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A Dual Mixed Formulation for Non-isothermal Oldroyd–StokesProblem

Published online by Cambridge University Press:  10 August 2011

M. Farhloul  and
A. Zine
M. Farhloul
Affiliation:
Département de Mathématiques et de Statistique, Université de Moncton Moncton, N.B., E1A 3E9, Canada
A. Zine*
Affiliation:
Université de Lyon, Ecole Centrale de Lyon, CNRS UMR 5208 Institut Camille Jordan 36, rue Guy de Collongue, 69134 Ecully, France
*
⋆ Corresponding author. E-mail: [email protected]
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Abstract

We propose a mixed formulation for non-isothermal Oldroyd–Stokes problem where the bothextra stress and the heat flux’s vector are considered. Based on such a formulation, adual mixed finite element is constructed and analyzed. This finite element method enablesus to obtain precise approximations of the dual variable which are, for the non-isothermalfluid flow problems, the viscous and polymeric components of the extra-stress tensor, aswell as the heat flux. Furthermore, it has properties analogous to the finite volumemethods, namely, the local conservation of the momentum and the mass.

Keywords

Oldroyd–Stokes problemnon–isothermdual mixed formulation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 5: Complex Fluids , 2011 , pp. 130 - 156
Copyright
© EDP Sciences, 2011

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