Analytical expressions for the velocity field and the tangential stresses that are induced due to a constantly accelerating edge in an Oldroyd-B fluid have been established for all values of material constants. The solutions that have been obtained satisfy the governing differential equations and all the imposed initial and boundary conditions. These solutions reduce to those for the Maxwell, s...

The effect of viscous heating on the linear stability of torsional flow of a viscoelastic fluid is analyzed. We consider an Oldroyd-B fluid subjected to a steady shearing motion in a cone–plate system with small gap. Previous experimental and analytical results show that in the isothermal case the flow is unstable to short wavelength disturbances for values of the Deborah number greater than so...

Singularities in the stress field of stagnation-point flow a viscoelastic fluid have been studied for various constitutive models. Analyzing analytical solutions these models is most effective way to study this problem. In paper, exact two-dimensional steady wall-free flows generic Oldroyd 8-constant model are obtained using different material parameter relations. For all solutions, compatibili...

In this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow. The Oldroyd B constitutive equation is used to model the viscoelastic stress. For the discretization, time derivatives are replaced by backward difference quotients, and the non-linear terms are linearized by lagging appropriate factors. The modeling ...

To understand observations of low Reynolds number mixing and flow transitions in viscoelastic fluids, we study numerically the dynamics of the Oldroyd-B viscoelastic fluid model. The fluid is driven by a simple time-independent forcing that, in the absence of viscoelastic stresses, creates a cellular flow with extensional stagnation points. We find that at O(1) Weissenberg number, these flows l...