Abstract: The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l10, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.
Abstract: The polymer foil used for manufacturing of
laminated glass members behaves in a viscoelastic manner with
temperature dependance. This contribution aims at incorporating
the time/temperature-dependent behavior of interlayer to our earlier
elastic finite element model for laminated glass beams. The model
is based on a refined beam theory: each layer behaves according
to the finite-strain shear deformable formulation by Reissner and
the adjacent layers are connected via the Lagrange multipliers
ensuring the inter-layer compatibility of a laminated unit. The
time/temperature-dependent behavior of the interlayer is accounted
for by the generalized Maxwell model and by the time-temperature
superposition principle due to the Williams, Landel, and Ferry.
The resulting system is solved by the Newton method with
consistent linearization and the viscoelastic response is determined
incrementally by the exponential algorithm. By comparing the model
predictions against available experimental data, we demonstrate that
the proposed formulation is reliable and accurately reproduces the
behavior of the laminated glass units.
Abstract: Fluid rheology may have essential impact on sound propagation in a liquid-filled pipe, especially, in a low frequency range. Rheological parameters of liquid are temperature-sensitive, which ultimately results in a temperature dependence of the wave speed and attenuation in the waveguide. The study is devoted to modeling of this effect at sound propagation in an elastic pipe with polymeric liquid, described by generalized Maxwell model with non-zero high-frequency viscosity. It is assumed that relaxation spectrum is distributed according to the Spriggs law; temperature impact on the liquid rheology is described on the basis of the temperature-superposition principle and activation theory. The dispersion equation for the waveguide, considered as a thin-walled tube with polymeric solution, is obtained within a quasi-one-dimensional formulation. Results of the study illustrate the influence of temperature on sound propagation in the system.
Abstract: The B'enard-Marangoni thermal instability problem for
a viscoelastic Jeffreys- fluid layer with internal heat generation is
investigated. The fluid layer is bounded above by a realistic free
deformable surface and by a plane surface below. Our analysis
shows that while the internal heat generation and the relaxation time
both destabilize the fluid layer, its stability may be enhanced by an
increased retardation time.