Non-Newtonian effects on lubricant thin film flows

Zhang, Rong; Li, Xin Kai

doi:10.1007/s10665-004-1342-z

Cited by 26 publications

(14 citation statements)

References 15 publications

(53 reference statements)

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“…Nevertheless, the spatial profile is decreasing after a significant delay. This feature is in concordance with the results of Akyildiz and Bellout [41], Zhang and Li [42], Georgiou and Vlassopoulos [43], Bair [44], Bair and Khonsari [45] who recorded that there was a reciprocal inhibition of the flow speed along the artery for increasing values of r.…”

Section: Numerical Results and Plotssupporting

confidence: 92%

Study of the Phan-Thien–Tanner Equation of Viscoelastic Blood Non- Newtonian Flow in a Pipe-Shaped Artery under an Emotion-Induced Pressure Gradient

Boubaker

Khan

2012

Zeitschrift Für Naturforschung A

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In this paper, a three-dimensional, unsteady state non-Newtonian fluid flow in a pipe-shaped artery of viscoelastic blood is considered in the presence of emotion-induced pressure gradient. The results have been expressed in terms of radial profiles of both axial velocity and viscosity and were presented numerically by using the shooting technique coupled with the Newtonian method and the Boubaker polynomials expansion scheme. The effects of some parameters on the dynamics are analyzed.

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Section: Numerical Results and Plotssupporting

confidence: 92%

Study of the Phan-Thien–Tanner Equation of Viscoelastic Blood Non- Newtonian Flow in a Pipe-Shaped Artery under an Emotion-Induced Pressure Gradient

Boubaker

Khan

2012

Zeitschrift Für Naturforschung A

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“…So, choosing a = ∇π ∈ L 2 (ω), the proof is concluded as by definition a satisfies equations (17), (18) and (20). Thus, the function φ defined by equation (23), with the previous choice for a, belongs to K(s, q 0 ) which is consequently nonempty.…”

Section: Theoretical Analysismentioning

confidence: 85%

“…Thus it remains to prove that the space is nonempty. Using Proposition 2.1, we look for a function satisfying equations (16)- (18) and (20). It is obvious that the function…”

Section: Theoretical Analysismentioning

confidence: 99%

“…In all this research, a nonlinear Reynolds equation is gained, allowing the pressure in the thin film to be directly computed. The same procedures can also include the free boundary upper surface of the flow (thin coating problem) or the inertia [10,20,21]. However, the goal of these last studies is different, as the primary unknown is not an equation for the pressure but an equation describing the evolution of the free boundary (a generalized shallow water equation).…”

Section: Introductionmentioning

confidence: 99%

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Viscoelastic fluids in a thin domain

Bayada

Chupin

2007

Quart. Appl. Math.

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Abstract. The present paper deals with viscoelastic flows in a thin domain. In particular, we derive and analyse the asymptotic equations of the Stokes-Oldroyd system in thin films (including shear effects). We present a numerical method which solves the corresponding problem and we present some related numerical tests which evidence the effects of the elastic contribution on the flow. Introduction.Much literature has been devoted to the research on non-Newtonian fluids, in a thin film, in both mathematical aspects and applications. It is well known that numerous biological fluids, blood or physiological secretions like tears or synovial fluids, show these non-Newtonian characteristics. In engineering applications people are interested in controling the flows characteristics to suit various requirements such as maintaining the fluid qualities in a wide range of temperatures and stresses. The introduction of additives leads to non-Newtonian behavior of the modern lubricant. Another application domain is linked to polymers, whose non-Newtonian characteristics appear in a wide range of applications such as the molding or injection processes.It is to be noticed that, in most practical applications, the geometry of the flow to be considered is anisotropic. A well-known case deals with the study of boundary layers for complex flows [6,7,14]. Another case, which is the subject of the present paper, is the lubrication problem in which the fluid is contained between two close surfaces in relative motion. These two applications lead to two very different mathematical models, essentially since the order of magnitude of the parameters in the approximation process is different. For example, in the boundary layer study, the Reynolds number is large

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“…Miladinova et al [12] studied the thin film flow of a power law fluid falling down an inclined plane and found a numerical solution. Analysis of lubrication flow of an upper-convected Maxwell fluid was carried out by Zhang and Li [13]. The field equation of micropolar fluids under a lubrication approach has been studied by Gan and Ji [14].…”

Section: Introductionmentioning

confidence: 99%