Unsteady motion of a viscous incompressible fluid in a tube with a deformable wall

Медведев, А. Е.

doi:10.1134/s0021894413040056

Cited by 4 publications

(1 citation statement)

References 6 publications

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“…The exact Poiseuille solution proposed to describe the movement of blood through vessels [33,34] has been repeatedly modified and generalized [2,31,41,42,47,49]. At present, the classical Poiseuille flow and its variations are widely used in biological hydrodynamics to study pathological processes in the cardiovascular system (for example, stenosis or aneurysm) [28,29]. The exact Poiseuille solution is used to study the functioning of the mammary gland during lactation [48], as well as to identify models of biological tissues [18,44].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Gradient Flow of a Vertical Vortex Fluid in a Thin Layer

Привалова¹,

Prosviryakov²,

Simonov³

2019

Nelin. Dinam.

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A new exact solution to the Navier -Stokes equations is obtained. This solution describes the inhomogeneous isothermal Poiseuille flow of a viscous incompressible fluid in a horizontal infinite layer. In this exact solution of the Navier -Stokes equations, the velocity and pressure fields are the linear forms of two horizontal (longitudinal) coordinates with coefficients depending on the third (transverse) coordinate. The proposed exact solution is two-dimensional in terms of velocity and coordinates. It is shown that, by rotation transformation, it can be reduced to a solution describing a three-dimensional flow in terms of coordinates and a two-dimensional flow in terms of velocities. The general solution for homogeneous velocity components is polynomials of the second and fifth degrees. Spatial acceleration is a linear function. To solve the boundaryvalue problem, the no-slip condition is specified on the lower solid boundary of the horizontal fluid layer, tangential stresses and constant horizontal (longitudinal) pressure gradients specified on the upper free boundary. It is demonstrated that, for a particular exact solution, up to three points can exist in the fluid layer at which the longitudinal velocity components change direction. It indicates the existence of counterflow zones. The conditions for the existence of the zero points of the velocity components both inside the fluid layer and on its surface under nonzero tangential stresses are written. The results are illustrated by the corresponding figures of the velocity component profiles and streamlines for different numbers of stagnation points.

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