Stability of non-linear constitutive formulations for viscoelastic fluids

Stability of Non-linear Constitutive Formulations for Viscoelastic Fluids provides a complete and up-to-date view of the field of constitutive equations for flowing viscoelastic fluids, in particular on their non-linear behavior, the stability of these constitutive equations that is their predictive power, and the impact of these constitutive equations on the dynamics of viscoelastic fluid flow in tubes. This book gives an overall view of the theories and attendant methodologies developed independently of thermodynamic considerations as well as those set within a thermodynamic framework to derive non-linear rheological constitutive equations for viscoelastic fluids. Developments in formulating Maxwell-like constitutive differential equations as well as single integral constitutive formulations are discussed in the light of Hadamard and dissipative type of instabilities

Spectral approximation for a nonlinear partial differential equation arising in thin film flow of a non-Newtonian fluid

WOS: 000295995300005Start-up thin film flow of fluids of grade three over a vertical longitudinally oscillating solid wall in a porous medium is investigated. The governing non-linear partial differential equation representing the momentum balance is solved by the Fourier-Galerkin approximation. The effect of the porosity, material constants as well as oscillations on the drainage rate and flow enhancement is explored and clarified. (C) 2011 Elsevier B.V. All rights reserved

UNSTEADY FLOW OF A NON-LINEAR VISCOELASTIC FLUID IN PIPES

ABSTRACT Flow of a viscoelastic fluid in round pipes is analyzed for the case where the pressure gradient is oscillatory with varying amplitude. The fluid is modelled according to Phan-ThienTanner´s constitutive equation. The analysis is carried out by using the perturbation method in which a material parameter is considered small. Velocity field and other kinematic and dynamic variables are evaluated for a range of relevant parameters. The results are compared with the base Newtonian and linear Maxwell flows. The effect of the PTT model in these type of flows is highlighted. INTRODUCTION The non-linear viscoelastic characteristics of some fluids induce many interesting phenomena in pipe flow, which have been recently investigated. Some of those phenomena are steady secondary flows [5], unsteady secondary flows [2] and heat transfer enhancemen

FEDSM2008-55058 AN INVERSE APPROACH TO MAGNETORHEOLOGICAL DAMPER DESIGN: HERSHEL-BULKLEY MODEL

ABSTRACT Magnetorheological fluids (MRF) are increasingly used for the design of dampers in many cases when a given response is critical for desired performance. Some recent examples are self-powered magnetorheological dampers, cable vibration control and wheeled vehicle dampers. Loads of this type can be very big, especially in the case of seismic-dampers as well as in heavy vehicles and aircraft landing gear. This problem can be more efficiently dealt with by using an inverse-problem strategy, where the required performance is specified a priori, and the fluid parameters are changed accordingly by means of a variable magnetic field. The effect on the flow of the time-variation of the parameters of the Herschel-Bulkley constitutive model is analyzed in this paper. In this way, the influence of a varying magnetic field on the unsteady flow of a magnetic fluid is explored. Yield stress, viscosity and power index are assumed time-dependent. In particular, linear variations in time of these parameters are considered, and the case where the yield stress and viscosity oscillate in time is explored in detail. The characteristics of the velocity field are analyzed for different values of the constants that determine the time structure of the constitutive parameters