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 - <p style="text-align: justify;">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.</p>