functions, is presented as a sum between the Newtonian solution and the corresponding nonNewtonian contribution. The solutions corresponding to the generalized Maxwell fluids, as well as the solutions for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, are obtained as limiting cases of the general solutions. In the absence of side walls, namely when the distance between walls...

We have implemented the log-conformation method for two-dimensional viscoelastic flow in COMSOL, a commercial high-level finite element package. The code is verified for an Oldroyd-B fluid flowing past a confined cylinder. We are also able to describe the well-known bistability of the viscoelastic flow in a crossslot geometry for a FENE-CR fluid, and we describe the changes required for perform...

This research addresses the mixed convection flow of an Oldroyd-B fluid in a doubly stratified surface. Both temperature and concentration stratification effects are considered. Thermal radiation and chemical reaction effects are accounted. The governing nonlinear boundary layer equations are converted to coupled nonlinear ordinary differential equations using appropriate transformations. Resul...

The influence of inertia and elasticity on the onset and stability of 3-D thermal convection is examined for highly elastic polymeric solutions with constant viscosity. These solutions are known as Boger fluids, and their rheology is approximated by the Oldroyd-B constitutive equation. The onset and the stability of steady convective patterns, namely rolls, hexagons and squares, are studied in ...

We prove an asymptotic relationship between the grade-two fluid model and a class of models for non-Newtonian fluids suggested by Oldroyd, including upper-convected lower-convected Maxwell models. This confirms earlier observation Tanner. provide new interpretation temporal instability negative coefficients. Our techniques allow simple proof convergence steady to Navier–Stokes as α→0 (under sui...

We perform a linear stability analysis of viscoelastic plane Couette and Poiseuille flows with free-slip boundary conditions. The fluid is described by the Oldroyd-B constitutive model, are driven suitable body force. find that both types flow become linearly unstable, we characterise spatial structure unstable modes. By performing condition homotopy from to no-slip boundaries, demonstrate mode...

The log conformation representation proposed in [1] has been implemented in a fem context using the DEVSS/DG formulation for viscoelastic fluid flow. We present a stability analysis in 1D and attribute the high Weissenberg problem to the failure of the numerical scheme to balance exponential growth. A slightly different derivation of the log based evolution equation than in [1] is also presente...