constitutive equations is proposed. This procedure is devised to transform a differential model (e.g. Oldroyd-B, White–Metzner (WM) and Phan-Thien–Tanner (PTT)) into another model which has just one differential equation to be solved. The resulting model is suitable for three-dimensional and time-dependent flows. A new generalized objective time derivative is employed in the procedure, lending important features to the transformed model. For example, for the case of the Oldroyd-B model, the transformed model is capable of predicting non-zero second normal stress differences. Calculations of the stress field have been performed with an Oldroyd-B based GTP model (the GTP[OldB] model) for a 4:1 contraction plane flow. The results obtained have been analyzed with the aid of a flow-type classifier, and were found to be in good agreement with the ones obtained with the original model.
ISSN:0377-0257
1873-2631
DOI:10.1016/S0377-0257(03)00042-9