Flow of a Bingham fluid in a non symmetric inclined channel

Fusi, Lorenzo; Farína, Angiolo

doi:10.1016/j.jnnfm.2016.04.007

Cited by 10 publications

(9 citation statements)

References 24 publications

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“…Starting with the pioneering works by Mosolov and Miasnikov [6] and Duvaut and Lions [7], a large number of mathematicians have worked on the theoretical analysis of Bingham fluids and other similar viscoplastic media (see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23] and the references therein).…”

Section: Remarkmentioning

confidence: 99%

On Flows of Bingham-Type Fluids with Threshold Slippage

Baranovskii

2017

Advances in Mathematical Physics

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We investigate a mathematical model describing 3D steady-state flows of Bingham-type fluids in a bounded domain under threshold-slip boundary conditions, which state that flows can slip over solid surfaces when the shear stresses reach a certain critical value. Using a variational inequalities approach, we suggest the weak formulation to this problem. We establish sufficient conditions for the existence of weak solutions and provide their energy estimates. Moreover, it is shown that the set of weak solutions is sequentially weakly closed in a suitable functional space.

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Section: Remarkmentioning

confidence: 99%

On Flows of Bingham-Type Fluids with Threshold Slippage

Baranovskii

2017

Advances in Mathematical Physics

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“…The system of nonlinear ordinary differential equations Eq. (17), (19) and (20) is solved analytically by the help of homotopy perturbation technique, the method appoints a homotopy modify to obtain an approximate series solution of differential equations. In view of the HPM [25][26][27], Eq.…”

Section: Methods Of Solutionsmentioning

confidence: 99%

“…foams, pastes, slurries, oils, ceramics, etc.) exhibit the fundamental character of viscoplasticity, that is the capability of lowing only if the stress is above some critical value [19][20][21]. However, Bingham model is not amenable to numerical analysis because in some complex applications, some parts of material flow behave as a solid.…”

Section: Introductionmentioning

confidence: 99%

MHD Peristaltic Transport of Bingham Blood Fluid with Heat and Mass Transfer Through a Non-Uniform Channel

Eldabe

Abou-zeid

Shawky

2020

ARFMTS

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In the present work, the flow of non-Newtonian Bingham blood fluid through non-uniform channel is investigated. The fluid is electrically conducting, and the external uniform magnetic field is applied on this motion. The heat and mass transfer are taken in consideration, so, Soret and Dufour effects are studied. The problem is modulated mathematically by a system of non-linear partial differential equations which govern the velocity, temperature and concentration distributions. The system of these equations is simplified under the assumptions of long wavelength and low Reynolds number, then it is solved analytically by using homotopy perturbation technique. These distributions are obtained as a function of the physical parameters of the problem. The effects of these parameters on the obtained solutions are discussed numerically and illustrated graphically through a set of figures. These parameters play an important role to control the values of solutions. The used Bingham model is applicable for the physiological transportation of blood in arteries.

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“…He obtains the basic motion, but he does not investigate its stability. Basic flows of Bingham type in inclined channels arise also in other settings, for instance lubrication flows [9,10].…”

Section: Introductionmentioning

confidence: 99%

Stability of the Plane Bingham–Poiseuille Flow in an Inclined Channel

Falsaperla

Giacobbe

Mulone

2020

Fluids

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We study the stability of laminar Bingham–Poiseuille flows in a sheet of fluid (open channel) down an incline with constant slope angle β∈(0,π/2). This problem has geophysical applications to the evolution of landslides. In this article, we apply to this problem recent results of Falsaperla et al. for laminar Couette and Poiseuille flows of Newtonian fluids in inclined channels. The stability of the basic motion of the generalised Navier–Stokes system for a Bingham fluid in a horizontal channel against linear perturbations has been studied. In this article, we study the flows of a Bingham fluid when the channel is oblique and we prove a stabilizing effect of the Bingham parameter B. We also study the stability of the linear system with an energy method (Lyapunov functions) and prove that the streamwise perturbations are always stable, while the spanwise perturbations are energy-stable if the Reynolds number Re is less than the critical Reynolds number Rc obtained solving a generalised Orr equation of a maximum variational problem.

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Flow of a Bingham fluid in a non symmetric inclined channel

Cited by 10 publications

References 24 publications

On Flows of Bingham-Type Fluids with Threshold Slippage

On Flows of Bingham-Type Fluids with Threshold Slippage

MHD Peristaltic Transport of Bingham Blood Fluid with Heat and Mass Transfer Through a Non-Uniform Channel

Stability of the Plane Bingham–Poiseuille Flow in an Inclined Channel

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