Asymptotic Approximation of the Nonsteady Micropolar Fluid Flow through a Circular Pipe

Pažanin, Igor; Radulović, Marko

doi:10.1155/2018/6759876

Cited by 3 publications

(1 citation statement)

References 20 publications

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“…The asymptotic behaviour of nonsteady Newtonian fluid flow in a curved three-dimensional thin pipe with moving walls has been considered by Castineira et al [19,20]). A higher-order model describing the nonsteady flow of a micropolar fluid through a straight pipe has been rigorously derived in [21,22] by the authors of this paper. In view of that and inspired by the applications, our aim here is to investigate a nonsteady micropolar flow through a pipe with an arbitrary (generic) central curve.…”

Section: Introductionmentioning

confidence: 99%

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

Pažanin

Radulović

2018

Applicable Analysis

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We consider the nonsteady flow of a micropolar fluid in a thin (or long) curved pipe via rigorous asymptotic analysis. Germano's reference system is employed to describe the pipe's geometry. After writing the governing equations in curvilinear coordinates, we construct the asymptotic expansion up to a second order. Obtained in the explicit form, the asymptotic approximation clearly demonstrates the effects of pipe's distortion, micropolarity and the time derivative. A detailed study of the boundary layers in space is provided as well as the construction of the divergence correction. Finally, a rigorous justification of the proposed effective model is given by proving the error estimates.

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Section: Introductionmentioning

confidence: 99%

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

Pažanin

Radulović

2018

Applicable Analysis

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Rigorous derivation of the asymptotic model describing a nonsteady micropolar fluid flow through a thin pipe

Beneš¹,

Pažanin²,

Radulović³

2018

Computers & Mathematics with Applications

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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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Asymptotic Approximation of the Nonsteady Micropolar Fluid Flow through a Circular Pipe

Cited by 3 publications

References 20 publications

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

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

Rigorous derivation of the asymptotic model describing a nonsteady micropolar fluid flow through a thin pipe

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

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