Newtonian Poiseuille flows with slip and non-zero slip yield stress

Kaoullas, George; Georgiou, Georgios C.

doi:10.1016/j.jnnfm.2013.02.005

Cited by 32 publications

(15 citation statements)

References 19 publications

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“…The above formulas were adapted to our case from [49]. The quantitiesw andQ given by (33) are dimensionless because of Formula (14).…”

Section: Non-dimensionalizationmentioning

confidence: 99%

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Drapaca

2018

Fractal Fract

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Cerebral aneurysms and microaneurysms are abnormal vascular dilatations with high risk of rupture. An aneurysmal rupture could cause permanent disability and even death. Finding and treating aneurysms before their rupture is very difficult since symptoms can be easily attributed mistakenly to other common brain diseases. Mathematical models could highlight possible mechanisms of aneurysmal development and suggest specialized biomarkers for aneurysms. Existing mathematical models of intracranial aneurysms focus on mechanical interactions between blood flow and arteries. However, these models cannot be applied to microaneurysms since the anatomy and physiology at the length scale of cerebral microcirculation are different. In this paper, we propose a mechanism for the formation of microaneurysms that involves the chemo-mechanical coupling of blood and endothelial and neuroglial cells. We model the blood as a non-local non-Newtonian incompressible fluid and solve analytically the Poiseuille flow of such a fluid through an axi-symmetric circular rigid and impermeable pipe in the presence of wall slip. The spatial derivatives of the proposed generalization of the rate of deformation tensor are expressed using Caputo fractional derivatives. The wall slip is represented by the classic Navier law and a generalization of this law involving fractional derivatives. Numerical simulations suggest that hypertension could contribute to microaneurysmal formation.

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“…The above formulas were adapted to our case from [49]. The quantitiesw andQ given by (33) are dimensionless because of Formula (14).…”

Section: Non-dimensionalizationmentioning

confidence: 99%

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Drapaca

2018

Fractal Fract

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“…In following, different types of slip boundary condition is discussed and shown that for some polymers even a second critical wall shear stress exists at which a transition to a stronger slip regime occurs. Kaoullas and Georgiou [32] and Georgiou and Kaoullas [33], showed that in the presence of slip yield stress both the classical no-slip boundary condition and an extension of the Navier's slip phenomenon can be observed depending on the value of the pressure gradient of Newtonian fluids. A similar behavior was observed for viscoelastic Poiseuille flow with slip yield stress [34].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Study of Oldroyd-B Visco-Elastic Fluid Flow Through Curved Pipes with Slip Effects in Polymer Flow Processing

Norouzi

Davoodi

Bég

et al. 2018

Int. J. Appl. Comput. Math

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“…Effect of slip condition in the flow field of Newtonian and non-Newtonian fluids has been investigated extensively [5][6][7][8][9][10][11][12][13][14][15][16] but research on heat transfer is scant. Analytical solutions for heat transfer and entropy generation of Newtonian fluid in microchannel were obtained by Anand [17] considering slip boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Forced convection heat transfer of Giesekus fluid with wall slip above the critical shear stress in pipes

Mohseni

Tissot

Badawi

2018

International Journal of Heat and Fluid Flow

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To cite this version:Mehdi Moayed Mohseni, Gilles Tissot, Michael Badawi. Forced convection heat transfer of Giesekus fluid with wall slip above the critical shear stress in pipes. Highlights Increasing slip effect increase Nusselt number in Br>0. Nusselt number decrease by increasing Brinkman number in Br>0.  For the cooling case fluid starts to warm up in Br>Br 1 .  Nusselt curve show a singularity in Br 2 .  Br 1 and Br 2 increase by Increasing slip effect. Abstract Forced convective heat transfer in pipes is investigated for viscoelastic fluids obeying the Giesekus constitutive equation including effect of slip condition by an approximated analytical method. The slip equation at wall is considered nonlinear Navier model with non-zero slip critical shear stress. The problem under consideration is steady, laminar and fully developed. Thermal boundary conditions are assumed peripherally and axially constant heat flux at wall. The fluid heating and cooling cases are considered for analysis. Dimensionless temperature profiles and Nusselt number are obtained by solving governing equations and the effects of slip parameters, viscous dissipation and fluid elasticity are 2 discussed. Results show that Nusselt number increases by increasing slip effect but decreases by increasing Brinkman number for the case of fluid heating. However, for the cooling case, the heat generated by viscous dissipation can overcome the effect of wall cooling at first critical Brinkman number and fluid starts to warm up. Also the Nusselt curve shows a singularity in a second critical Brinkman number.

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Newtonian Poiseuille flows with slip and non-zero slip yield stress

Cited by 32 publications

References 19 publications

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Poiseuille Flow of a Non-Local Non-Newtonian Fluid with Wall Slip: A First Step in Modeling Cerebral Microaneurysms

Theoretical Study of Oldroyd-B Visco-Elastic Fluid Flow Through Curved Pipes with Slip Effects in Polymer Flow Processing

Forced convection heat transfer of Giesekus fluid with wall slip above the critical shear stress in pipes

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