An attempt is made to investigate the peristaltic motion of a Giesekus fluid in a planar channel under long wavelength and low Reynolds number approximations. Under these assumptions, the flow problem is modelled as a second-order nonlinear ordinary differential equation. Both approximate and exact solution of this equation are presented. The validity of the approximate solution is examined by ...

a theoretical solution is presented for the forced convection heat transfer of a viscoelastic fluid obeying the giesekus constitutive equation in a concentric annulus under steady state, laminar, and purely tangential flow. a relative rotational motion exists between the inner and the outer cylinders, which induces the flow. a constant temperature was set in both cylinders, in this study. the f...

In the discipline of non-Newtonian materials, the ability to control viscoelastic stresses is very desirable in ascertaining important properties of the influenced materials. We apply the nonlinear geometric control theory to examine the controllability of various popular constitutive models with imposed homogeneous extensional flow. The subsequent constitutive laws considered here include the ...

A method will be given to determine lower bounds for the invariants of a configuration tensor in 3D flows. For some well-known differential models these lower bounds will be given. Except for the Giesekus and the FENE-P model the lower bounds are the values in equilibrium.

One of the most classical closures approximation of the FENE model of polymeric flows is the one proposed by Peterlin, namely the FENE-P model. We prove global existence of weak solutions to the FENE-P model. The proof is based on the propagation of some defect measures that control the lack of strong convergence in an approximating sequence. Using a similar argument, we also prove global exist...

We derive a self-similar solution which describes the asymptotic behavior of a jet of a Giesekus fluid as the breakup point is approached.

We investigate finite amplitude stability of spatially inhomogeneous steady state an incompressible viscoelastic fluid which occupies a mechanically isolated vessel with walls kept at non-uniform temperature. For wide class models including the Oldroyd-B model, Giesekus FENE-P Johnson–Segalman and Phan–Thien–Tanner model we prove that is stable subject to any perturbation.

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...