In this study, we are interested in the asymptotic modeling of the two-dimensional stationary flow of a viscous incompressible fluid around wing airfoil. The aim of the present paper is to use the method of matched asymptotic expansions to study the laminar boundary layer behavior over a NACA (National Aeronautic and Space Administration) airfoil. At large Reynolds number and using singular perturbations methods, we distinguish the problems inside and outside the boundary layer. These problems are coupled under asymptotic constraints according to the least degeneration principle. Using the affinity hypothesis for the velocity field in the boundary layer, and assuming that the transverse velocity is of order ꓳ(Re-1/2), we establish an approached composite solution, and follows the aerodynamic coefficients (drag and lift) are determined. The results obtained show that accurate modeling is possible for laminar incompressible flow. The predicted solutions obtained compare well with the results of a NACA43013 airfoil produced by the Ansys fluent.

The object of this paper is the modeling a supersonic flow of inviscid fluid around a dihedral airfoil. Based on the thin airfoils theory and the non-dimensional stationary Steichen equation of a two-dimensional supersonic flow in isentropic evolution, we obtain a solution for the downstream velocity potential of the oblique shock at the second order of relative thickness. This result has been dealt by the asymptotic analysis and characteristics method. In order to validate our model, the results are discussed in comparison with theoretical and experimental results. Indeed, firstly, the comparison of the results of our model, has shown that they are quantitatively acceptable compared to the existing theoretical results. Finally, an experimental study was conducted using the AF300 supersonic wind tunnel. In this experiment, we have considered the incident upstream Mach number over a symmetrical dihedral airfoil wing. The validation and the accuracy of the results support our model.

In the recent years, blood flow through an aorta has been the main focus of many investigators. It shows particular interest in analyzing human aortic stiffness and blood flow behavior. Mainly, an unsteady state is applied for incompressible fluid, which is assumed to be newtonian. Artery is considered an elastic tube and the wall boundaries are isotropic. The analytical modeling of blood involves adopting an asymptotic approach according to a small aspect radio,which is inversely proportionalto Reynolds number. The wall has been assumed a thin shell, which generates a small axisymmetric vibration. The mathematical model of the wall is developed using the thin shell theory based on geodesic curvature parameter. In the end, the analytical results simulation is applied to have better understanding of the effects of blood flow behavior over the elasticity aortic wall properties.

In this paper, we asymptotically investigate a confined fluid flow in a flexible tube with a variable section. The fluid is considered to be newtonian, incompressible and it elapses in elastic and isotropic shell. This study provides a review of recent analysing the effects of the elastic wall tube properties over the fluid behaviour. The unsteady fluid flow will be analysed following the singular perturbations theory according to a large Reynolds number and a small aspect radio. The wall is assumed to be a thin shell that generate a small axisymmetric vibration. This model is mathematically developed by using the thin shell linear theory that is governed by a geodesic curvature parameter.