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Journal of Applied Mechanics and Technical Physics

2013 year, number 4

Unsteady Motion of a Viscous Incompressible Fluid in a Tube with a Deformable Wall

A. E. Medvedev
Keywords: viscous incompressible fluid, Navier–Stokes equations, analytical solution, Poiseuille flow


A flow of a viscous incompressible fluid in a deformable tube is considered. Solutions of unsteady three-dimensional Navier–Stokes equations are obtained for low-Reynolds-number flows in the tube (under the condition of small deformations of the wall): generalized peristaltic flow and flow with elliptical deformations of the vessel walls. At small unsteady deformations of the tube walls, the solutions satisfy the equations and boundary conditions with an error smaller than the tube wall deformation level by an order of magnitude. In the case of elliptical deformations of the vessel, the solution agrees well with experimental data.