Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip

Ferrás, Luís Jorge Lima; Nóbrega, J. M.; Pinho, F.T.

doi:10.1016/j.jnnfm.2012.03.004

Cited by 97 publications

(45 citation statements)

References 23 publications

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“…It is also required that the tangent velocity vector, u t , should point in the opposite direction to the tangent stress vector τ t , that is, the relationship between these two quantities is given by where the function || f ( τ t )|| takes the form in Equation for each of the various slip laws and the parameters k l , k nl , k H 1 , k H 2 , k A 1 , k A 2 and m are the corresponding slip coefficients. The interested reader is referred to for more details about these models.…”

Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

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Implementation of slip boundary conditions in the finite volume method: new techniques

Ferrás

Nóbrega

Pinho

2012

Numerical Methods in Fluids

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SUMMARY Two different techniques for the implementation of the linear and nonlinear slip boundary conditions into a finite volume method based numerical code are presented. For the linear Navier slip boundary condition, an implicit implementation in the system of equations is carried out for which there is no need for any relaxation, especially when handling high slip coefficients. For three different nonlinear slip boundary conditions, two different methods are devised, one based on solving a transcendental equation for the boundary and the other on the linearization of the slip law. For assessment purposes, comparison is made between these new methods and the usual iterative process. With these new methods, the convergence difficulties, typical of the iterative procedure, are eliminated, and for some of the test cases, the convergence rate even increased with the slip velocity. The details of these implementations are given first for a simple geometry using orthogonal meshes and Cartesian coordinates followed by their generalization to non‐Cartesian coordinates and nonorthogonal meshes. The developed code was tested in the benchmark slip‐stick and 4:1 contraction flows, evidencing the robustness of the proposed procedures. Copyright © 2013 John Wiley & Sons, Ltd.

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Section: Governing Equations and Numerical Methodsmentioning

confidence: 99%

“…and the parameters k l , k nl , k H1 , k H 2 , k A1 , k A2 and m are the corresponding slip coefficients. The interested reader is referred to [19] for more details about these models.…”

Section: Boundary Conditionsmentioning

confidence: 99%

Implementation of slip boundary conditions in the finite volume method: new techniques

Ferrás

Nóbrega

Pinho

2012

Numerical Methods in Fluids

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“…Here, we analyze the case of a Sisko model with slip boundary conditions in Couette and Poiseuille flows. According to [9], we show that in the laminar flow case the problem is as follows: The coefficient a is the consistency coefficient and µ ∞ , that is, the infinite shear rate viscosity [14].…”

Section: Introductionmentioning

confidence: 99%

“…The solution of the problem could be acquired numerically. But the full analytic solution cannot be achieved unless for a few particular cases, m = 0.5, m = 1 (linear), m = 2 and m = 3 Ferrás et al [9]. In this paper, we propose a new approximation method to resolve a problem of laminar flow of a generalized Newtonian fluid with slip boundary conditions using a Sisko model.…”

Section: Introductionmentioning

confidence: 99%

Explicit solution for some generalized fluids in laminar flow with slip boundary conditions

Chamekh¹,

Elzaki²

2018

J. Math. Computer Sci.

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In this study, we present a new approximation method to give an explicit solution of a laminar flow using a Sisko model. This is a problem of a generalized Newtonian fluid with slip boundary conditions. The proposed method is based on the variational iteration method (VIM) combined with an approximation step. This method is validated where the exact solution is available. In addition, in order to enrich the discussion, a numerical method is presented. The results illustrate that the VIM may be more effective that the finite difference method for a dilatant fluid. However, the VIM will be inappropriate for pseudoplastic fluid cases.

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“…Yang and Zhu [23] have analyzed the squeeze flow of Bingham fluid in the small gap between parallel disks with the Navier slip condition. Ferrás et al [24] presented analytical solutions of both Newtonian and inelastic nonNewtonian fluids with slip boundary conditions for Couette and Poiseuille flows. Hron et al [25] established closed form analytical solution for the flows of incompressible non-Newtonian fluids with Navier's slip conditions at the boundary.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions

Devakar

Sreenivasu²,

Shankar

2014

International Journal of Engineering Mathematics

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We establish, in this paper, the closed form analytical solutions of steady fully developed flows of couple stress fluid between two concentric cylinders, generated due to the constant pressure gradient or the translatory motion of the outer cylinder or both, using the slip boundary conditions. The classical solutions for Newtonian fluid in the hydrodynamic case appear as a limiting case of our solutions. The velocity profiles of the flows are presented and the effect of various parameters on velocity is discussed. The results indicate that the presence of couple stresses decreases the velocity of the fluid.

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Analytical solutions for Newtonian and inelastic non-Newtonian flows with wall slip

Cited by 97 publications

References 23 publications

Implementation of slip boundary conditions in the finite volume method: new techniques

Implementation of slip boundary conditions in the finite volume method: new techniques

Explicit solution for some generalized fluids in laminar flow with slip boundary conditions

Analytical Solutions of Some Fully Developed Flows of Couple Stress Fluid between Concentric Cylinders with Slip Boundary Conditions

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