Parameters identification for the unsteady helical flows of a generalized Oldroyd-B fluid model based on its numerical solution

Unsteady Helical Flows of a Maxwell Fluid

where T is the stress tensor, p the hydrostatic pressure, S the extra-stress tensor, A the first RivlinEricksen tensor and μ the dynamic viscosity. Many common fluids show this “Newtonian” behavior and in fact the whole discipline of classical fluid mechanics is based upon this equation. However, the constitutive equation (1) does not show any of the normal stress effects or relaxation phenomen...

Effect of Slip Condition on Unsteady Flows of an Oldroyd-B Fluid between Parallel Plates

The unsteady flows of an incompressible Oldroyd-B fluid between two infinite parallel plates are considered when the slippage between the plate and the fluid is valid. The relative velocity between the fluid and plate is assumed to be proportional to the shear rate at the plates. The flow is generated by moving one of the plates or application of the constant pressure gradient giving arise to t...

Visualization of Numerical Unsteady Fluid Flows

Instantaneous streamlines are commonly used to visualize particle paths in steady flows. It is shown, however, that streaklines are often more appropriate for unsteady flows. The typical size of unsteady flow simulations makes interactive visualization difficult if not impossible. Two common approaches for visualizing unsteady flows are described. The advantages and disadvantages of each are di...

Some exact solutions for the helical flow of a generalized Oldroyd-B fluid in a circular cylinder

Numerical approximation of viscoelastic Oldroyd-B flows in curved pipes

The aim of this paper is to study a finite element numerical approximation of steady flows of an incompressible viscoelastic Oldroyd-B fluid in curved pipes of arbitrary cross-section and curvature ratio. Using rectangular toroidal coordinates, existence and uniqueness of approximated solutions are proved as well as a priori error estimates, under a natural restriction on the pipe curvature ratio.