Asymptotic analysis of the nonsteady micropolar fluid flow through a curved pipe

Pažanin, Igor; Radulović, Marko

doi:10.1080/00036811.2018.1553036

Cited by 6 publications

(4 citation statements)

References 24 publications

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“…Another possibility for further research is to consider the lubrication process of a rotating shaft with a time-dependent micropolar fluid flow. The governing non-stationary micropolar fluid system of equations is given by (see, e.g., [6] and [27]):…”

Section: Discussionmentioning

confidence: 99%

“…where u 0 , w 0 , u 1 , and w 1 are given by (10), (16), (19), and (26), p 0 and p 1 are the solutions of the Reynolds problems (12)- (14) and (21)- (24), while B 0 , b 0 , W 0 , B 1 , b 1 , W 1 are the solutions of the problems (27), (28), (29), (30), and H 0 , h 0 , Y 0 , H 1 , h 1 , Y 1 are solutions of the analogous problems posed on the opposite side z = l. Although we have corrected the boundary layer effects by constructing the appropriate boundary layer correctors in Section 3.3, the residual in the divergence equation is not small enough to obtain satisfactory error estimates. In order to correct this, we construct the divergence corrector in the forthcoming section.…”

Section: Asymptotic Solutionmentioning

confidence: 99%

“…The rigorous mathematical treatments of a thin curved pipe stationary flow including an investigation of the effects of flexion and torsion on the flow were provided by Marušić-Paloka for a Newtonian fluid (see [24]) and by Pažanin for a micropolar fluid (see [25]). On the other hand, the nonstationary flows were the subject of investigation by Castineira, Marušić-Paloka, Pažanin, and Rodriguez for a Newtonian fluid (see [26]) and Pažanin and Radulović for a micropolar fluid (see [27]). Finally, the rigorous mathematical justification of an asymptotic model for the lubrication problem with a Newtonian fluid in a curved domain, namely a rotating shaft appearing in real-life situations, was provided by Duvnjak and Marušić-Paloka (see [28,29]).…”

Section: Introductionmentioning

confidence: 99%

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Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid

2020

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Motivated by the lubrication processes naturally appearing in numerous industrial applications (such as steam turbines, pumps, compressors, motors, etc.), we study the lubrication process of a slipper bearing consisting of two coaxial cylinders in relative motion with an incompressible micropolar fluid (lubricant) injected in the thin gap between them. The asymptotic approximation of the solution to the governing micropolar fluid equations is given in the form of a power series in terms of the small parameter ε representing the thickness of the shaft. The regular part of the approximation is obtained in the explicit form, allowing us to acknowledge the effects of fluid’s microstructure clearly through the presence of the microrotation viscosity in the expressions for the first-order velocity and microrotation correctors. We provide the construction of the boundary layer correctors at the upper and lower boundary of the shaft along with the construction of the divergence corrector, allowing us to improve our overall estimate. The derived effective model is rigorously justified by proving the error estimates, evaluating the difference between the original solution of the considered problem and the constructed asymptotic approximation.

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Section: Discussionmentioning

confidence: 99%

Section: Asymptotic Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid

2020

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“…[2], [3], [4]) as well as rigorous results (see e.g. [5], [6], [7], [8]) providing various effective models for micropolar fluid flows. A comprehensive survey of the mathematical theory underlying the micropolar fluid model can be found in [9].…”

Section: Introductionmentioning

confidence: 99%

On The Lubrication of a Rotating Shaft with Incompressible Micropolar Fluid

Paloka¹,

Pažanin²,

Radulović³

2020

Topical Problems of Fluid Mechanics 2020

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In this work, we investigate the lubrication process of a slipper bearing. The slipper bearing consists of two coaxial cylinders in relative motion, where an incompressible micropolar fluid (lubricant) is injected in a thin gap between them. We compute the asymptotic approximation of the solution to the governing micropolar system as a power series in terms of the small parameter ε representing the thickness of the shaft. The proposed approximation is given in the explicit form, allowing us to clearly observe the effects of the micropolar nature of the fluid.

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Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes

Pažanin,

Radulović,

Rukavina

2024

Math Methods in App Sciences

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In this paper, we analyze the time‐dependent flow of an incompressible micropolar fluid in a multiple‐pipe system. Motivated by the applications, we assume that the pipes have circular cross‐section and that the ratio between pipes' thickness and its length is small, denoted by the parameter . Far from the junction, the fluid exhibits different behavior depending on the magnitude of the viscosity coefficients with respect to the small parameter . Focusing on the critical case described by the strong coupling between velocity and microrotation, the complete asymptotic expansion of the solution (up to an arbitrary order) is built. To improve the accuracy of the asymptotic approximation, we introduce the boundary layer correctors near the pipes' ends and take into account the interior layer correction in the vicinity of the junction as well. The convergence is also proved via error estimates, providing the rigorous justification of the proposed effective model.

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Asymptotic analysis of the nonsteady micropolar fluid flow through a curved pipe

Cited by 6 publications

References 24 publications

Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid

Justification of the Higher Order Effective Model Describing the Lubrication of a Rotating Shaft with Micropolar Fluid

On The Lubrication of a Rotating Shaft with Incompressible Micropolar Fluid

Asymptotic analysis of the nonsteady micropolar fluid flow through a system of thin pipes

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