Asymptotic solution for a micropolar flow in a curvilinear channel

Abstract

International audienceThis paper is concerned with an asymptotic approach for a micropolar flow through a thin curvilinear channel. A priori estimates (which we obtain together with the existence and the uniqueness of the solution) are used to establish the error between the exact solution and the asymptotic one and to justify the asymptotic analysis. We obtain the expression of an expansion of order K and we study the general problems for the boundary layer functions. Under some additional assumptions on the data we obtain satisfactory error estimate

Asymptotic Behavior of Micropolar Fluid Flow Through a Curved Pipe

“…In this section we write each differential operator occurring in the system (6)- (8) in curvilinear coordinates (x i ). For that purpose, we employ the following formulae:…”

“…In this section we develop some geometric tools that will be used for writing the governing equations (6)- (8) in curvilinear coordinates.…”

“…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.…”

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

“…In this way, we obtain a coupled system of partial differential equations that are well suited for modeling the behavior of various non-Newtonian fluids including liquid crystals, animal blood, muddy fluids, certain polymeric fluids, and even water at small scales. For this reason, there exist a vast number of recent results concerning the engineering applications of the model, primarily in biomedicine and blood flow modeling (see, e.g., [2][3][4][5]), as well as a number of papers providing rigorous mathematical treatment of various effective models for micropolar fluids (see, e.g., [6][7][8][9][10][11]). A comprehensive survey of the modern mathematical theory underlying the micropolar fluid model can be found in the monograph [12].…”

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

“…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.…”