Unsteady Flow of Two Immiscible Fluids under an Oscillatory Time-dependent Pressure Gradient in a Channel with One Porous Floor

Сай, Катерина Сергіївна; ., N.S. Swamy; Nataraja, H. R.; Tiwari, Sanjib; Rao, B. N.

doi:10.3923/tasr.2006.194.203

Cited by 3 publications

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“…Sai et al 13 investigated the flow of two immiscible fluids in a channel with one permeable wall caused by an oscillatory pressure gradient. They found slip conditions on the channel wall but assumed continuous velocities and shear stresses at the fluid–fluid interface.…”

Section: Introductionmentioning

confidence: 99%

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

Alrabaiah

Vieru

Yook

2022

Sci Rep

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The unsteady, magneto-hydrodynamic generalized Couette flows of two immiscible fluids in a rectangular channel with isothermal walls under the influence of an inclined magnetic field and an axial electric field have been investigated. Both fluids are considered electrically conducting and the solid boundaries are electrically insulated. Approximate analytical solutions for the velocity, induced magnetic, and temperature fields have been determined using the Laplace transform method along with the numerical Stehfest's algorithm for the inversion of the Laplace transforms. Also, for the nonlinear differential equation of energy, a numerical scheme based on the finite differences has been developed. A particular case has been numerically and graphically studied to show the evolution of the fluid velocity, induced magnetic field, and viscous dissipation in both flow regions.

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Section: Introductionmentioning

confidence: 99%

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

Alrabaiah

Vieru

Yook

2022

Sci Rep

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Two‐layer flows of generalized immiscible second grade fluids in a rectangular channel

Luo

Alarifi

Vieru

2019

Math Methods in App Sciences

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Unsteady one-dimensional flows of two incompressible and immiscible generalized second grade fluids in a rectangular channel are studied. A constant pressure gradient acts in the flow direction, while the channel walls have oscillating translational motions in their planes. The generalization considered in this paper consists into a mathematical model based on constitutive equations of second grade fluid with Caputo time-fractional derivative in which the history of the shear stress influences the velocity gradient. The velocity and shear stress fields in the Laplace transform domain are obtained. Numerical solutions for the real velocity and shear stress have been found by employing the Stehfest numerical algorithm for the inverse Laplace transform. The influence of the fractional parameters on the velocity and shear stress has been studied by numerical simulations and graphical illustrations. It is found that the memory effects are significant only for small values of the time t. K E Y W O R D S fractional calculus, immiscible fluids, memory effects, two-layer flow

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Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

Bouchgl

Aniss

2021

Int. J. Appl. Mechanics

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We investigate the effect of horizontal periodic oscillation on the interfacial instability of two immiscible and viscous fluids of different densities in a fully saturated porous media. A linear stability analysis of the viscous and time-dependent basic flow leads to a periodic oscillator describing the evolution of the interfacial perturbation amplitude. The horizontal oscillation leads to the occurrence of two types of instability, the Kelvin–Helmholtz’s instability and the parametric resonance. These instabilities appear at the frontier between water and petroleum and have a practical interest in oil reservoir engineering. The results show that, an increase of the oscillation frequency destabilizes the Kelvin–Helmholtz instability and displaces the parametric instability regions toward the short wavelength perturbation. Also, we examine mainly how the other physical parameters of the system affect the instabilities for various permeability and porosity values of the porous medium as well as for relative heights of the two fluid layers.

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Unsteady Flow of Two Immiscible Fluids under an Oscillatory Time-dependent Pressure Gradient in a Channel with One Porous Floor

Cited by 3 publications

References 0 publications

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

Induced magnetic field and viscous dissipation on flows of two immiscible fluids in a rectangular channel

Two‐layer flows of generalized immiscible second grade fluids in a rectangular channel

Effect of Periodic Oscillation on the Interfacial Instability of Two Superposed Fluid Layers in a Fully Saturated Porous Media

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