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

C. Cox and H. Lee & D. Szurley

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

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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.

  • History

Published online: 2007-04

  • AMS Subject Headings

65N30

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