Stability of a plane Poiseuille flow of a finite linear viscoelastic fluid

1973 ◽  
Vol 16 (6) ◽  
pp. 790 ◽  
Author(s):  
G. Tackels
Keyword(s):  
Viscoelastic Fluid ◽  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Linear Viscoelastic ◽  
Finite Linear ◽  
Linear Viscoelastic Fluid

scholarly journals Onset of Thermal Instabilities in the Plane Poiseuille Flow of Weakly Elastic Fluids: Viscous Dissipation Effects

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 432
Author(s):  
Silvia C. Hirata ◽  
Mohamed Najib Ouarzazi
Keyword(s):  
Linear Stability ◽  
Viscous Dissipation ◽  
Viscoelastic Fluid ◽  
Poiseuille Flow ◽  
Hydrodynamic Instability ◽  
Plane Poiseuille Flow ◽  
Volumetric Heating ◽  
Fluid Elasticity ◽  
Different Temperatures ◽  
Elastic Fluids

The onset of thermal instabilities in the plane Poiseuille flow of weakly elastic fluids is examined through a linear stability analysis by taking into account the effects of viscous dissipation. The destabilizing thermal gradients may come from the different temperatures imposed on the external boundaries and/or from the volumetric heating induced by viscous dissipation. The rheological properties of the viscoelastic fluid are modeled using the Oldroyd-B constitutive equation. As in the Newtonian fluid case, the most unstable structures are found to be stationary longitudinal rolls (modes with axes aligned along the streamwise direction). For such structures, it is shown that the viscoelastic contribution to viscous dissipation may be reduced to one unique parameter: γ=λ1(1−Γ), where λ1 and Γ represent the relaxation time and the viscosity ratio of the viscoelastic fluid, respectively. It is found that the influence of the elasticity parameter γ on the linear stability characteristics is non-monotonic. The fluid elasticity stabilizes (destabilizes) the basic Poiseuille flow if γ<γ* (γ>γ*) where γ* is a particular value of γ that we have determined. It is also shown that when the temperature gradient imposed on the external boundaries is zero, the critical Reynolds number for the onset of such viscous dissipation/viscoelastic-induced instability may be well below the one needed to trigger the pure hydrodynamic instability in weakly elastic solutions.

Unsteady Flow of a Non-Linear Viscoelastic Fluid in Pipes

2004 ◽  
Author(s):  
Mario F. Letelier ◽  
Nicola´s Madariaga ◽  
Dennis A. Siginer
Keyword(s):  
Velocity Field ◽  
Constitutive Equation ◽  
Pressure Gradient ◽  
Perturbation Method ◽  
Viscoelastic Fluid ◽  
Material Parameter ◽  
Ptt Model ◽  
Linear Viscoelastic ◽  
Dynamic Variables ◽  
Linear Viscoelastic Fluid

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-Thien-Tanner’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.

On the asymptotic behavior of a linear viscoelastic fluid

2012 ◽  
Vol 35 (7) ◽  
pp. 769-775 ◽  
Author(s):  
Mauro Fabrizio ◽  
Barbara Lazzari ◽  
Roberta Nibbi
Keyword(s):  
Asymptotic Behavior ◽  
Viscoelastic Fluid ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Fluid
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