Asymptotic Methods for Micropolar Fluids in a Tube Structure

Dupuy, Delphine; Panasenko, Grigory; Stavre, Ruxandra

doi:10.1142/s0218202504003428

Cited by 39 publications

(16 citation statements)

References 15 publications

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“…In particular, the nonlinear coupled systems (1) and (2) can be used to model the behavior of liquid crystals, polymeric fluids and blood under some circumstances (see for instance [2], [4], [23] and the references therein). These systems have been mainly analyzed by G. Lukaszewicz in [22].…”

Section: Introductionmentioning

confidence: 99%

Local Exact Controllability of Micropolar Fluids

Fernández-Cara

Guerrero

2006

J. math. fluid mech.

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This paper is devoted to prove the local exact controllability to the trajectories of micropolar fluids with distributed controls supported in small sets. First, we deduce new Carleman inequalities for associated linearized systems which leads to null controllability at any time T > 0. Then, we deduce a local result concerning the exact controllability to the trajectories of the whole nonlinear system. The arguments are presented separately in the two-dimensional and three-dimensional cases, since the required techniques are different.

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Section: Introductionmentioning

confidence: 99%

Local Exact Controllability of Micropolar Fluids

Fernández-Cara

Guerrero

2006

J. math. fluid mech.

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“…The isothermal flow of a micropolar fluid was successfully considered both in 2D, see Dupuy et al (2004Dupuy et al ( , 2008 and in a more realistic 3D case, see Pažanin (2011a,b). Taking into account the thermal effects as well, non-isothermal flows have gained much attention in the recent years, see e.g.…”

Section: Introductionmentioning

confidence: 99%

Heat flow through a thin cooled pipe filled with a micropolar fluid

Beneš¹,

Pažanin²,

Suárez‐Grau³

2015

jtam

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In this paper, a non-isothermal flow of a micropolar fluid in a thin pipe with circular cross--section is considered. The fluid in the pipe is cooled by the exterior medium and the heat exchange on the lateral part of the boundary is described by Newton's cooling condition. Assuming that the hydrodynamic part of the system is provided, we seek for the micropolar effects on the heat flow using the standard perturbation technique. Different asymptotic models are deduced depending on the magnitude of the Reynolds number with respect to the pipe thickness. The critical case is identified and the explicit approximation for the fluid temperature is built improving the known result for the classical Newtonian flow as well. The obtained results are illustrated by some numerical simulations.

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“…Our work is strongly motivated by recent papers of Dupuy, Panasenko and Stavre [7,8] in which the authors rigorously derive the asymptotic models for 2-D micropolar flow through a periodically constricted tube and a thin curvilinear channel. Although 2-D setting (in which the microrotation is a scalar function) has often been employed, especially in blood motion modeling, it represents only the first step to more realistic 3-D setting.…”

Section: Introductionmentioning

confidence: 99%