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Volume 4, Issue 3-4
Finite Element Approximation of the Non-Isothermal Stokes-Oldroyd Equations

C. Cox, H. Lee & D. Szurley

Int. J. Numer. Anal. Mod., 4 (2007), pp. 425-440.

Published online: 2007-04

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  • Abstract

We consider the Stokes-Oldroyd equations, defined here as the Stokes equations with the Newtonian constitutive equation explicitly included. Thus a polymer-like stress tensor is included so that the dependent variable structure of a viscoelastic model is in place. The energy equation is coupled with the mass, momentum, and constitutive equations through the use of temperature-dependent viscosity terms in both the constitutive model and the momentum equation. Earlier works assumed temperature-dependent constitutive (polymer) and Newtonian (solvent) viscosities when describing the model equations, but made the simplifying assumption of a constant solvent viscosity when carrying out analysis and computations; we assume no such simplification. Our analysis coupled with numerical solution of the problem with both temperature-dependent viscosities distinguishes this work from earlier efforts.

  • Keywords

viscous fluid, non-isothermal, finite elements, Stokes-Oldroyd.

  • AMS Subject Headings

65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-4-425, author = {}, title = {Finite Element Approximation of the Non-Isothermal Stokes-Oldroyd Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2007}, volume = {4}, number = {3-4}, pages = {425--440}, abstract = {

We consider the Stokes-Oldroyd equations, defined here as the Stokes equations with the Newtonian constitutive equation explicitly included. Thus a polymer-like stress tensor is included so that the dependent variable structure of a viscoelastic model is in place. The energy equation is coupled with the mass, momentum, and constitutive equations through the use of temperature-dependent viscosity terms in both the constitutive model and the momentum equation. Earlier works assumed temperature-dependent constitutive (polymer) and Newtonian (solvent) viscosities when describing the model equations, but made the simplifying assumption of a constant solvent viscosity when carrying out analysis and computations; we assume no such simplification. Our analysis coupled with numerical solution of the problem with both temperature-dependent viscosities distinguishes this work from earlier efforts.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/870.html} }
TY - JOUR T1 - Finite Element Approximation of the Non-Isothermal Stokes-Oldroyd Equations JO - International Journal of Numerical Analysis and Modeling VL - 3-4 SP - 425 EP - 440 PY - 2007 DA - 2007/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/870.html KW - viscous fluid, non-isothermal, finite elements, Stokes-Oldroyd. AB -

We consider the Stokes-Oldroyd equations, defined here as the Stokes equations with the Newtonian constitutive equation explicitly included. Thus a polymer-like stress tensor is included so that the dependent variable structure of a viscoelastic model is in place. The energy equation is coupled with the mass, momentum, and constitutive equations through the use of temperature-dependent viscosity terms in both the constitutive model and the momentum equation. Earlier works assumed temperature-dependent constitutive (polymer) and Newtonian (solvent) viscosities when describing the model equations, but made the simplifying assumption of a constant solvent viscosity when carrying out analysis and computations; we assume no such simplification. Our analysis coupled with numerical solution of the problem with both temperature-dependent viscosities distinguishes this work from earlier efforts.

C. Cox, H. Lee & D. Szurley. (1970). Finite Element Approximation of the Non-Isothermal Stokes-Oldroyd Equations. International Journal of Numerical Analysis and Modeling. 4 (3-4). 425-440. doi:
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