Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids

Meur, Hervé Le

doi:10.1051/m2an/1997310201851

Cited by 8 publications

(1 citation statement)

References 12 publications

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“…He observed that both density and viscosity stratification can cause interfacial Kelvin-Helmholtz instability. Herve Le Meur [9] has studied the uniqueness and the existence of the multilayered Poiseuille/ Couette fluid flow in pipes/channel and observed that interpolated Oldroyd derivative parameter and the viscosity ratios are significant for a unique solution. Kalogirou and Blyth [10] have considered the Couette-Poiseuille flow of the two-layered superposed fluids to discuss stability.…”

Section: Introductionmentioning

confidence: 99%

Multi-layer flows of immiscible fractional second grade fluids in a rectangular channel

Rauf

Muhammad

2020

SN Appl. Sci.

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Multi-layer laminar unsteady flows of immiscible fractional second grade fluids in a rectangular channel made by two parallel plates are studied. The fluid motion is produced by the motion of parallel walls in their plane and by the timedependent pressure gradient in the presence of the linear fluid-fluid interface conditions. The mathematical model is based on the generalized constitutive equations for the shear stress described by the time-fractional Caputo derivative. Integral transforms (finite Fourier sine transform and Laplace transform) have been used to obtain analytical and semi-analytical solutions for velocity, shear stress and the temperature fields. In the case of semi-analytical solutions, the Talbot's algorithms are used for the inverse Laplace transform. The numerical calculations are carried out with the help of Mathcad software, and the results are illustrated graphically. It has been found that the memory effects have a significant influence on the motion of the fluids. Keywords n-layered immiscible fluids • Fractional second grade fluids • Analytical and semi analytical solutions • Integral transforms Mathematics Subject Classification 76-XX • 76T30 • 76D50 Nomenclature i Density i Dynamic viscosity i Kynamic viscosity u 0 Characteristic velocity G i Elastic modulus i Shear stress u i (y, t) Velocity P Pressure h Distance between two plates X (y,) Laplace transform of the function X(y, t) E i , i (⋅) Mittag-Leffler function G 1 , 2 , 3 (t,) G-Lorenzo Hartely function

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Section: Introductionmentioning

confidence: 99%

Multi-layer flows of immiscible fractional second grade fluids in a rectangular channel

Rauf

Muhammad

2020

SN Appl. Sci.

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Steady Flows of Viscoelastic Fluids in Domains with Outlets to Infinity

Pileckas

Sequeira²,

Videman³

2000

J. math. fluid mech.

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The equations governing the motion of incompressible viscoelastic fluids of RivlinEricksen and Oldroyd type are investigated in domains with cylindrical and paraboloidal outlets to infinity. For sufficiently small fluxes, prescribed in each outlet, existence and uniqueness of solutions are proven in weighted Hölder spaces. In domains with paraboloidal outlets the solution is obtained as a perturbation of the corresponding Navier-Stokes solution and in domains with cylindrical outlets as a perturbation of a flux carrier, constructed by joining together the exact solutions found in each outlet. These exact solutions are shown to be either rectilinear flows of Poiseuille type or flows composed of a rectilinear and of a transverse secondary component. Mathematics Subject Classification (2000). 35Q35, 35M10, 76D05, 76A10.

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The influence of fractional time-derivative on the helical flows of generalized multi-layer immiscible second grade fluids in a cylindrical domain

Rauf

Batool

Shah

et al. 2023

Ain Shams Engineering Journal

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Non-uniqueness and linear stability of the one-dimensional flow of multiple viscoelastic fluids

Cited by 8 publications

References 12 publications

Multi-layer flows of immiscible fractional second grade fluids in a rectangular channel

Multi-layer flows of immiscible fractional second grade fluids in a rectangular channel

Steady Flows of Viscoelastic Fluids in Domains with Outlets to Infinity

The influence of fractional time-derivative on the helical flows of generalized multi-layer immiscible second grade fluids in a cylindrical domain

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