Existence and Uniqueness of the Flow of Second-Grade Fluids with Slip Boundary Conditions

Roux, Christiaan Le

doi:10.1007/s002050050164

Cited by 76 publications

(42 citation statements)

References 30 publications

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“…In experimental physiology such a layer is observed when blood flow through capillary vessels is studied [21]. The fluids that exhibit slip effect have many applications, for instance, the polishing of artificial heart valves and internal cavities [22]. Moreover, the slip phenomenon is supported by the molecular theories [23][24][25][26].…”

Section: Introductionmentioning

confidence: 83%

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Fundamental flows with nonlinear slip conditions: exact solutions

Ellahi

Hayat

Mahomed

et al. 2010

Z. Angew. Math. Phys.

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In this article, we use nonlinear slip conditions to investigate three fundamental flows. Constitutive equations of the third grade fluid give rise to nonlinear equations. Exact analytic solutions of the nonlinear equations with nonlinear boundary conditions are developed. Numerical values between the dimensionless third grade and slip parameters are tabulated. Graphs are plotted and discussed. (2000). 76B05 · 76P05. Mathematics Subject Classification

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Section: Introductionmentioning

confidence: 83%

“…However, some investigations [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42] deal with the flows of non-Newtonian fluids involving the slip conditions. The objective of the present investigation is to study the Couette, Poiseuille and generald Couette flows in the presence of a slip condition.…”

Section: Introductionmentioning

confidence: 99%

Fundamental flows with nonlinear slip conditions: exact solutions

Ellahi

Hayat

Mahomed

et al. 2010

Z. Angew. Math. Phys.

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“…It should be noted that the equations of this model are identical to the equations of the second-grade fluid model under the assumptions that α 1 + α 2 = 0 and α 1 = κ (see [26] for more details).…”

Section: Motions In Cylindrical Tubesmentioning

confidence: 99%

“…Much more attention was paid to the second-grade fluid (see [26] with a long list of references dealing with this topic). In particular, a number of exact solutions for this model have been studied [27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

Frolovskaya

Пухначев

2018

Polymers

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Abstract:The qualitative properties of solutions of a hereditary model of motion of aqueous solutions of polymers, its modification in the limiting case of short relaxation times, and a similar second grade fluid model are studied. Unsteady shear flows are considered. In the first case, their properties are similar to those of motion of a usual viscous fluid. Other models can include weak discontinuities, which are retained in the course of fluid motion. Exact solutions are found by using the group analysis of the examined systems of equations. These solutions describe the fluid motion in a gap between coaxial rotating cylinders, the stagnation point flow, and the motion in a half-space induced by plane rotation (analog of the Karman vortex). The problem of motion of an aqueous solution of a polymer in a cylindrical tube under the action of a streamwise pressure gradient is considered. In this case, a flow with straight-line trajectories is possible (analog of the Hagen-Poiseuille flow). In contrast to the latter, however, the pressure in the flow considered here depends on all three spatial variables.

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“…Hayat et al [24] studied the effect of the slip condition on flows of an Oldroyd 6-constant fluid. Roux [25] discussed the solvability of the equations of motion for an incompressible fluid of grade two subject to nonlinear partial slip boundary conditions in a bounded simply-connected domain. Liakos [26] studied the steady-state, isothermal flow of a viscoelastic fluid obeying an Oldroyd-type constitutive law with slip boundary condition.…”

Section: Introductionmentioning

confidence: 99%

MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity

Mahmoud

Waheed

2012

Journal of the Egyptian Mathematical Society

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In this work, the effects of slip velocity on the flow and heat transfer for an electrically conducting micropolar fluid over a permeable stretching surface with variable heat flux in the presence of heat generation (absorption) and a transverse magnetic field are investigated. The governing partial differential equations describing the problem are converted to a system of non-linear ordinary differential equations by using the similarity transformation, which is solved numerically using the Chebyshev spectral method. The effects of the slip parameter on the flow, micro-rotation and temperature profiles as well as on the local skin-friction coefficient, the wall couple stress and the local Nusselt number are presented graphically. The numerical results of the local skin-friction coefficient, the wall couple stress and the local Nusselt number are given in a tabular form and discussed.

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Existence and Uniqueness of the Flow of Second-Grade Fluids with Slip Boundary Conditions

Cited by 76 publications

References 30 publications

Fundamental flows with nonlinear slip conditions: exact solutions

Fundamental flows with nonlinear slip conditions: exact solutions

Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

MHD flow and heat transfer of a micropolar fluid over a stretching surface with heat generation (absorption) and slip velocity

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